Cement paste creep cross-scale prediction method and system based on stress correlation

Abstract

According to the cement paste creep cross-scale prediction method and system based on stress correlation provided by the invention, the creep behavior of the cement paste under the microcosmic indentation scale and the macroscopic uniform stress scale is uniformly described by introducing the stress correlation viscosity parameters; and predicting the long-term macroscopic creep performance of the material by using a short-time microscopic indentation test result. According to the method, the problem of mismatching of macro and micro creep time scales in the prior art is effectively solved, the acceleration effect of the stress level on the creep characteristic time can be revealed, and continuous cross-scale mapping of the creep characteristic time is realized. The method has the advantages of being clear in physical significance, high in calculation precision and high in applicability, and reliable theoretical basis and calculation means can be provided for rapid evaluation and long-term service performance prediction of the creep performance of the cement-based material.

Description

A Stress-Related Method and System for Predicting Cement Paste Creep Across Scales Technical Field

[0001] This invention relates to the technical field of civil engineering materials, specifically to a method and system for predicting the creep of cement paste across scales based on stress correlation. Background Technology

[0002] As the service life of engineering structures increases, cement-based materials undergo significant creep deformation under long-term loading. Creep leads to reduced structural stiffness, redistribution of internal forces, and cumulative deformation, thereby affecting the normal service performance and long-term safety of concrete structures. Therefore, accurately assessing and predicting the creep behavior of cement-based materials is a crucial technical problem that urgently needs to be solved in the field of civil engineering. Traditional research on the creep of cement paste and concrete mainly relies on macroscopic uniaxial creep tests. These tests are time-consuming and costly, often requiring hundreds of days or even longer to obtain effective data, making it difficult to meet the needs of rapid assessment and parameter calibration in engineering projects. In recent years, nano- and micro-indentation techniques have been widely used for the rapid characterization of the creep properties of cement paste and its main hydration products due to their advantages such as high loading stress and short testing time. Related studies have shown that short-time nano- and micro-indentation creep tests can obtain response curves with similar characteristics to macroscopic creep behavior, providing a new technical approach for multi-scale research on the creep of cement-based materials.

[0003] However, nano- and micro-indentation tests differ significantly in time scale from macro-creep tests, with the corresponding creep characteristic times often differing by several orders of magnitude. This makes it difficult to directly predict the long-term macro-creep performance of materials using micro-indentation test results. Existing studies mostly establish the relationship between micro- and macro-creep parameters through homogenization methods or empirical mapping relationships. However, these methods mainly focus on spatial scale conversion and cannot adequately address the time scale mismatch problem under different test conditions. In addition, some scholars have attempted to introduce methods such as discrete delay spectroscopy to compare and analyze micro- and macro-creep behaviors. However, these methods usually only establish a correspondence at discrete time points and cannot achieve a continuous mapping of creep behavior in the time domain. At the same time, most existing models do not fully consider the influence of stress level differences on creep characteristic times, making it difficult to reveal the intrinsic mechanism of significant creep acceleration in nano- and micro-indentation tests. Their applicability and prediction accuracy still have certain limitations.

[0004] Therefore, in order to achieve reliable prediction of the long-term macroscopic creep performance of cement paste based on short-time microscopic tests, there is an urgent need for a creep analysis and prediction method that can consider the influence of stress level and achieve a unified characterization of creep characteristics across time scales. Summary of the Invention

[0005] This invention is made to solve the above-mentioned problems, and aims to provide a method and system for cross-scale prediction of cement paste creep based on stress correlation.

