Thermal-mechanical coupling simulation-based method for evaluating thermal insulation property of light regenerated building block

Abstract

The invention relates to a thermal insulation evaluation method for a light recycled building block based on thermal coupling simulation, which comprises the following steps: modeling the recycled building block into a heterogeneous multiphase complex, and introducing a three-layer structure field of micro pores, mesoscopic aggregates and macroscopic blocks; a partition coupling strategy is adopted, a microstructure variability-heat flux density disturbance-stress field reconstruction causal chain is constructed, and macroscopic thermal insulation performance fluctuation caused by thermal deformation is captured; tracking a thermal stress concentration area caused by temperature difference change through thermal and force coupling simulation; analyzing the influence of a thermal stress migration path on local structure integrity, pore change and crack evolution; constructing a thermal stress and structure disturbance factor framework, and evaluating the influence degree of the structure local deformation on the thermal resistance; extracting high-dimensional feature data; establishing a heat and force characteristic space; constructing a response surface equation, and mapping a change track of the thermal insulation performance in a heat and force coupling response space; a time and structure response composite scoring system is formed, real coupling of multiple physical fields is achieved, and limitation of traditional evaluation is broken through.

Description

Technical Field

[0001] The invention relates to a thermal insulation evaluation method for lightweight recycled building blocks based on thermal-mechanical coupling simulation. Background Art

[0002] Currently, in the thermal insulation evaluation process of lightweight recycled blocks, although more and more researchers have begun to focus on the introduction of thermo-mechanical coupling simulation methods, striving to achieve full-process modeling and performance evaluation from thermal response to structural response through multi-physics field analysis, a series of obvious technical bottlenecks and limitations still exist in practical applications. These deficiencies not only limit the engineering applicability of the models, but also, to a certain extent, affect the reliability and predictive ability of the evaluation results. First, most existing thermo-mechanical coupling simulation methods rely on standard finite element platforms such as COMSOL, ABAQUS, or ANSYS to establish thermal-mechanical solution models. Although these platforms have strong modeling capabilities, their meshing and element approximation methods are difficult to accurately reproduce the microstructure of lightweight recycled blocks, which are typically heterogeneous, have strong structural discontinuities, contain a large number of pores, and contain recycled aggregate interfaces. In particular, when involving foaming regions, interface transition zones, crack tips, and weak interface bonding zones, they often have to simplify the treatment due to resolution limitations or numerical stability requirements, resulting in distorted descriptions of local thermal flow disturbances and stress concentration evolution. In addition, the acquisition of material constitutive parameters of thermo-mechanical coupling models in engineering often relies on idealized assumptions or extrapolation of limited sample points in experiments. The input data such as thermal expansion coefficient, thermal conductivity, and elastic modulus have significant uncertainty. These physical parameters may fluctuate in actual use due to changes in humidity, aging, and the dosage of recycled components. If the spatial and temporal variability of the material's physical properties is not fully considered, deviations are likely to accumulate in the simulation, weakening the effectiveness of the predictive performance.

[0003] Secondly, in thermomechanical coupling simulations, the description of pore structure evolution and microcrack development processes typically relies on simplified models, such as phase field methods and damage mechanics models. However, these models are difficult to apply to multiphase materials such as lightweight recycled blocks. This is because the complex morphology, varying scale distribution, and uncontrollable connectivity of the pores make it difficult to accurately capture the thermal-crack coupling mechanism. The correlation between crack initiation and the direction of the thermal gradient cannot be precisely fitted, resulting in delayed or even misaligned identification when predicting thermally induced damage paths, which in turn affects the reasonable prediction of overall thermal resistance trends. Furthermore, most current thermomechanical coupling simulation studies have not fully considered the nonlinear interaction between the structure and the thermal field under dynamic conditions. In particular, in areas with drastic day-night temperature differences or repeated thermal cycling conditions, the stress release and re-accumulation within the material exhibit significant path dependence and historical evolution characteristics. Static or simplified loading models clearly cannot reproduce this true behavior, resulting in evaluation results that underestimate the degree of degradation of the material's thermal insulation capacity after long-term service. More notably, existing evaluation methods generally lack a means of quantitatively expressing how thermal stress-induced structural perturbations affect the reconstruction of heat flow paths. Although some literature has proposed using alternative values ​​for thermal bridge coefficients or crack thermal conductivity to simulate changes in heat transfer paths, these methods mostly rely on empirical settings and lack the ability to perform data-driven modeling based on microstructural perturbations. This makes it difficult to generalize to the situation where multiple structural parameter combinations change, resulting in their predictive capabilities being limited to fixed models and unable to achieve adaptive expansion across structures and material systems. Furthermore, there is still a lack of an effective communication mechanism between the thermomechanical coupling evaluation system and material design. Current thermomechanical coupling simulations are primarily used to evaluate the performance of existing materials or test samples. However, there is a lack of clear feedback paths for inferring material composition design, optimizing pore structure distribution, and improving interface strength based on performance targets. Consequently, the evaluation results cannot truly be applied to the material design end, reducing thermal simulation to a post-hoc verification tool rather than a feedforward design guide. In addition, the current methods have no unified definition and extraction standards for microstructure disturbance factors. Deformation rate factors, crack evolution indicators, pore reconstruction quantitative models, etc. are mostly obtained from individual research experience. A standardized, universal, and performance-related factor framework has not yet been formed, which makes it difficult to compare or reproduce the results between different studies. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for evaluating the thermal insulation properties of lightweight recycled building blocks based on thermomechanical coupling simulation, thereby solving some of the drawbacks and shortcomings pointed out in the background art.

[0005] The present invention solves the above-mentioned technical problems by adopting the following technical solutions: a method for evaluating the thermal insulation properties of lightweight recycled blocks based on thermomechanical coupling simulation, comprising: modeling the recycled blocks as a heterogeneous multiphase complex, introducing a three-layer structural field of microscopic pores, mesoscopic aggregates, and macroscopic blocks; adopting a partitioned coupling strategy to map microstructural parameters including pore connectivity and aggregate morphology into local response functions of thermal conduction and thermal expansion; constructing a causal chain of microstructural variability → heat flux density perturbation → stress field reconstruction to capture fluctuations in macroscopic thermal insulation properties caused by thermal deformation;

[0006] Through coupled thermal and mechanical simulation, we tracked the areas of thermal stress concentration caused by temperature differences; analyzed the impact of thermal stress migration paths on local structural integrity, porosity changes, and crack evolution; and established a framework for thermal stress and structural perturbation factors to assess the impact of local structural deformation on thermal resistance.

[0007] Based on the simulation data, high-dimensional feature data including temperature gradient, heat flux, maximum stress, and stress gradient are extracted; the thermal and mechanical feature space is established through principal component analysis and partial least squares regression dimensionality reduction methods; and a response surface equation is constructed to map the variation trajectory of thermal insulation performance in the thermal and mechanical coupled response space.

[0008] The thermal residence time index TRT-I is defined to measure the material's ability to maintain a stable temperature range per unit time; the thermal and stress coupling stability coefficient TMS-C is defined to evaluate the amplitude and recovery ability of structural field disturbances under temperature fluctuations; and the two are combined to form a composite scoring system for time and structural response.

[0009] Furthermore, the response surface equation and the composite scoring system are used as optimization function objectives; a multi-objective optimization framework is constructed with aggregate ratio, foaming agent content, and porosity control as design variables; a reverse search is conducted to find a ratio scheme that meets the insulation target, including insulation time ≥ X hours and TMS-C ≥ Y; and a design and control path that integrates performance, structure, and parameters is formed.

[0010] Furthermore, the method for capturing the fluctuation of macroscopic thermal insulation performance caused by thermal deformation includes:

[0011] S1. Establish a microstructural heterogeneous model for lightweight recycled blocks. Divide the block material into multiple microstructural response regions. Based on the pore connectivity, aggregate distribution density, and interface quality micro-characteristic parameters of each region, differentiated local thermal conductivity and thermal expansion coefficients are assigned to construct a thermomechanical coupling input parameter set.

[0012] S2. Using a partition coupling strategy, a multi-physics field coupling model of heat and force inside the block is constructed to simulate the joint evolution of the temperature field and the stress field, and to track the perturbation path of the heat flux density and the local thermal stress concentration phenomenon caused by it.

[0013] S3. Analyze the causal relationship between the thermal flow disturbance zone and the stress field reconstruction, and identify the structural response characteristics induced by thermal stress, including the microcrack initiation location, stress gradient migration trend, and interface failure area;

[0014] S4. Map the local response into macroscopic thermal insulation performance fluctuation parameters, including temperature difference maintenance capacity, thermal hysteresis time, and thermal stress peak change rate indicators, and construct a dynamic evaluation model of thermal insulation performance driven by thermal deformation.

[0015] Furthermore, the division of the microstructure response area is based on the pore connectivity index, recycled aggregate interface bonding strength, particle size distribution and cavity distribution morphology, and modeling parameter extraction is achieved through image reconstruction and material testing data; the simulation process of the heat flux density disturbance achieves non-uniform heat flux distribution tracking by setting different heat conduction blocks, records the path bending, aggregation or scattering effects of heat energy in the structure, and serves as input for subsequent stress analysis.