[0006] This invention provides a method for cross-scale prediction of cement paste creep based on stress correlation, characterized by the following steps: S1: Material parameter and test condition determination step, determining the micro-indentation test parameters, macro-mechanical parameters, and loading stress level of hydrated calcium silicate and cement paste; S2: Nonlinear viscoelastic-plastic constitutive model construction step, constructing a nonlinear viscoelastic-plastic constitutive model based on the parameters determined in S1, wherein the viscosity parameter of the nonlinear viscoelastic-plastic constitutive model is a function of the equivalent stress level; S3: Nano-micro indentation numerical simulation and parameter inversion step, establishing a nano-micro indentation finite element model based on the nonlinear viscoelastic-plastic constitutive model, combined with genetic algorithm... The method involves inverting and identifying constitutive parameters of hydrated calcium silicate and cement paste; S4: Establishment and verification of macroscopic creep finite element model, applying the constitutive parameters obtained from the inversion to the macroscopic creep finite element model to simulate the macroscopic creep process of cement paste, and verifying the macroscopic-microscopic consistency of the nonlinear viscoelastic-plastic constitutive model by comparing with the macroscopic creep test results; S5: Cross-scale prediction step, based on the verified nonlinear viscoelastic-plastic constitutive model, simulating the creep response of cement paste under different stress levels, extracting creep characteristic time and establishing a quantitative relationship between creep characteristic time and stress level, realizing cross-scale prediction of macroscopic creep behavior based on microscopic indentation test results.

[0007] The stress-correlation-based method for predicting the creep of cement paste across scales provided by this invention may also have the following features: In S1, the micro-indentation test parameters include: indenter type, maximum loading force, loading and unloading time and duration; the macro-mechanical parameters include: elastic modulus, Poisson's ratio and compressive strength.

[0008] The stress-correlation-based method for predicting the creep of cement paste across scales provided by this invention may also have the following features: In S2, the method for constructing the nonlinear viscoelastic-plastic constitutive model is as follows: a nonlinear viscoelastic-plastic constitutive model composed of multiple Kelvin elements and plastic elements is established, wherein the viscosity parameter in the nonlinear viscoelastic-plastic constitutive model is a function of the equivalent stress level; the nonlinear viscoelastic-plastic constitutive model is embedded into the finite element analysis platform in the form of a user subroutine.

[0009] The stress-correlation-based method for predicting the creep of cement paste across scales provided by this invention may also have the following feature: In S2, the constitutive equation of the nonlinear viscoelastic-plastic constitutive model includes the following sub-steps:

[0010] S2-1: Calculate the viscoelastic stress in the test, expressed as:

[0011]

[0012] In the formula, This represents the stress at the start of the incremental step. This represents the deviatoric stress increment calculated assuming viscoelastic strain. This represents the volumetric stress increment calculated assuming viscoelastic strain. This represents the stress at the end of the incremental step calculated assuming viscoelastic strain.

[0013] S2-2: Calculation of the yield function under the test stress state , is represented as:

[0014]

[0015] In the formula, Let represent the Mises equivalent stress under viscoelastic stress, and r represent the isotropic hardening function. Indicates yield stress.

[0016] S2-3: Determine whether the material yields, expressed as:

[0017]

[0018] S2-4: The equivalent plastic strain increment is calculated using the central difference method and expressed as:

[0019]

[0020]

[0021] In the formula, p is the equivalent plastic strain, h is the hardening constant, and G is the shear modulus. For the viscosity parameters of the independent sticking pot unit, For the equivalent plastic strain increment, Increment for the current time step.

[0022] S2-5: Calculate plastic strain, viscoelastic strain, and stress increment, expressed as:

[0023]

[0024]

[0025]

[0026] In the formula, For viscoplastic strain, viscoelastic strain, This represents the total strain increment.

[0027] S2-6: Update the state variable, represented as:

[0028]

[0029]

[0030] In the formula, This represents the total stress at the end of the previous time step. This represents the stress increment caused by the strain increment at the current time step. This represents the equivalent plastic strain at the end of the current time step. The equivalent plastic strain at the start of the current time step. This represents the equivalent plastic strain increment at the current time step.

[0031] The stress-correlation-based cross-scale prediction method for cement paste creep provided by this invention may also have the following features: In S3, the inversion identification method is as follows: a two-dimensional axisymmetric nano-micro indentation finite element model is established, the indenter is set as a rigid body, and hydrated calcium silicate and cement paste are described using a nonlinear viscoelastic-plastic constitutive model; a parameter inversion process is constructed through a genetic algorithm, using the contact creep curve obtained from the micro-indentation test as the objective function, to invert and identify the viscoelastic-plastic constitutive parameters in the nano-micro indentation finite element model until the numerical simulation curve and the contact creep curve reach consistency within a predetermined error range. The loss function is as follows:

[0032]

[0033] In the formula, N is the number of data points for the objective function, which is determined by the indentation holding time. One data point is taken every 1 second to calculate the objective function. and These represent the contact creep function values ​​in numerical simulation and indentation test, respectively.

[0034] The stress-correlation-based method for predicting the creep of cement paste across scales provided by this invention may also have the following features: In S4, the geometric dimensions and loading regime of the macro-creep finite element model are consistent with the corresponding macro-creep test, the dynamic explicit analysis step is used for solving, and mass scaling technology is introduced to ensure that the simulation process meets the quasi-static loading conditions.

[0035] The stress-correlation-based method for predicting the creep of cement paste across scales provided by this invention may also have the following feature: wherein, in S4, the simulation of the macroscopic creep process of cement paste is carried out under uniform stress conditions.

[0036] The stress-correlation-based method for predicting the creep of cement paste across scales provided by this invention may also have the following features: In S5, the method for establishing the quantitative relationship between creep characteristic time and stress level is as follows: Based on the verified nonlinear viscoelastic-plastic constitutive model, different stress level conditions are simulated, and the creep response of cement paste under each stress condition is numerically calculated to obtain the corresponding creep degree-time curve; the creep compliance function is used to fit and analyze the creep degree-time curve under each level condition, extract the creep characteristic time of cement paste under different stress levels, and establish the quantitative relationship between creep characteristic time and stress level.

[0037] The stress-correlation-based method for predicting the creep of cement paste across scales provided in this invention may also have the following feature: the creep compliance function is calculated as follows:

[0038]

[0039] In the formula, Let be the creep compliance function. For the duration of operation, Loading time; The elastic modulus of cement paste; Let be the elastic modulus of the k-th Kelvin element; Let be the delay time of the k-th Kelvin unit, and , These are the viscosity parameters for independent sticking pot units.

[0040] This invention also provides a stress-correlation-based multi-scale prediction system for cement paste creep, characterized by: a material parameter and test condition determination module, which determines the micro-indentation test parameters, macro-mechanical parameters, and loading stress levels of hydrated calcium silicate and cement paste; a nonlinear viscoelastic-plastic constitutive model construction module, which constructs a nonlinear viscoelastic-plastic constitutive model based on the parameters determined in the material parameter and test condition determination module, wherein the viscosity parameter of the nonlinear viscoelastic-plastic constitutive model is a function of the equivalent stress level; and a nano-micro indentation numerical simulation and parameter inversion module, which establishes a nano-micro indentation finite element model based on the nonlinear viscoelastic-plastic constitutive model, combined with genetic... The algorithm performs inversion identification of constitutive parameters for hydrated calcium silicate and cement paste. The macro-creep finite element model establishment and verification module applies the constitutive parameters obtained from the inversion identification to the macro-creep finite element model to simulate the macro-creep process of cement paste. By comparing with the macro-creep test results, the macro-micro consistency of the nonlinear viscoelastic-plastic constitutive model is verified. The cross-scale prediction module, based on the verified nonlinear viscoelastic-plastic constitutive model, simulates the creep response of cement paste under different stress levels, extracts creep characteristic time and establishes a quantitative relationship between creep characteristic time and stress level, realizing cross-scale prediction of macro-creep behavior based on micro-indentation test results.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] This invention constructs a nonlinear viscoelastic-plastic constitutive model that considers the variation of viscosity parameters with stress level. It integrates indentation test data under microscopic high stress and short timescales with macroscopic low stress and long timescale creep behavior into a unified theoretical framework. This allows for effective prediction of the macroscopic creep performance of cement paste using only short-term nano-micro indentation test data, without the need for long-term macroscopic creep tests, significantly shortening the experimental cycle for evaluating material creep performance. Furthermore, verification results show that the method of this invention can reasonably reflect the influence of stress level on creep characteristic time, overcome the mismatch between microscopic and macroscopic creep timescales, and possesses good computational stability and engineering applicability. Attached Figure Description

[0043] Figure 1 is a flowchart of the method and system for predicting the creep of cement paste across scales based on stress correlation in an embodiment of the present invention.

[0044] Figure 2 is a schematic diagram of the nonlinear viscoelastic-plastic constitutive model in an embodiment of the present invention.