[0016] In the above scheme, based on the porous composite structure of the material, a response area division mechanism and a heat flow disturbance tracking mechanism are introduced, combined with a customized high-order mathematical function model to realize the coupled characterization of the heat conduction path variability and the structural disturbance factor.

[0017] The material is divided into multiple microstructural response sub-region units based on the following:

[0018] Pore ​​connectivity index (χ): indicates the degree of interconnection of open pores in a unit volume; recycled aggregate interface bonding strength (σ int ): indicates the interface binding capacity; particle size distribution variance (Δ d ): represents the degree of mixing of different particle sizes; cavity geometric deviation coefficient (φ cav ): reflects the complexity of cavity morphology.

[0019] The heat flux density disturbance is simulated by setting irregular heat conduction distribution blocks to capture the bending, aggregation, and scattering path characteristics of heat energy in the material, and use them as input variables for stress migration simulation.

[0020] In order to quantify the response trend of the microstructure disturbance area to the change of thermal resistance, the following function is defined:

[0021]

[0022] in:

[0023] Ψ res : potential energy function of the structural response induced by thermal flow disturbance, used to characterize the degree of local thermal-mechanical activation of the microstructure unit (unit is virtual potential energy index); Ω: represents the integration domain, covering the spatial area A of all divided response units and the simulation time period t; χ: pore connectivity index, with a value range of [0,1]; φcav : Cavity geometry deviation coefficient, describing the cavity complexity; α, β: empirical index, controlling the weight of the influence of cavity and connectivity on the response potential energy; The disturbance gradient in the heat flux direction reflects the abnormality of the heat energy path; δ: thermal disturbance trigger threshold, when > stress migration occurs; κ: thermal perturbation sensitivity factor, which controls the steepness of the activation function; σ int : aggregate interface bonding strength; Δ d : standard deviation of particle size distribution; γ: structural weighting coefficient, used to enhance the regulatory effect of interface properties on response; ε: fine-tuning constant, preventing the denominator from approaching zero.

[0024] Furthermore, the thermal stress reconstruction process is based on the local thermal expansion difference caused by the temperature gradient, simulating the stress concentration evolution between interfaces, stress release around the aggregate and the disturbance behavior of the structural integrity, and extracting key areas as thermal failure risk points.

[0025] Furthermore, the thermal insulation performance fluctuation parameters include thermal hysteresis time, thermal stability maintenance time, heat flow variation rate, and structural disturbance frequency, which are used to establish a macroscopic thermal insulation performance response surface.

[0026] Furthermore, the method for constructing a thermal stress and structural disturbance factor framework includes:

[0027] S1. Establish a multi-physics coupling model for lightweight recycled building blocks, integrate the heterogeneous microstructural characteristics of the material, and set thermal and force boundaries to enable dynamic coupling calculation of temperature and stress fields;

[0028] S2. Identify the thermal stress migration path during the simulation process, extract the local stress concentration area formed along the path, and identify the structural disturbance characteristics caused by stress migration;

[0029] S3. Based on the thermal stress concentration effect, a structural disturbance factor framework is constructed, wherein the structural disturbance factors include: local deformation rate factor, crack evolution factor, pore reconstruction factor and stress disturbance amplitude factor;

[0030] S4. Perform heat flux reconstruction analysis on the structural disturbance area, measure the change in heat flux density before and after the disturbance, and quantify the thermal resistance reduction ratio of the corresponding area.

[0031] Furthermore, the identification of the thermal stress migration path includes tracking the spatial movement trajectory of the stress peak, the direction of stress gradient change and its change rate, which are used to analyze the thermal stress diffusion mechanism; the local deformation rate factor is used to characterize the degree of deformation of the material unit in the local area under the action of thermal stress; the crack evolution factor identifies the microstructural destruction path driven by thermal stress by recording the initiation, expansion and connectivity behavior of microcracks during the simulation process.

[0032] The above scheme achieves quantitative modeling and risk prediction of the microstructural damage process by coupling the stress field tracking mechanism with the microstructural response factor extraction mechanism. The specific steps include:

[0033] By using a multi-physics field simulation platform, we continuously track the stress peak movement trajectory, stress gradient direction change and its change rate during the time evolution of the thermal stress field, so as to obtain the dynamic diffusion pattern of thermal stress.

[0034] Extraction of microstructure disturbance factors: local deformation rate factor (Λ d ): Characterizes the instantaneous or cumulative deformation of the material unit due to thermal stress; crack evolution factor (Ξ c ): The reaction path of microcracks to thermal stress migration is revealed through time series records of crack initiation, propagation paths, and connection rates; the two constitute the core set of disturbance variables.

[0035] In order to comprehensively characterize the interaction effect between thermal stress migration path and structural perturbation factor, the following function is constructed:

[0036]

[0037] in:

[0038] Φ dyn : dynamic stress-disturbance coupled response function, which measures the microstructural activation intensity induced by stress migration; Ω: integration domain, which represents the summation area within a specific time t and spatial volume V; Λ d : local deformation rate factor, which indicates the amplitude of local structural deformation in the unit volume and comes from the rate of change of the displacement field; The derivative of stress gradient with respect to time describes the degree of mutation in the stress concentration area in the stress migration path; c : Crack evolution factor, which expresses the strength of the structural weakening chain formed during the crack initiation and expansion process; Δ θ : the offset angle between the crack propagation direction and the thermal gradient direction; η: the thermally driven crack activation coefficient, which controls the intensity of the influence of the crack factor on the overall function; Perturbation frequency factor, used to control the periodic contribution of stress fluctuation to structural disturbance; σ The spatial distance function of the stress peak movement path is used to quantify the nonlinearity of the stress peak displacement path; μ, ν are empirical parameters used to control the weight of the structural response and stress field disturbance.

[0039] Furthermore, the pore reconstruction factor is used to reflect the changes in the geometric shape and connectivity of local pores under the action of thermal stress, including the transformation of closed pores into through pores and pore expansion. The stress perturbation amplitude factor is used to quantify the degree of stress fluctuation in a specific local area, and is obtained by analyzing the changes in stress values ​​at multiple times in the same area.

[0040] Furthermore, the thermal resistance reduction ratio is used to describe the ratio of the decrease in heat flux per unit area before and after structural disturbance, reflecting the degree of weakening of the heat conduction path caused by microstructural changes; the correlation model between the structural disturbance factor and the thermal resistance reduction ratio is constructed using regression modeling, response surface analysis or data-driven machine learning methods.

[0041] Compared with traditional single heat conduction evaluation models or empirical test paths, the thermal insulation evaluation method of lightweight recycled building blocks proposed in this paper based on thermomechanical coupling simulation has significant benefits in terms of the depth of thermal physical modeling, the accuracy of capturing structural response mechanisms, and the practicality of material optimization. The specific manifestations are as follows:

[0042] Through coupled thermal and mechanical simulation, the stress migration path and structural response behavior of masonry blocks under the influence of temperature gradients are dynamically tracked. This breaks through the traditional single-field evaluation method that only uses thermal conductivity or steady-state thermal resistance as indicators, and more comprehensively reflects the comprehensive performance of thermal stability and structural adaptability of materials in actual service environments.

[0043] By constructing response indicators such as local deformation rate factor, crack evolution factor, pore reconstruction factor and stress perturbation amplitude factor, a quantitative description of the internal microstructural disturbance process of the block material can be obtained. This can identify thermally induced damage behaviors such as crack initiation and pore topology reconstruction in advance, thus providing microscale risk warning capabilities.

[0044] In order to solve the problem of difficulty in evaluating structural micro-damage caused by thermal stress, a new response indicator, thermal resistance weakening ratio, is proposed to accurately characterize the decreasing trend of heat flux per unit area before and after disturbance, provide a quantitative basis for macroscopic thermal resistance fluctuations, and make up for the problem that traditional thermal performance models lack response to the dynamic evolution of structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 This is a flow chart of the thermal insulation evaluation method of lightweight recycled building blocks based on thermomechanical coupling simulation of the present invention.

[0046] Figure 2 This is a flow chart of the method for capturing macroscopic thermal insulation performance fluctuations caused by thermal deformation according to the present invention.

[0047] Figure 3 A flow chart of the method for constructing a framework of thermal stress and structural disturbance factors for the present invention. DETAILED DESCRIPTION

[0048] The following is a detailed description of the specific embodiments of the present invention with reference to the accompanying drawings.