[0045] Figure 3 is a schematic diagram of the nano-micro indentation finite element model in an embodiment of the present invention.

[0046] Figure 4 is a diagram showing the results of inversion identification in an embodiment of the present invention. In Figure 4, (a) is a diagram of the genetic algorithm optimization process; and (b) is a comparison diagram of the indentation depth-time curves of numerical simulation and indentation test results.

[0047] Figure 5 is a schematic diagram of the macroscopic creep finite element model in an embodiment of the present invention.

[0048] Figure 6 is a comparison of the creep degree function obtained from macroscopic creep test and finite element simulation in an embodiment of the present invention.

[0049] Figure 7 shows the quantitative relationship between creep characteristic time and stress level in an embodiment of the present invention. Detailed Implementation

[0050] To make the technical means, creative features, objectives and effects of this invention easy to understand, the following embodiments, in conjunction with the accompanying drawings, specifically illustrate the stress-related cross-scale prediction method and system for cement paste creep based on the present invention.

[0051] This embodiment provides a method for predicting the creep of cement paste across scales based on stress correlation, including the following steps:

[0052] Figure 1 is a flowchart of the method and system for predicting the creep of cement paste across scales based on stress correlation in an embodiment of the present invention.

[0053] As shown in Figure 1, step S1 is the material parameter and test condition determination step, which determines the micro-indentation test parameters, macro-mechanical parameters, and loading stress level of hydrated calcium silicate and cement paste. Specifically:

[0054] Cement paste specimens with a water-cement ratio of 0.38 were selected as the research object. First, their macroscopic mechanical parameters were determined, including an elastic modulus of 30,000 MPa, a Poisson's ratio of 0.2, and a compressive strength of 86 MPa. The elastic modulus and Poisson's ratio were obtained by inverse calculation using indentation loading-unloading curves, while the compressive strength was determined using macroscopic compressive strength test values.

[0055] Simultaneously, the conditions for the micro-indentation test (i.e., nano-micro indentation test) were determined, including the Berkovich indenter type, maximum loading force of 20 N, loading and unloading time of 15 s, and holding time of 300 s. The micro-indentation test was conducted on the surface of cement paste specimens. By selecting representative indentation points (mainly corresponding to the hydrated calcium silicate gel region), the displacement-time curves obtained during the indentation holding stage were recorded, and the contact creep function was calculated as characterization data of the micro-creep behavior of hydrated calcium silicate.

[0056] Step S2 is the construction step of the nonlinear viscoelastic-plastic constitutive model. Based on the parameters determined in S1, a nonlinear viscoelastic-plastic constitutive model is constructed. The viscosity parameters of the nonlinear viscoelastic-plastic constitutive model are functions of the equivalent stress level, specifically:

[0057] Figure 2 is a schematic diagram of the nonlinear viscoelastic-plastic constitutive model in an embodiment of the present invention.

[0058] As shown in Figure 2, a nonlinear viscoelastic-plastic constitutive model composed of multiple Kelvin and plastic elements is established based on the viscoelastic-plastic theory. The viscosity parameter in the nonlinear viscoelastic-plastic constitutive model is a function of the equivalent stress level to reflect the accelerated creep characteristics of materials under high stress conditions.

[0059] The nonlinear viscoelastic-plastic constitutive model is embedded into the finite element analysis platform as a user subroutine.

[0060] The constitutive equations of the nonlinear viscoelastic-plastic constitutive model include the following sub-steps:

[0061] S2-1: Calculate the viscoelastic stress in the test, expressed as:

[0062]

[0063] In the formula, This represents the stress at the start of the incremental step. This represents the deviatoric stress increment calculated assuming viscoelastic strain. This represents the volumetric stress increment calculated assuming viscoelastic strain. This represents the stress at the end of the incremental step calculated assuming viscoelastic strain.

[0064] S2-2: Calculation of the yield function under the test stress state , is represented as:

[0065]

[0066] In the formula, Let represent the Mises equivalent stress under viscoelastic stress, and r represent the isotropic hardening function. This represents the yield stress.

[0067] S2-3: Determine whether the material yields, expressed as:

[0068]

[0069] S2-4: The equivalent plastic strain increment is calculated using the central difference method and expressed as:

[0070]

[0071]

[0072] In the formula, p is the equivalent plastic strain, h is the hardening constant, and G is the shear modulus. For the viscosity parameters of the independent sticking pot unit, For the equivalent plastic strain increment, This is the increment for the current time step.

[0073] S2-5: Calculate plastic strain, viscoelastic strain, and stress increment, expressed as:

[0074]

[0075]

[0076]

[0077] In the formula, For viscoplastic strain, viscoelastic strain, This represents the total strain increment.

[0078] S2-6: Update the state variable, represented as:

[0079]

[0080]

[0081] In the formula, This represents the total stress at the end of the previous time step. This represents the stress increment caused by the strain increment at the current time step. This represents the equivalent plastic strain at the end of the current time step. The equivalent plastic strain at the start of the current time step. This represents the equivalent plastic strain increment at the current time step.

[0082] Step S3 is the numerical simulation and parameter inversion step for nano-micro indentation. Based on the nonlinear viscoelastic-plastic constitutive model, a nano-micro indentation finite element model is established. A genetic algorithm is then used to invert and identify the constitutive parameters of hydrated calcium silicate and cement paste. Specifically:

[0083] Figure 3 is a schematic diagram of the nano-micro indentation finite element model in an embodiment of the present invention.

[0084] As shown in Figure 3, a two-dimensional axisymmetric nano-micro indentation finite element model of cement paste is established. The indenter is set as a rigid body, and the cement paste is described by a nonlinear viscoelastic-plastic constitutive model. In this model, hydrated calcium silicate is the main microscopic component of cement paste, and its mechanical behavior is characterized by the corresponding parameters in the nonlinear viscoelastic-plastic constitutive model.

[0085] Figure 4 is a diagram showing the results of inversion identification in an embodiment of the present invention. In Figure 4, (a) is a diagram of the genetic algorithm optimization process; and (b) is a comparison diagram of the indentation depth-time curves of numerical simulation and indentation test results.

[0086] A parameter inversion process is constructed using a genetic algorithm. The contact creep curve obtained from micro-indentation experiments is used as the objective function to invert and identify the viscoelastic-plastic constitutive parameters in the nano-micro indentation finite element model until the numerical simulation curve and the contact creep curve reach consistency within a predetermined error range. The loss function is as follows:

[0087]

[0088] In the formula, N is the number of data points for the objective function, which is determined by the indentation holding time. One data point is taken every 1 second to calculate the objective function. and The values ​​represent the contact creep function values ​​in the numerical simulation and the indentation test, respectively. The inversion results are shown in Figure 4.

[0089] Step S4 is the establishment and verification step of the macroscopic creep finite element model. The constitutive parameters obtained from the inversion identification are applied to the macroscopic creep finite element model to simulate the macroscopic creep process of cement paste. By comparing with the results of macroscopic creep experiments, the macroscopic-microscopic consistency of the nonlinear viscoelastic-plastic constitutive model is verified, specifically as follows:

[0090] Figure 5 is a schematic diagram of the macroscopic creep finite element model in an embodiment of the present invention.

[0091] As shown in Figure 5, based on the constitutive parameters obtained after inversion identification, a macroscopic creep finite element model of cement paste was established, with its geometric dimensions and loading regime consistent with the corresponding macroscopic creep test. The macroscopic creep finite element model is a cylinder with a diameter of 20 mm and a height of 160 mm, under which a vertical stress of 15.6 MPa is applied. For boundary conditions and solution settings, fully consolidated constraints are applied to the bottom surface of the model. C3D8R (eight-node hexahedral reduced integral) elements are used for mesh generation, and a dynamic explicit analysis step is employed for solving. To improve computational efficiency, mass scaling techniques are introduced, and the ratio of kinetic energy to internal energy throughout the simulation process is monitored to ensure that the quasi-static loading conditions are met.

[0092] Figure 6 is a comparison of the creep degree function obtained from macroscopic creep test and finite element simulation in an embodiment of the present invention.

[0093] The macroscopic creep process of cement paste was numerically simulated under uniform stress conditions, and the calculated creep degree function was compared with the macroscopic experimental results to verify the applicability of the nonlinear viscoelastic-plastic constitutive model at the macroscopic scale. The verification results are shown in Figure 6.