[0049] Combined with attachment Figure 1The present invention is based on a thermal insulation evaluation method for lightweight recycled building blocks based on thermomechanical coupling simulation, which restores the real characteristics of complex recycled building block materials into numerical simulations to achieve accurate prediction of their thermal insulation performance under real thermomechanical coupling conditions. It is necessary to model the lightweight recycled building blocks as a heterogeneous multiphase complex. The model cannot rely solely on average macroscopic thermal or mechanical parameters, but must fully express the multi-scale structure of the material. On this basis, a three-layer structural field is constructed, including a micropore layer, a mesoaggregate layer, and a macroblock layer. The micropore layer mainly reflects the pore distribution, connectivity, and pore size statistical characteristics of the material. These data are usually obtained through X-ray CT scanning and high-resolution image reconstruction technology, and then image processing algorithms such as edge detection, region segmentation, and connected domain analysis are used to quantify the pore morphology and connectivity. The mesoaggregate layer focuses on the size, shape, interface distribution, and density of the recycled aggregate. The data source can be further hierarchical annotation of the scanned image and particle-level image analysis, and is calibrated in combination with physical experiments (such as screening tests or laser particle size analysis). The macro-block layer describes boundary layer conditions such as overall geometry, load boundaries, and installation methods. Data can come from CAD drawings, physical measurements, or structural design specifications. A partitioned coupling strategy is employed in the modeling process, whereby the overall block is divided into multiple response units based on spatially distributed structural characteristics, each of which is independently assigned physical properties. This involves a parameter mapping mechanism, whereby microstructural data such as the pore connectivity index (indicating the degree of local thermal insulation) and the aggregate morphology factor (controlling the formation of thermal bridging) are converted into response functions such as local thermal conductivity, thermal diffusivity, and thermal expansion coefficient using custom mapping rules. This mapping is based on empirical relationships derived from multiple sets of experiments and backfitting. Parameter regression optimization is performed within the training set using finite element simulation and field measurement comparisons to ensure that the simulated parameters reflect the actual thermal conduction behavior. A complete causal chain is constructed: microstructural variability, heat flux perturbation, and stress field reconstruction. In local microstructural regions (such as densely populated areas and aggregate interfaces), sudden changes in thermal conductivity can cause perturbations in heat flow, including heat flux bending, heat accumulation, or heat leakage paths. Through simulation, we can observe local mutations or directional reconstructions of the heat flux vector field. These abnormal points are potential areas of thermal stress concentration. Due to the uneven thermal gradient, these areas will cause local thermal stress concentration. The model uses a thermomechanical coupling solver to jointly process the temperature field and stress field to derive the stress reconstruction path. The stress field reconstruction will further affect local structural deformation or the occurrence of microcracks, causing changes in local heat conduction performance, which in turn affects the overall thermal insulation performance. In this causal chain, the transfer relationship between all variables is continuous and cannot be captured by a static average model. It must be obtained in a dynamic, coupled, multi-scale simulation environment.Therefore, the time-stepping method is adopted in the model training process, combined with the thermal-mechanical dual load input, to dynamically output data such as heat flux density maps, temperature field distribution maps, and stress cloud maps at multiple time points. Key indicators are extracted through these results, such as temperature lag time, thermal stability duration, stress peak drift path, etc., and finally a functional relationship with macroscopic thermal insulation performance indicators (such as equivalent thermal resistance and heat consumption rate) is established.

[0050] Dynamic linkage between temperature and stress fields is achieved to simulate the actual structural response and thermal conduction behavior of masonry blocks in complex thermal environments. This method relies on constructing a thermal-mechanical multiphysics model. Using a finite element modeling platform such as COMSOL Multiphysics, ABAQUS, or ANSYS, a thermally coupled mechanics module is set up to simulate the evolution of thermal stress concentration caused by temperature changes within the recycled masonry block under specific thermal boundary conditions (such as diurnal temperature fluctuations and thermal shock). The modeling process consists of three parts: a realistic microstructural geometry model based on CT scans is established to obtain information about the pore distribution, aggregate particle boundaries, and interfaces within the masonry block; image processing techniques are used for preprocessing, including image denoising, binarization, region segmentation, and 3D reconstruction, to extract geometric structural units suitable for simulation; and thermal and mechanical properties, such as thermal conductivity, thermal expansion coefficient, elastic modulus, and Poisson's ratio, are assigned to each material component. These data are obtained through experimental measurements (thermal conductivity, differential scanning calorimetry, micro-nanomechanical testing, etc.). These data are then standardized and normalized before simulation to ensure uniformity and comparability across different data sources. During the simulation execution phase, by setting steady-state and transient thermal boundaries and applying realistic loads (such as deadweight and external constraints), the model calculates the temperature distribution and corresponding thermal stress evolution at different time points. The focus is on how regions of rapid temperature change induce heterogeneous reconstruction of the stress field. In the simulation results, thermal stress peaks initially appear at material interfaces, pore edges, and aggregate transition zones. By tracing the temporal and spatial drift of these stress concentration points, a map of thermal stress migration paths is generated. These paths not only reveal the fluid nature of stress but also demonstrate its deep coupling with material structural heterogeneity. Furthermore, to analyze the impact of thermal stress migration on local structural integrity, the model uses the stress peak migration region as a local analysis unit, extracting the deformation rate, porosity changes, and crack evolution within this region. Porosity changes are calculated by comparing the element volume before and after deformation in the simulation. Crack evolution is based on the damage mechanics module settings, which simulates the initiation, extension, and connectivity of microcracks at specific stress thresholds and records the temporal trends of their direction, length, and number. The method further proposes a thermal stress-structure perturbation factor framework, which constructs an evaluation system based on a set of specific indicators. These indicators include the local deformation rate factor (characterizing the magnitude of local thermally induced structural deformation), the crack evolution factor (recording the crack growth rate and morphological changes), the pore reconstruction factor (reflecting the changes in local pore connectivity under stress), and the stress perturbation amplitude factor (measuring the degree of severe fluctuations in stress gradients within the same region). These perturbation factors are calculated from the data fields output by the simulation, such as the deformation rate derived from the displacement field, the crack growth path extracted from the damage field, and the perturbation amplitude obtained from the gradient map of the stress field.During the data modeling phase, multi-factor regression analysis or data-driven machine learning models (such as random forest or support vector regression) are used to establish a functional relationship between the set of perturbation factors and the change in equivalent thermal resistance, thereby achieving predictive modeling of the impact of structural response on thermal performance. During the model training process, the perturbation factors under different structural units are used as input variables, and the thermal resistance changes at the corresponding time steps are used as label data to form a training sample set. The training set uses a simulation platform to batch generate samples under various boundary conditions and microstructure parameter combinations, and then performs normalization and feature screening to improve the training effect. The training model will continuously optimize the prediction accuracy and verify the generalization ability through cross-validation.

[0051] To quantitatively model the dynamics of thermal insulation performance under complex multi-physics responses, the massive amount of physical data generated during the coupled thermal-mechanical simulation is converted into usable mathematical eigenvectors. A high-dimensional feature space is then established and further reduced to extract the most representative response factors for performance prediction. A coupled thermal-mechanical simulation of lightweight recycled masonry materials is performed using a finite element simulation platform (such as COMSOL Multiphysics or ABAQUS). Temperature boundaries are set for day-night temperature fluctuations, alternating hot and cold conditions, steady-state and transient conditions, as well as structural mechanics boundaries caused by deadweight, restrained loads, or thermal expansion. During the simulation, temperature, heat flux vector, stress, and strain field data are collected over multiple time steps. Each simulation output node contains multiple physical quantities, which are automatically extracted through a script. These include key indicators such as temperature gradient (i.e., temperature change per unit distance), heat flux magnitude and direction, maximum principal stress value, and spatial gradient of the stress field (i.e., the rate of change of stress within the structure). These quantities form the initial high-dimensional feature set. These raw feature data are stored as multidimensional matrices with hundreds or thousands of dimensions. Due to the collinearity, redundancy, and noise issues inherent in high-dimensional features, data preprocessing is essential. First, all features are normalized and scaled to the interval [0, 1] or [-1, 1]. Principal component analysis (PCA) is then used to perform linear dimensionality reduction on the feature matrix. By extracting the principal components in the direction of maximum variance, the number of variables is reduced while retaining the key information. Furthermore, to better establish the mapping relationship between input and output, a partial least squares regression (PLSR) algorithm is introduced. This algorithm can directly correlate thermal insulation performance indicators (such as equivalent thermal resistance, holding time, and thermal hysteresis coefficient) while extracting the principal components of the features, thereby constructing a model that combines both feature extraction and mapping capabilities. After dimensionality reduction, the resulting principal feature space is used to construct a thermal-mechanical coupling response space. Each point in this space represents the structural response state of the material under a set of temperature and stress states, and the corresponding change in thermal insulation performance can be considered as a response value in this space. In order to achieve a functional description of the relationship between heat and force input and thermal insulation performance output, response surface modeling technology is further adopted. By setting a polynomial response surface model or a fitting method based on radial basis function (RBF), a continuous functional relationship of thermal insulation performance as a characteristic main factor is constructed, namely the response surface equation. This response surface equation is expressed as a resolvable trajectory or surface, revealing how the thermal insulation performance exhibits a nonlinear fluctuation trend under the coupling drive of thermal gradient, heat flux density and stress gradient. During the training process, a large amount of sample data with different thermal boundaries and different material structure configurations is generated through simulation as input feature points, and thermal insulation performance indicators are used as output labels. The least squares method or regularization fitting is used to optimize the parameters to construct a response surface function with strong generalization ability.After the response surface training is completed, it can be directly used to quickly predict the thermal insulation performance of the blocks under different working conditions, or used for reverse optimization of design parameters, that is, input the target thermal insulation performance and reversely infer the optimal thermal-mechanical response path or structural design combination.