[0094] Step S5 is the cross-scale prediction step. Based on the validated nonlinear viscoelastic-plastic constitutive model, it simulates the creep response of cement paste under different stress levels, extracts the creep characteristic time, and establishes a quantitative relationship between the creep characteristic time and the stress level. This enables cross-scale prediction of macroscopic creep behavior based on micro-indentation test results. Specifically:

[0095] Based on the validated nonlinear viscoelastic-plastic constitutive model, we simulated different stress levels and numerically calculated the creep response of cement paste under various stress conditions to obtain the corresponding creep degree-time curves.

[0096] Figure 7 shows the quantitative relationship between creep characteristic time and stress level in an embodiment of the present invention.

[0097] The creep compliance function was used to fit and analyze the creep degree-time curves under various working conditions. The creep characteristic time of cement paste under different stress levels was extracted and a quantitative relationship function between the creep characteristic time and the stress level was established, as shown in Figure 7. This allows the creep characteristic time obtained under high stress and short time scale in micro indentation test to be mapped to macro low stress and long time scale conditions, thus enabling the prediction of the long-term macro creep performance of cement paste.

[0098] Specifically, the creep compliance function is calculated as follows:

[0099]

[0100] In the formula, Let be the creep compliance function. For the duration of operation, Loading time; The elastic modulus of cement paste; Let be the elastic modulus of the k-th Kelvin element; Let be the delay time of the k-th Kelvin unit, and , These are the viscosity parameters for independent sticking pot units.

[0101] This embodiment also provides a stress-correlation-based multi-scale prediction system for cement paste creep, including:

[0102] The material parameters and test conditions determination module is used to implement step S1, namely: determining the micro-indentation test parameters, macro-mechanical parameters and loading stress level of hydrated calcium silicate and cement paste;

[0103] The nonlinear viscoelastic-plastic constitutive model construction module is used to implement step S2, namely: based on the parameters determined in the material parameters and experimental conditions determination module, a nonlinear viscoelastic-plastic constitutive model is constructed. The viscosity parameters of the nonlinear viscoelastic-plastic constitutive model are functions of the equivalent stress level.

[0104] The nano-micro indentation numerical simulation and parameter inversion module is used to implement step S3, namely: establishing a nano-micro indentation finite element model based on a nonlinear viscoelastic-plastic constitutive model, and using a genetic algorithm to invert and identify the constitutive parameters of hydrated calcium silicate and cement paste.

[0105] The macro-creep finite element model establishment and verification module is used to implement step S4, namely: applying the constitutive parameters obtained by inversion identification to the macro-creep finite element model to simulate the macro-creep process of cement paste, and verifying the macro-micro consistency of the nonlinear viscoelastic-plastic constitutive model by comparing it with the macro-creep test results.

[0106] The cross-scale prediction module is used to implement step S5, namely: based on the validated nonlinear viscoelastic-plastic constitutive model, simulate the creep response of cement paste under different stress levels, extract the creep characteristic time and establish a quantitative relationship between the creep characteristic time and the stress level, so as to realize cross-scale prediction of macroscopic creep behavior based on the micro-indentation test results.

[0107] The role and effect of the embodiments

[0108] The method and system for predicting the cross-scale creep of cement paste based on stress correlation according to the present invention have the following beneficial effects:

[0109] This invention constructs a nonlinear viscoelastic-plastic constitutive model that considers the variation of viscosity parameters with stress level. It integrates indentation test data under microscopic high stress and short timescales with macroscopic low stress and long timescale creep behavior into a unified theoretical framework. This allows for effective prediction of the macroscopic creep performance of cement paste using only short-term nano-micro indentation test data, without the need for long-term macroscopic creep tests, significantly shortening the experimental cycle for evaluating material creep performance. Furthermore, verification results show that the method of this invention can reasonably reflect the influence of stress level on creep characteristic time, overcome the mismatch between microscopic and macroscopic creep timescales, and possesses good computational stability and engineering applicability.

[0110] In step S2 of this invention, based on the theory of viscoelastic-plastic mechanics, a nonlinear viscoelastic-plastic constitutive model composed of multiple Kelvin and plastic elements is adopted. The viscosity parameter is defined as a function of the equivalent stress level, which can accurately describe the characteristics of accelerated creep of materials under high stress conditions and provide a unified constitutive basis for subsequent cross-scale prediction.