[0052] In order to more comprehensively and dynamically reflect the response behavior of masonry materials to the thermal environment in actual use, two key original indicators are introduced, namely the Thermal Retention Time Index (TRT-I) and the Thermal-Mechanical Stability Coefficient (TMS-C). On this basis, a composite scoring system for time and structural response under dynamic working conditions is constructed, thereby achieving a highly timely, highly sensitive and multi-dimensional evaluation of thermal insulation performance. To define TRT-I, it is necessary to build a thermal-mechanical multi-physics model of lightweight recycled blocks in a thermal-mechanical coupling simulation platform (such as COMSOL Multiphysics or ABAQUS), run the simulation under the set temperature boundaries (such as day and night temperature difference, external wall heat flow impact), record the response process of the internal temperature change of the block over time, extract temperature time series data at multiple monitoring points, and set a reasonable "thermal stability interval" (for example, temperature fluctuation does not exceed ±2°C). The time period for the material to maintain this temperature interval per unit time is counted and divided by the total simulation time to obtain the standardized TRT-I value. The larger the value, the better the material can maintain thermal stability. During the data acquisition process, the temperature data of each time step is exported into a matrix form through node tracking, and then the time axis is expanded. Data preprocessing includes missing value interpolation, signal smoothing (such as moving average method), outlier processing, etc., to ensure that the temperature curve change is physically reasonable. Dynamic window statistics are used in the TRT-I calculation process to improve accuracy. The calculation of TMS-C focuses on The basic idea behind studying the structural perturbation response of materials under temperature fluctuations is to simulate how temperature changes induce stress fluctuations or deformation field changes. Specifically, the method extracts time series stress and deformation field data under thermal coupling loads. Key response points or regions are selected, and the stress fluctuation amplitude (e.g., the difference between maximum and minimum stresses) and recovery rate per unit time are recorded. Specifically, the TMS-C method considers two dimensions: the perturbation amplitude (how strong the perturbation is) and the recovery capacity (whether the material can recover after the perturbation). Therefore, the calculation requires first normalizing the stress-time data at each simulation node, calculating the fluctuation range, and then fitting a function to determine the slope of the post-perturbation stable regression trend. TMS-C is then defined as a functional fusion of the structural perturbation amplitude and recovery rate. During this process, stress data preprocessing includes time synchronization, extreme value identification, filtering and denoising, and then synthesizing a regional index using regional averaging to enhance the representativeness of the overall stability assessment.When constructing a composite scoring system, TRT-I and TMS-C are used as representative variables for thermal stability and structural adaptability, respectively. To ensure the comparability of the two dimensions in the scoring system, TRT-I and TMS-C must first be normalized, using Min-Max scaling or Z-score standardization, and weighting different indicators. The weight coefficients are set based on experimental verification or expert experience (for example, 60% for the thermal dimension and 40% for the mechanical dimension). Finally, a comprehensive score R-Score is generated through weighted linear combination or nonlinear fusion (such as weighted harmonic mean). This score can be directly used in application scenarios such as thermal insulation performance ranking, material grade classification, performance prediction, and production ratio optimization. During the model training process, in order to establish the mapping relationship between TRT-I and TMS-C and the actual structural design parameters, the calculated TRT-I and TMS-C indicators can be used as label values, and influencing factors such as porosity, aggregate morphology, thermal conductivity, elastic modulus, etc. can be selected as input feature variables to construct a multi-input and multi-output supervised learning model (such as a multivariate linear regression model or a neural network model). The training set comes from multiple simulation schemes. After feature screening, feature cross-combination and standardization, modeling training is carried out. The prediction ability is evaluated through cross-validation and the structural design parameters are optimized.

[0053] For the intelligent and goal-oriented design control of the performance of block materials, the response surface equation constructed by thermal-mechanical coupling simulation and the composite scoring system are used as the optimization objective function, and then a multi-objective optimization framework is established around structural parameters and thermal insulation performance indicators. The closed-loop control mechanism of the performance-structure-parameter trinity is realized through the reverse search method. To construct the optimization objective function, a large amount of thermal-mechanical coupling simulation work must be completed first. Different material design parameter combinations (such as aggregate ratio, foaming agent dosage, overall porosity, etc.) are set in the simulation platform, and thermal-mechanical multi-physics field simulation is run to extract key data such as temperature field, stress field, and heat flux density. Based on the simulation results, the corresponding performance response variables under each design parameter combination are extracted, including the insulation time (that is, the length of time the internal temperature is maintained in the comfortable range) and the thermal-mechanical coupling stability coefficient TMS-C (used to describe the stress stability performance of the structure under thermal disturbance). These response variables are regressed and fitted with the input parameters to construct the response surface equation. The response surface model can use polynomial regression, support vector regression, radial basis function fitting or Gaussian process modeling. The specific selection depends on the number of samples and the degree of nonlinearity. All data need to be normalized during modeling to prevent the difference in characteristic dimensions from affecting the modeling accuracy. At the same time, the cross-validation method is used to test the generalization ability of the model, and the mean square error or R is selected. 2As a fitting performance indicator, a dual-response objective function was generated: holding time = f4 (aggregate ratio, porosity, foaming agent content) and TMS-C = f2 (aggregate ratio, porosity, foaming agent content). After constructing the objective function, it was further integrated with a composite scoring system consisting of the thermal residence time index (TRT-I) and TMS-C, which measures thermal stability and structural resilience. The weighted combination of the two yields a comprehensive performance score (R-Score). This scoring system, along with the response surface function, serves as the target output of the optimization model. Based on this, a multi-objective optimization framework was constructed, with the optimization variables set as controllable block ratio parameters, including aggregate ratio (e.g., 30%-60%), foaming agent content (e.g., 5%-20%), and total porosity (e.g., 25%-60%). These variables were used to form an initial sample set through experimental design methods (e.g., Latin hypercube sampling or orthogonal testing) to construct the optimization domain. The optimization goal is to maximize the holding time and the TMS-C value while satisfying engineering constraints. For example, the holding time must be no less than X hours, and the TMS-C must be no less than the Y threshold. Additional constraints such as the material density range and the adaptability of the molding process can be added. The entire optimization problem can be solved using a multi-objective evolutionary algorithm (such as NSGA-II, MOPSO, or multi-objective Bayesian optimization). During the optimization process, the model generates new parameter combinations in each generation, which are input into the response surface model to predict the performance score. The optimal non-inferior solution set that meets the target conditions is retained, and the iterations are continued until convergence. The final output is a set of optimal or near-optimal material ratio schemes. Each scheme clearly corresponds to its comprehensive performance in TRT-I, TMS-C, and holding time. Users can flexibly choose from these solutions according to the actual application scenario. The advantage of this optimization process is that it replaces a large number of physical experiments by modeling, significantly saving cost and time, and realizing a structural control path driven by performance inversely.

[0054] Example 1:

[0055] Combined with attachment Figure 1 In this example, a passive housing project in a severely cold northern region required the development of a new lightweight recycled building block that meets energy-saving standards (insulation layer thermal conductivity ≤ 0.20 W / m·K, thermal inertia index greater than 60 min) while also balancing crack resistance and thermal shock resistance. The research team selected a lightweight building block made from 30% recycled ceramsite, 50% construction waste sand, and 20% foaming agent as a prototype and conducted a performance evaluation based on thermal-mechanical coupling.

[0056] In the S1 stage, researchers first used micro-CT scanning to obtain images of the internal microstructure of the blocks. 3The sample slices were reconstructed into three-dimensional structural data, and the local pore connectivity index (range 0.22-0.61), aggregate volume distribution density (0.35-0.48), and aggregate-matrix interface bonding uniformity index (0.68-0.91) were calculated using image processing algorithms. 3 The above data were mapped to the local thermal conductivity (ranging from 0.08W / m·K to 0.18W / m·K) and thermal expansion coefficient (ranging from 7.2×10 -6 / ℃ to 1.5×10 -5 / ℃), forming the input parameter tensor, which is imported into the simulation platform as the thermal-mechanical coupling input variable.

[0057] Entering the S2 stage, the research team built a complete thermal-mechanical coupling model on the COMSOL Multiphysics platform, and set the simulation conditions as follows: the temperature difference between day and night on the outside is from -15°C to +10°C, which cycles once every hour, and the inside is kept constant at 20°C. The thermal boundary is set as a combination of radiation + convection boundary, and the force boundary includes the weight of the block and the top preload of 50kPa. The simulation runs for 48 hours with a time step of 15 minutes, outputting the temperature field, heat flux vector field, stress field and deformation field. Through visual analysis, it was found that an obvious heat flux disturbance zone was formed near the recycled aggregate aggregation area, and the heat flux was "bent and focused" in this area, causing a sharp increase in local thermal stress. The stress peak suddenly increased from the original 30MPa to 49MPa, and the thermal stress mainly migrated along the aggregate boundary, showing obvious migration path characteristics.

[0058] During the S3 phase, researchers further analyzed the structural response in the thermal stress peak region and, using stress-strain field extraction tools, assessed the microcrack risk in the disturbed region. They found four microcracks, approximately 2.5 mm in length, forming at the leading edge of the stress concentration path. The angle between the crack propagation direction and the heat flux direction was less than 15°, confirming that thermally induced stress migration was the primary driver of crack evolution. Furthermore, in the weakly bonded region at the boundary, interface failure occurred earlier than in other areas, with the local deformation rate 2.7 times higher than the average, confirming the triggering effect of interface stress reconstruction.