[0111] In step S3 of this invention, a nonlinear viscoelastic-plastic constitutive model is used to simultaneously describe the creep behavior of cement paste and its main hydration product, calcium silicate hydrate, at different scales and stress levels within a unified constitutive framework. By combining a nano-micro indentation finite element model with a genetic algorithm, the microscopic constitutive parameters of calcium silicate hydrate and the overall macroscopic parameters of cement paste can be identified simultaneously. This effectively overcomes the problem of mismatch between macroscopic and microscopic creep timescales in existing technologies, reveals the accelerating effect of stress level on creep characteristic time, and achieves continuous cross-scale mapping of creep characteristic time.

[0112] In step S4 of this invention, the constitutive parameters obtained based on inversion identification are applied to the macroscopic creep finite element model of cement paste. By comparing and verifying with the macroscopic creep test results, the applicability of the method of this invention at the macroscopic scale and the consistency of macroscopic and microscopic descriptions are proved, and the prediction results are reliable and highly accurate.

[0113] In step S5 of this invention, by establishing a quantitative relationship between creep characteristic time and stress level, the creep characteristic time obtained under high stress and short time scale in micro-indentation test is mapped to macro-low stress and long time scale conditions, thereby enabling the prediction of long-term macro-creep performance of cement paste and providing a reliable theoretical basis for a deeper understanding of the nonlinear creep mechanism of cement-based materials.

[0114] This invention is not only applicable to cement paste, but can also be extended to predicting the creep properties of other cement-based materials. The method of this invention can directly utilize short-time nano-micro indentation test data, eliminating the need for long-term macroscopic creep tests. It provides an efficient and reliable technical means for rapid performance evaluation, formulation optimization, and long-term service performance prediction of cement-based materials, and has broad application prospects.

[0115] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to this invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for predicting the creep of cement paste across scales based on stress correlation, characterized in that, The process includes the following steps: S1: Determining material parameters and test conditions, including the microscopic indentation test parameters, macroscopic mechanical parameters, and loading stress levels of hydrated calcium silicate and cement paste; S2: Constructing a nonlinear viscoelastic-plastic constitutive model, based on the parameters determined in S1, to construct a nonlinear viscoelastic-plastic constitutive model, where the viscosity parameters of the nonlinear viscoelastic-plastic constitutive model are functions of the equivalent stress level; S3: Numerical simulation and parameter inversion of nano- and micro-indentation, based on the nonlinear viscoelastic-plastic constitutive model, establishing a nano- and micro-indentation finite element model, and using a genetic algorithm to perform numerical simulation and parameter inversion of the constitutive parameters of the hydrated calcium silicate and the cement paste. S4: Establishment and verification of the macroscopic creep finite element model. The constitutive parameters obtained by the inversion identification are applied to the macroscopic creep finite element model to simulate the macroscopic creep process of cement paste. By comparing with the macroscopic creep test results, the macroscopic-microscopic consistency of the nonlinear viscoelastic-plastic constitutive model is verified. S5: Cross-scale prediction step. Based on the verified nonlinear viscoelastic-plastic constitutive model, the creep response of the cement paste under different stress levels is simulated. The creep characteristic time is extracted and a quantitative relationship between the creep characteristic time and the stress level is established to realize cross-scale prediction of macroscopic creep behavior based on the microscopic indentation test results.

2. The method for predicting the cross-scale creep of cement paste based on stress correlation according to claim 1, characterized in that: in, In S1, the micro-indentation test parameters include: indenter type, maximum loading force, loading and unloading time and duration; the macro-mechanical parameters include: elastic modulus, Poisson's ratio and compressive strength.

3. The method for predicting the cross-scale creep of cement paste based on stress correlation according to claim 1, characterized in that: in, In S2, the method for constructing the nonlinear viscoelastic-plastic constitutive model is as follows: a nonlinear viscoelastic-plastic constitutive model composed of multiple Kelvin elements and plastic elements is established, wherein the viscosity parameter in the nonlinear viscoelastic-plastic constitutive model is a function of the equivalent stress level; the nonlinear viscoelastic-plastic constitutive model is embedded into the finite element analysis platform in the form of a user subroutine.