[0059] In the S4 stage, the researchers mapped the above microscopic response results into macroscopic thermal insulation performance parameters. The temperature stability time period was extracted (the duration for which the internal temperature was maintained at 18-22°C). The results showed that the total maintenance time in the first day and night cycle was 9.8 hours, which was 16% lower than that of the crack-free sample. The thermal hysteresis time was measured, that is, the delay time for the internal temperature to remain stable after a sudden change in the external environment. The actual measurement was 71 minutes, which was 12% lower than the ideal model. The peak change rate of thermal stress was then calculated. The stress fluctuation in the crack area reached ±21MPa, which was significantly enhanced compared to the overall stress mean fluctuation of ±9MPa. These results were constructed as the input of the dynamic thermal insulation performance model, and the mapping equation between the microstructure perturbation factor and the thermal insulation index was established through regression analysis.

[0060] Ultimately, the simulation and evaluation process clearly revealed how a series of mechanisms, such as local thermal deformation causing heat flow disturbances, thermal stress concentration, and microcrack evolution, in real service conditions of the blocks gradually transmit to the dynamic fluctuations of the overall thermal insulation performance, and provide quantitative guidance for subsequent material optimization. To meet the engineering goals (insulation time ≥ 10h, thermal hysteresis time ≥ 75min, TMS-C ≥ 0.8), the research team adjusted the aggregate volume ratio to 38%, fine-tuned the foaming agent to 18%, and optimized the compaction process to control the porosity to around 42%. After updating the parameters and re-simulating, it was found that the thermal stress peak dropped to 42MPa, the crack initiation point was reduced to 1, and the final insulation time was increased to 10.7 hours, and the thermal hysteresis time reached 76 minutes, successfully meeting the engineering performance requirements.

[0061] On the influencing mechanism of microstructural heterogeneity inside lightweight recycled blocks, especially the causal coupling relationship between the thermal flux perturbation path and the structural stress response, a thermal flux perturbation-induced structural response potential energy function model based on the microstructural response sub-area division is established to reveal how the local microstructure of the material determines its sensitivity to thermal deformation-induced stress, and ultimately promote the dynamic changes of thermal resistance performance.

[0062] First, in the image data acquisition stage, researchers used X-ray micro-CT to 3 The block slices were 3D reconstructed with an image resolution of 8 μm. The reconstructed 3D pore structure image was then segmented using machine learning-assisted image segmentation techniques. The segmented structure was then divided into 400 microstructural response sub-regions using a cubic partitioning method. The following structural parameters were extracted for each sub-region: the pore connectivity index χ, calculated as the volume of connected pores divided by the total pore volume, with a measured range of [0.28, 0.71]; the cavity geometry deviation coefficient φ cav , obtained by calculating the deviation of the three-dimensional center of gravity drift of the cavity from the theoretical regular sphere, ranging from [0.12, 0.46]; the interface bonding strength of recycled aggregate σ intThe bond strength in MPa was calculated by combining nanoindentation experiments and interface shear tests, with a range of [3.5, 12.6] MPa; the particle size distribution variance Δ d The particle size is calculated after the edge recognition of the aggregate in the scanned image, with a variance range of [0.002mm 2 ,0.045mm 2 ].

[0063] Substitute the above parameters into the custom thermal flow disturbance response function model:

[0064]

[0065] The parameter values ​​in this simulation are set as: α = 1.2, β = 0.9, κ = 0.85, δ = 15W / m 2 ,γ=0.6、ε=1×10 -3 , the integration region Ω covers 400 subregions and is integrated with a step size of 5 minutes under a 24-hour hot load cycle time.

[0066] Heat flux perturbation gradient The method of obtaining is to derive the heat flux vector field at each time step in the simulation platform, calculate the local heat flux change rate of each sub-area unit according to the main heat flow direction, and calculate its gradient approximately by Gaussian difference. 12~34W / m 2 In the range, about 36% of the sub-areas exceed the disturbance threshold δ.

[0067] After the data is put into the formula, all units are integrated over the entire cycle and the output is Ψ res The results show that the high value area of ​​the response potential energy function (i.e. the area highly sensitive to thermal stress) is mainly concentrated in the areas of χ>0.6 and φ cav >0.35, σ int <6MPa and Δ d >0.03mm 2 These areas significantly overlap with the heat flux disturbance path and match the simulated stress peak migration trajectory by more than 88%, proving that the function has strong predictive and spatial positioning capabilities.

[0068] In terms of evaluating outputs, the research team found that res When the stress in a specific area exceeds the critical value (the selected threshold is 1800 units of potential energy index), the average fluctuation rate in the stress field in this area increases to 2.3 times the original value, and the probability of crack formation in subsequent temperature loading increases by 68%, further confirming the logical chain between thermal disturbance leading to structural weakening and decreased thermal resistance.

[0069] By integrating this function model with the thermal-mechanical coupling simulation module, the researchers successfully established a complete closed-loop path from microstructural parameter acquisition → local thermal disturbance path identification → stress reconstruction mechanism analysis → thermal insulation performance prediction. In the subsequent optimization stage, res Incorporating the design variable sensitivity analysis framework, it was found that the pore connectivity χ and particle size distribution variance Δ d are the main controlling factors. Under the premise of keeping the overall material density unchanged, optimizing these two factors can reduce the peak heat flux disturbance by 21% and increase the structural stability coefficient (TMS-C) by 12%, thereby increasing the insulation time from 10.7 hours to 11.6 hours, forming a material microstructure regulation strategy based on the control of heat flow path response potential energy.

[0070] After completing the modeling of the microstructural response potential energy function and identifying high-risk sub-areas, the research team further focused on the thermal stress reconstruction process at the macrostructural level. The goal was to capture stress concentration, aggregate edge instability, and interface structural disturbances caused by local thermal expansion differences due to temperature gradients, in order to accurately identify potential failure risk points under thermal-mechanical coupling and provide precise input for subsequent material optimization. The process began with data acquisition. Based on the previous thermal-mechanical coupling simulation model, the team further improved the resolution and established a three-dimensional thermal-mechanical coupling finite element model for the block specimen. Wall units with dimensions of 300mm×300mm×100mm were selected and detailed aggregate distribution and pore structure were implanted inside. The model was refined to the interface area and foaming channel around each aggregate, divided into more than 800,000 units to ensure that micro-local deformations could be accurately tracked. The thermal boundary was set to a constant indoor temperature of 20°C and a sinusoidal loading of -18°C to +8°C outdoors according to diurnal variations. The thermal conduction boundary simulation included two composite boundaries: radiation and forced convection. The mechanical boundary included the material's own weight and the compressive stress of the wall structure. The total simulation duration was 72 hours, with a time step of 10 minutes, ensuring that the gradual evolution of thermal stress with temperature difference could be continuously observed. After the simulation began, the research team focused on extracting node data in the area with the most significant temperature gradient and based on the material thermal expansion parameters (experimentally measured at 7.5×10 -6 / ℃~1.4×10 -5 / ℃) to calculate the differences in the degree of expansion response at different locations, and found that the volume expansion deviation caused by temperature changes in the pore edge and aggregate envelope area was significantly higher than that in the matrix area, with the maximum displacement difference reaching 0.42mm, resulting in high-gradient stress fluctuations. Further analysis of the stress distribution cloud map revealed that a stress peak band was formed in the interface area between the aggregate and the matrix, and the stress value soared from an average of 28MPa to 61MPa, significantly exceeding the average stress field fluctuations of the structure. By tracking these high-stress areas in time series, it was found that the stress was not statically distributed, but spatially migrated with the temperature cycle, manifested as stress concentration jumps and diffusion along the aggregate boundary, and negative stress reverse fluctuations were generated in the stress release area near some cavities, resulting in cumulative growth of local structural deformation. During the data processing process, the researchers derived the space-time series data of the stress field and temperature field, performed differential analysis on them at each time step, obtained the stress gradient change rate curve, and then superimposed the stress-displacement function of the adjacent nodes of the interface, extracted the stress release rate change at the aggregate edge, and identified the transfer path of stress from concentration to release.

[0071] To identify areas at high risk of thermal failure, the research team constructed a structural perturbation factor combination model, integrating three core indicators: the stress gradient range index, defined as the difference between the maximum and minimum stress values ​​within a local region divided by the mean stress; the deformation heterogeneity index, defined as the standard deviation of the deformation differences between local nodes; and the thermal expansion stress response ratio, defined as the change in equivalent stress response per unit temperature gradient. All indicators were normalized and clustered. Using the K-means clustering algorithm, the entire structure was divided into five response-level zones. Level 5 high-risk areas were primarily concentrated in aggregate clusters, cavity interfaces, and the two-phase material interface zone, accounting for 9.3% of the total area. However, 60% of stress fluctuations before instability originated in these areas. To further quantify thermal risk, the team used the thermal-stress data from these areas as training data and fed them into logistic regression and decision tree models to train a binary thermal instability predictor. The prediction accuracy reached 87.2%, providing a strong basis for subsequent structural strengthening.

[0072] In summary, the modeling of the thermal stress reconstruction process begins with the differential thermal expansion caused by temperature gradients. By capturing stress concentration locations, tracking stress release paths, identifying structural perturbation response factors, and establishing a statistical mapping relationship between microphysical characteristics and thermal failure risks, the team successfully completed the modeling loop from simulation data to failure warning. Ultimately, in the optimized version of the block structure, the research team introduced an interface enhancer treatment in high-risk areas, lowered the maximum aggregate particle size to 10mm, and optimized the foaming agent distribution. This reduced the maximum stress to 48MPa, the local instability rate by 42%, and significantly improved the corresponding thermal insulation performance indicators.

[0073] After completing the microstructural response function modeling and thermal stress reconstruction analysis, the research team further introduced a thermal insulation performance fluctuation parameter system centered on thermal hysteresis time, thermal stability maintenance time, heat flow variation rate, and structural perturbation frequency in order to achieve prediction and rapid optimization decisions for macro thermal insulation performance. Based on this, a macro thermal insulation performance response surface model was established, thereby realizing a quantitative prediction system for input structural design parameters and output performance response trends. The team selected 12 groups of different block ratio parameters (covering different aggregate ratios, foaming agent dosages, and interface enhancement treatment processes) in the thermal-mechanical coupling simulation platform for full-cycle (72-hour) multi-physics field simulation. The simulation results exported high-dimensional data such as temperature field, heat flow vector field, stress field, and displacement field containing 6000+ time steps. The data collection points were concentrated in representative areas: the central solid area, the pore aggregation area, the aggregate boundary area, and the weak bond zone at the interface, forming a multi-source time series data set. Thermal hysteresis time is a key indicator for evaluating the delay in internal temperature response under external temperature disturbance. The data acquisition method is as follows: set a trigger threshold at each sampling point (for example, when the external temperature suddenly changes by 5°C, the internal temperature response changes by 1°C), record the delay time as the hysteresis indicator, and the average thermal hysteresis time ranges from 48 minutes to 97 minutes in different structural designs; the thermal stability maintenance time indicates the duration for which the internal temperature remains in the comfortable temperature zone (18-24°C). The cumulative time is calculated within the same simulation cycle, and the data range is The heat flux variability reflects the intensity of heat flux fluctuations per unit time. It is calculated as the variance of the heat flux vector divided by the square of its mean. The measured range is 0.04 to 0.17, with larger values ​​indicating more unstable heat conduction paths. The structural perturbation frequency, calculated by counting the number of local stress mutations (e.g., transient stress changes >15%) in the structure and dividing it by the total simulation time, ranges from 0.06 to 0.22 times / min. These perturbations are primarily concentrated in areas with poor interface bonding or concentrated pores. These data were uniformly normalized and Z-score normalization was used to compress data across different dimensions to prevent inter-dimensional features from interfering with the accuracy of the response surface model. Principal component analysis (PCA) was then used to extract the main influencing dimensions. Thermal hysteresis time and thermal stability maintenance time were found to be the primary thermal dimension factors, accounting for 48% of the total variance, while the heat flux variability and structural perturbation frequency primarily reflect the dynamic response of the coupled field, accounting for 37% of the total variance. On this basis, with these four parameters as response variables and structural design parameters (aggregate ratio, porosity, foaming agent content, interface strength) as input factors, a four-dimensional response surface function was established. The function form was selected as a quadratic polynomial response surface model, and the least squares method was used for parameter fitting. The training sample included 12 groups of simulation schemes, each group containing the above four response variables and four input variables. After model training, the cross-validation method was used for evaluation. The average prediction error was controlled within 6%, and the goodness of fit R 2It reaches 0.92, with good prediction accuracy. The macro thermal insulation performance response surface finally generated can not only be used for the rapid prediction of thermal insulation performance under any combination of structural parameters, but can also be embedded in a multi-objective optimization framework to achieve goal-oriented formula reverse design. For example, if the project requires a thermal lag time ≥ 80 minutes, a thermal stability maintenance time ≥ 10 hours, and at the same time ensure that the heat flow variation rate is ≤ 0.08, the system can reversely infer the feasible ratio range through the response surface model, output multiple near-optimal solutions (such as aggregate ratio 35% to 42%, porosity 38% to 44%, foaming agent content 16% to 19%, interface strength > 9MPa), and verify in subsequent experiments that its actual thermal insulation performance is better than the existing solution.

[0074] Example 2:

[0075] Based on Example 1, after completing the thermal stress reconstruction identification and thermal insulation performance response surface modeling, the research team further conducted an in-depth analysis of the detailed mechanism of the structural stability of the blocks under thermal cycling conditions, and introduced a thermal stress and structural perturbation factor framework to identify, quantify and predict the weakening effect of microstructural changes caused by local thermal stress on the overall thermal resistance performance.

[0076] In the S1 phase, the team first established a three-dimensional multi-physics coupling model of the lightweight recycled block in COMSOL Multiphysics based on the block geometry model constructed by the previous scan. The model size was 400mm×400mm×100mm, including a three-phase structure of recycled ceramsite aggregate, foaming pore area, and cement matrix area. The aggregate diameter distribution was controlled within 6–14mm. To reflect the heterogeneity, a custom material module was used to give each phase different thermal and mechanical properties, such as thermal conductivity (aggregate: 0.27W / m·K, matrix: 0.42W / m·K, foaming pore area: 0.08W / m·K), thermal expansion coefficient (aggregate: 8.5×10 -6 / ℃, matrix: 1.2×10 -5 The model was designed with a thermal boundary of 20°C indoors and a sinusoidal temperature fluctuation of -15°C to +10°C outdoors, with a 24-hour cycle for a total of 72 hours. The force boundary consisted of a vertical deadweight load and a 20 kPa wall-conducted pressure. The model was calculated with a 10-minute step, using a dynamic coupled solution.

[0077] In the S2 stage, after the simulation is completed, the stress field under the time step is exported, and the "extreme path tracking function" in COMSOL is used to analyze the spatial drift of the principal stress over time, identify the area forming a stable migration path, and construct the stress migration trajectory with the maximum principal stress point at each step. In the simulation results, the researchers found that the high-value thermal stress area gradually expanded outward along the aggregate boundary and the pore distribution aggregation, showing obvious "path-related concentration behavior". For example, in 24 to 36 hours, the stress value in the aggregate-matrix interface area increased from 28MPa to 54MPa, and a structural disturbance response was formed along with the migration process. The team extracted the stress data of the nodes in these path areas and tracked their deformation field responses to identify the structural disturbance areas induced by stress migration. Some nodes showed nonlinear abrupt changes in the stress-strain curve, indicating crack initiation.

[0078] In the S3 phase, the team constructed a structural perturbation factor framework and extracted the following four types of perturbation indicators through simulation: ① Local deformation rate factor (LDRF), defined as the ratio of the average displacement of nodes in a local area to the overall average displacement. The simulation found that the average LDRF in the thermal stress concentration area was 1.82, indicating that this area deformed approximately 82% more than the normal area. ② Crack evolution factor (CEF), based on the crack phase field parameters extracted in the damage mechanics module, quantifies the crack length growth rate. In the simulation, the high CEF value is concentrated in the sharp corners of the aggregate, with a maximum crack propagation rate of 0.26 mm / h. ③ Pore reconstruction factor (PRF), based on the volume mesh tracking of the change in pore morphology over time, found that some closed pores were connected to form heat conduction channels under the induction of thermal stress, and the local PRF reached 0.41 (indicating a 41% topological change in the pore morphology). ④ Stress perturbation amplitude factor (SDF), which refers to the ratio of the stress change range per unit time during thermal loading. This value reached 0.62 in the interface failure zone, far higher than the overall average of 0.25. All disturbance factors are normalized and used to construct a disturbance sensitivity distribution map to mark the potential area of ​​thermal instability.

[0079] In the S4 stage, the team used the high-value areas of the above-mentioned disturbance factors as the analysis objects, extracted the heat flux density data before and after the simulation, and calculated the rate of change of heat flux per unit time in the area. It was found that the direction of heat flux in some areas changed, and the heat flux density increased from the initial 42W / m 2 Reduced to 27W / m 2, showing obvious heat transfer short circuit or thermal bridge formation. In order to quantify its impact on thermal resistance, the thermal resistance reduction ratio (TRDR) calculation is introduced, that is, the comparison of the equivalent thermal resistance before and after the local disturbance. The measured TRDR in the typical disturbance area reaches -23%, that is, the effective thermal resistance in this area has dropped by nearly a quarter. Combined with the response surface prediction, the reduction in the thermal resistance of the local structure leads to a decrease in the overall wall insulation performance of about 0.8 hours of lag maintenance time, which exceeds the energy-saving deviation tolerance set by the project. Based on the disturbance factor distribution and TRDR analysis results, the research team adopted the following optimization strategies in the subsequent block structure: improving the interface bonding strength from the original 3.6MPa to 7.4MPa, controlling the aggregate size to less than 10mm, and redistributing the foaming agent to make the porosity more uniform. After optimization, the simulation shows that the LDRF is reduced to 1.23, the SDF is reduced by 45%, the local TRDR is reduced to -9%, and the thermal stability maintenance time is restored to 10.6 hours, meeting the design requirements.

[0080] The project has advanced to the quantitative modeling stage of the relationship between the microscopic thermal stress migration path and the structural damage response of the block material under long-term service environment. In order to solve the problem that local thermal stress-induced failure cannot be identified in advance, the research team carried out a verification simulation experiment based on the stress-disturbance coupling function model, and constructed a function Φ dyn To achieve thermal stress migration path Deep coupling analysis between microstructural response intensities and combined with material microscale response factors can predict failure risks.

[0081] First, in the multi-physics simulation platform COMSOL Multiphysics, the team used the previously constructed three-dimensional model of heterogeneous microstructures to perform periodic thermal loading on the lightweight recycled blocks (the external ambient temperature was simulated as a sine function ranging from -20°C to +12°C, with a period of 24 hours and a total simulation time of 72 hours. The thermal boundary was a radiation + convection composite boundary, and the force boundary was a vertical deadweight + horizontal residual stress of 20kPa). The model introduced real interface weak bonding areas and pore aggregation areas. The principal stress field output by the simulation was sampled every 10 minutes, and the stress peak trajectory line s was generated by identifying the position change of the principal stress extreme point in three-dimensional space at each time step. σ (t), and the degree of nonlinearity (defined as the deviation from the shortest straight line path, measured in the range of 8 mm to 26 mm) was calculated using polynomial curve fitting to express the complexity of the migration path.

[0082] Then enter the disturbance factor extraction stage, the local deformation rate factor Λ d The instantaneous deformation or cumulative displacement induced by thermal stress in the unit body is calculated by calculating the time derivative of the displacement field of each sub-unit grid. In the simulation, the weak zone Λ dThe range is 0.08 to 0.35 (indicating that the maximum local deformation rate is 3.5 times the overall average deformation rate); the crack evolution factor Ξ c The crack evolution variable is extracted from the phase field crack module, which represents the crack length growth rate per unit time multiplied by the crack extension direction consistency weight. The maximum value in the actual measurement is 0.18 and the minimum is 0.02. In addition, the angle Δ between the crack extension direction and the heat flux gradient direction is θ It is distributed between 5° and 60° and is used to quantify the degree of consistency between the crack and the main heat migration path. The smaller the value, the easier it is to form a thermal bridge path, and the larger the value, the more deviation there is between crack propagation and thermal stress migration.

[0083] Substitute the following function:

[0084]

[0085] Among them, μ=1.3, ν=1.8, η=4.5, The above parameters are obtained by comparing Φ dyn The integration region Ω covers the simulation volume (including about 96,000 elements in the high stress area) and the 72-hour simulation period.

[0086] After solving the function, we get Φ of each region dyn The distribution diagram of the values ​​shows that an obvious high-value response band is formed at the aggregate aggregation and pore connection, with the maximum value reaching 1480 (unit is normalized potential energy index). At the same time, the final length of the crack in the corresponding area reaches 11.4mm in the simulation, accompanied by a local heat flux from 38W / m 2 Reduced to 24W / m 2 , the thermal resistance reduction ratio TRDR reaches -27%. Further analysis of Φ dyn The fitting curve between the thermal resistance reduction ratio and the determination coefficient R 2 =0.89, indicating that the function has a high prediction accuracy in characterizing the structural failure mechanism induced by thermal stress migration.

[0087] Based on the output of this function, the team will dyn The area is marked as a thermally weak area, and attempts are made to control the occurrence of failure through design adjustments: in the structural scheme, the foaming agent content is controlled to reduce the pore connectivity, and the interface modification process is adjusted to make σ int From 5.6MPa to 10.1MPa, the result is Λ d Down to 0.14,Ξ c reduced to 0.06, and finally the Φ in the high response area dyn The peak value dropped by 42%, the crack evolution length was shortened to 4.1 mm, the TRDR dropped to -10%, and the overall insulation maintenance time was extended by 0.9 hours.

[0088] The project has entered the stage of in-depth modeling of the dynamic evolution mechanism of the microstructure. The research team focused particularly on the topological reconstruction process of the pore structure under thermal stress and the influence mechanism of the violent fluctuation behavior of the local stress field on the overall thermal insulation performance of the material. They further proposed and implemented a quantification method for two types of key disturbance factors - pore reconstruction factor and stress disturbance amplitude factor, which serve as the core input parameters for the micro-dynamic response monitoring and performance prediction model in this invention.

[0089] In the simulation modeling stage, the researchers used X-ray CT technology to collect pore structure images of multiple samples with different aggregate ratios based on the real block microscopic three-dimensional structure obtained by the previous scan. Each sample was 100mm thick. 3 Volume reconstruction with a resolution of 5μm was performed. After image segmentation and connectivity analysis, the pore area was extracted and the surface area, volume, principal axis length, pore centroid trajectory, and connectivity label of each pore unit were calculated. These characteristic parameters were recorded at multiple time nodes to characterize dynamic changes. The thermal-mechanical coupling simulation used the structural thermal coupling module of the COMSOL platform to simulate the same pore structure under a 72-hour cycle of thermal cycling loading. The thermal boundary was an external sinusoidal load from -18°C to +15°C, and the internal temperature was fixed at 20°C. The structural deadweight and thermal expansion force were applied together, and the nonlinear geometric deformation analysis function was enabled to capture the internal pore evolution of the material under high temperature difference conditions. In the simulation output results, the topological properties of the same pore unit were extracted at each time step, including whether it changed from a closed pore to a connected pore, whether volume expansion, structural rupture, or adjacent pores merged, etc., and its state change time, evolution path, and local material stress state were recorded.

[0090] The calculation of the pore reconstruction factor does not rely on traditional static porosity indicators, but focuses on units where the topological structure has undergone essential changes. Each pore is given a dynamic label, and it is calculated whether it changes from a closed state to a through-hole state during the thermal cycle (based on the rupture of the pore wall and connection with the adjacent pores), and whether it has experienced key geometric events such as an expansion of the pore diameter exceeding 10% and an increase in surface complexity (judged by a decrease in sphericity). Finally, the pore reconstruction factor is defined in the range of 0 to 1 by a weighted method of the topological state change rate + volume change rate + connectivity change. Among the measured samples, the pore reconstruction factor of some high-stress areas reaches 0.62, indicating that thermal stress induces drastic pore evolution behavior locally, while the value in normal areas is generally below 0.15. By mapping the pore reconstruction factor to the heat flux change area, the research team found that in areas with reconstruction values ​​higher than 0.5, the heat conduction path undergoes obvious bending or short-circuiting in the simulation, and the local thermal resistance drops by more than 20%, verifying the strong interference of the dynamic evolution of the pore structure on the heat conduction behavior.

[0091] Meanwhile, the quantification method for the stress perturbation amplitude factor is based on statistical analysis of the principal stress variation over time output by the simulation. The team deployed multiple monitoring units in the thermal stress concentration zone, extracted the principal stress value at each time step, calculated the maximum-minimum difference of the time series at each monitoring point, and divided it by the mean as the perturbation coefficient, defined as the stress perturbation amplitude factor. Field measurements revealed that in the central region of the stress migration path, the perturbation factor generally ranged from 0.35 to 0.58, with a local extreme value of 0.71, while it was below 0.15 in the non-perturbation zone. To avoid local high-frequency noise interference, the team used the Savitzky-Golay filter method to smooth the original stress series. The perturbation rhythm was then extracted using a sliding window difference method. The perturbation frequency (number of changes per unit time) and perturbation amplitude were further factored into the evaluation to derive the final factor score. Comparing the spatial mapping of this factor with the crack initiation points revealed that stress overload cracks occurred in over 80% of the high-perturbation zones. The region where the pore reconstruction factor overlapped formed the core risk zone most susceptible to thermal instability.

[0092] Finally, the research team input the pore reconstruction factor and stress perturbation amplitude factor into the dynamic thermal insulation performance prediction model, constructed a prediction function through regression analysis with the thermal resistance decrease rate, and trained the model under 12 groups of different material design schemes. The average prediction error was controlled within 6.4%, and the microstructure evolution behavior was successfully incorporated into the macro performance prediction system. In the subsequent material optimization stage, the distribution area of ​​high-factor regions was reduced by controlling the particle size distribution of the foaming agent and improving the interface bonding process, achieving a 31% decrease in local thermal resistance fluctuations, an extension of 0.7 hours in insulation time, and a 47% reduction in crack density.

[0093] These disturbance factors are further transformed into quantitative prediction capabilities for macroscopic thermal insulation performance. The thermal resistance reduction ratio is introduced to measure the degree of attenuation of heat flux transmission capacity caused by material structural disturbances. By building a data-driven correlation modeling mechanism, the microscopic disturbance mechanism and the macroscopic performance evolution trend are connected, thus forming a complete thermal response evaluation chain. The definition of the thermal resistance reduction ratio is based on the comparative analysis of high-resolution heat flux vector fields in thermal-mechanical coupling simulations. The research team selected the same spatial unit area before and after structural disturbances (for example, before and after microcrack formation, before and after pore topology changes) in the simulation model, extracted the average heat flux value per unit area, and calculated the heat flux reduction rate according to the formula. It is defined as the ratio of the original flux to the flux after disturbance, that is, the thermal resistance reduction ratio. The physical meaning is: the unit structural disturbance leads to a relative decrease in unit heat transfer capacity. During the data acquisition process, the team set up an automated data extraction script in COMSOL to extract the heat flux vector distribution of selected areas (such as crack formation points, aggregate boundaries, and cavity aggregation zones) every 10 minutes, and converted the vector field into a scalar flux density value through numerical integration. The total sample size reached 8,640 regional time nodes.

[0094] In order to map the microstructure disturbance factor to the thermal resistance reduction ratio, the team used three modeling methods for comparison: one is multivariate linear regression modeling, using the local deformation rate factor (Λ d ), crack evolution factor (Ξ c ), pore reconstruction factor (PRF) and stress disturbance amplitude factor (SDF) as independent variables, thermal resistance reduction ratio as dependent variable, and the fitting coefficient is solved by least square method, and regression R 2 The value is 0.81, indicating that the linear model has a certain predictive power but is limited by the nonlinear disturbance response characteristics. The second is response surface analysis (RSM). After the principal component analysis (PCA) dimensionality reduction process, a quadratic polynomial response surface is constructed. The number of sample points is 216 groups, and the input variables are sampled in an orthogonal design. The prediction surface output by the model shows the trend of the change of the thermal resistance reduction ratio under the combination of multiple factors, which significantly enhances the interpretability of the interaction between variables. 2 It was improved to 0.89 and used for subsequent design optimization search path.

[0095] The third method is to build a data-driven machine learning model, using random forest regression (RF) and support vector regression (SVR) algorithms to establish nonlinear mapping models between structural perturbation factors and thermal resistance reduction ratios. The data set is divided into a training set (80%) and a validation set (20%). Five-fold cross-validation is used to evaluate model performance. The random forest model parameters are set to 150 trees and a maximum depth of 8; the SVR model uses a radial basis kernel function (RBF), with a kernel width parameter γ = 0.4 and a penalty factor C = 10. The results show that the random forest model achieves R on the test set. 2 =0.93, mean absolute error MAE =0.014, and the SVR model R 2 =0.91, performing slightly worse than RF, but being more sensitive in boundary disturbance regions. Ultimately, the team chose to integrate the outputs of the two models to construct a hybrid predictor, improving prediction robustness in extreme disturbance scenarios.

[0096] Once established, the model can be used to input any combination of structural perturbation factors and quickly output the corresponding predicted thermal resistance reduction ratio. Visual analysis is also provided by combining it with a response surface trend plot. In actual engineering applications, the model has been successfully used to evaluate three different masonry materials. The predicted thermal resistance reduction ratio for Plan A (porosity 38%, aggregate ratio 42%, and interface enhancer content 5%) was 0.14, for Plan B it was 0.08, and after optimization, for Plan C it dropped to 0.05. These differences are highly consistent with the experimentally measured insulation duration differences, with an error within ±5%, providing a clear basis for final material recommendations.

[0097] The basic principles, main features, and advantages of the present invention are shown and described above. Those skilled in the art should understand that the present invention is not limited to the foregoing embodiments. The foregoing embodiments and descriptions are merely illustrative of the principles of the present invention. Various changes and modifications may be made to the present invention without departing from the spirit and scope of the present invention. Such changes and modifications are intended to fall within the scope of the present invention. The scope of protection claimed in the present invention is defined by the appended claims and their equivalents.

Claims

1. A thermal insulation evaluation method for lightweight recycled blocks based on thermal-mechanical coupling simulation, characterized by The following steps are involved: The recycled building blocks are modeled as heterogeneous multiphase composites, introducing a three-layer structural field consisting of microscopic pores, mesoscopic aggregates, and macroscopic blocks. A partitioned coupling strategy is employed to map microstructural parameters, including pore connectivity and aggregate morphology, into local response functions of thermal conduction and thermal expansion. A causal chain is constructed, from microstructural variability to heat flux perturbation to stress field reconstruction, to capture fluctuations in macroscopic thermal insulation performance caused by thermal deformation. Track the thermal stress concentration areas caused by temperature difference changes through thermal and mechanical coupling simulation; Analyze the impact of thermal stress migration paths on local structural integrity, porosity changes, and crack evolution; construct a thermal stress and structural perturbation factor framework to evaluate the impact of local structural deformation on thermal resistance; Based on the simulation data, high-dimensional feature data including temperature gradient, heat flux, maximum stress, and stress gradient are extracted; through principal component analysis and partial least squares regression dimensionality reduction methods, the thermal and force feature space is established; Construct a response surface equation to map the changing trajectory of thermal insulation performance in the thermal and mechanical coupling response space; The thermal residence time index TRT-I is defined to measure the material's ability to maintain a stable temperature range per unit time; the thermal and stress coupling stability coefficient TMS-C is defined to evaluate the amplitude and recovery ability of structural field disturbances under temperature fluctuations; and the two are combined to form a composite scoring system for time and structural response.

2. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 1 is characterized in that The response surface equation and composite scoring system are used as optimization function objectives; a multi-objective optimization framework is constructed with aggregate ratio, foaming agent content, and porosity control as design variables; a reverse search is conducted to find a ratio scheme that meets the insulation target, including an insulation time ≥ X hours and TMS-C ≥ Y; and a design and control path that integrates performance, structure, and parameters is formed.

3. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 2 is characterized in that The method for capturing the fluctuation of macroscopic thermal insulation performance caused by thermal deformation includes: S1. Establish a microstructural heterogeneous model for lightweight recycled blocks. Divide the block material into multiple microstructural response regions. Based on the pore connectivity, aggregate distribution density, and interface quality micro-characteristic parameters of each region, differentiated local thermal conductivity and thermal expansion coefficients are assigned to construct a thermomechanical coupling input parameter set. S2. Using a partition coupling strategy, a multi-physics field coupling model of heat and force inside the block is constructed to simulate the joint evolution of the temperature field and the stress field, and to track the perturbation path of the heat flux density and the local thermal stress concentration phenomenon caused by it. S3. Analyze the causal relationship between the thermal flow disturbance zone and the stress field reconstruction, and identify the structural response characteristics induced by thermal stress, including the microcrack initiation location, stress gradient migration trend, and interface failure area; S4. Map the local response into macroscopic thermal insulation performance fluctuation parameters, including temperature difference maintenance capacity, thermal hysteresis time, and thermal stress peak change rate indicators, and construct a dynamic evaluation model of thermal insulation performance driven by thermal deformation.

4. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 3 is characterized in that The microstructure response area is divided based on the pore connectivity index, recycled aggregate interface bonding strength, particle size distribution, and cavity distribution morphology, and modeling parameters are extracted through image reconstruction and material testing data. The simulation process of the heat flux density disturbance achieves non-uniform heat flux distribution tracking by setting different heat conduction blocks, recording the path bending, aggregation, or scattering effects of heat energy in the structure, and serving as input for subsequent stress analysis.

5. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 4 is characterized in that The thermal stress reconstruction process is based on the local thermal expansion difference caused by temperature gradient, simulating the evolution of stress concentration between interfaces, stress release around aggregates and structural integrity disturbance behavior, and extracting key areas as thermal failure risk points.

6. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 5 is characterized in that The thermal insulation performance fluctuation parameters include thermal hysteresis time, thermal stability maintenance time, heat flow variation rate, and structural disturbance frequency, which are used to establish a macroscopic thermal insulation performance response surface.

7. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 1 is characterized in that The method for constructing a thermal stress and structural disturbance factor framework includes: S1. Establish a multi-physics coupling model for lightweight recycled building blocks, integrate the heterogeneous microstructural characteristics of the material, and set thermal and force boundaries to enable dynamic coupling calculation of temperature and stress fields; S2. Identify the thermal stress migration path during the simulation process, extract the local stress concentration area formed along the path, and identify the structural disturbance characteristics caused by stress migration; S3. Based on the thermal stress concentration effect, a structural disturbance factor framework is constructed, wherein the structural disturbance factors include: local deformation rate factor, crack evolution factor, pore reconstruction factor and stress disturbance amplitude factor; S4. Perform heat flux reconstruction analysis on the structural disturbance area, measure the change in heat flux density before and after the disturbance, and quantify the thermal resistance reduction ratio of the corresponding area.

8. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 7 is characterized in that Identification of the thermal stress migration path includes tracking the spatial movement trajectory of the stress peak, the direction of stress gradient change and its change rate, which are used to analyze the thermal stress diffusion mechanism; The local deformation rate factor is used to characterize the degree of deformation of the material unit in the local area under the action of thermal stress; the crack evolution factor identifies the microstructural failure path driven by thermal stress by recording the initiation, expansion and connectivity of microcracks during the simulation process.

9. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 8 is characterized in that The pore reconstruction factor is used to reflect the changes in the geometric shape and connectivity of local pores under the action of thermal stress, including the transformation of closed pores into through pores and pore expansion. The stress perturbation amplitude factor is used to quantify the degree of stress fluctuation in a specific local area and is obtained by analyzing the changes in stress values ​​at multiple times in the same area.

10. The thermal insulation evaluation method of lightweight recycled building blocks based on thermal-mechanical coupling simulation according to claim 9 is characterized in that The thermal resistance reduction ratio is used to describe the ratio of the decrease in heat flux per unit area before and after structural disturbance, reflecting the degree of weakening of the heat conduction path caused by microstructural changes; the correlation model between the structural disturbance factor and the thermal resistance reduction ratio is constructed using regression modeling, response surface analysis or data-driven machine learning methods.

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