4. The method for predicting the cross-scale creep of cement paste based on stress correlation according to claim 3, characterized in that: in, In step S2, the constitutive equation of the nonlinear viscoelastic-plastic constitutive model includes the following sub-steps: S2-1: Calculate the test viscoelastic stress, expressed as: In the formula, This represents the stress at the start of the incremental step. This represents the deviatoric stress increment calculated assuming viscoelastic strain. This represents the volumetric stress increment calculated assuming viscoelastic strain. S2-2: The stress at the end of the incremental step calculated under the assumed viscoelastic strain, representing the stress at which the stress is calculated. , is represented as: In the formula, Let represent the Mises equivalent stress under viscoelastic stress, and r represent the isotropic hardening function. S2-3: Determines whether a material yields, expressed as: (This refers to the yield stress.) S2-4: The equivalent plastic strain increment is calculated using the central difference method and expressed as: ， In the formula, p is the equivalent plastic strain, h is the hardening constant, and G is the shear modulus. For the viscosity parameters of the independent sticking pot unit, For the equivalent plastic strain increment, S2-5: Calculates the increments of plastic strain, viscoelastic strain, and stress, representing the current time step increment as follows: ， ， In the formula, For viscoplastic strain, viscoelastic strain, For the total strain increment, S2-6: update the state variables, expressed as: ， In the formula, This represents the total stress at the end of the previous time step. This represents the stress increment caused by the strain increment at the current time step. This represents the equivalent plastic strain at the end of the current time step. The equivalent plastic strain at the start of the current time step. This represents the equivalent plastic strain increment at the current time step.

5. The method for predicting the cross-scale creep of cement paste based on stress correlation according to claim 1, characterized in that: in, In S3, the inversion identification method is as follows: a two-dimensional axisymmetric nano-micro indentation finite element model is established, the indenter is set as a rigid body, and hydrated calcium silicate and cement paste are described by a nonlinear viscoelastic-plastic constitutive model; a parameter inversion process is constructed through a genetic algorithm, using the contact creep curve obtained from the micro-indentation test as the objective function, to invert and identify the viscoelastic-plastic constitutive parameters in the nano-micro indentation finite element model until the numerical simulation curve and the contact creep curve reach the same range within a predetermined error. The loss function is as follows: In the formula, N is the number of data points for the objective function, which is determined by the indentation holding time. One data point is taken every 1 second to calculate the objective function. and These represent the contact creep function values ​​in numerical simulation and indentation test, respectively.

6. The method for predicting the creep of cement paste across scales based on stress correlation according to claim 1, characterized in that: in, In S4, the geometric dimensions and loading regime of the macroscopic creep finite element model are consistent with those of the corresponding macroscopic creep test. The solution is obtained by dynamic explicit analysis step, and mass scaling technology is introduced to ensure that the simulation process meets the quasi-static loading conditions.

7. The method for predicting the cross-scale creep of cement paste based on stress correlation according to claim 1, characterized in that: in, In S4, the simulation of the macroscopic creep process of cement paste is carried out under uniform stress conditions.

8. The method for predicting the creep of cement paste across scales based on stress correlation according to claim 1, characterized in that: in, In S5, the method for establishing the quantitative relationship between creep characteristic time and stress level is as follows: Based on the verified nonlinear viscoelastic-plastic constitutive model, different stress level conditions are simulated, and the creep response of cement paste under various stress conditions is numerically calculated to obtain the corresponding creep degree-time curve; the creep compliance function is used to fit and analyze the creep degree-time curve under each level condition, extract the creep characteristic time of cement paste under different stress levels, and establish the quantitative relationship between creep characteristic time and stress level.

9. The method for predicting the cross-scale creep of cement paste based on stress correlation according to claim 8, characterized in that: wherein, The creep compliance function is calculated as follows: In the formula, Let be the creep compliance function. For the duration of operation, Loading time; The elastic modulus of cement paste; Let be the elastic modulus of the k-th Kelvin element; Let be the delay time of the k-th Kelvin unit, and ， These are the viscosity parameters for independent sticking pot units.

10. A cross-scale prediction system for cement paste creep based on stress correlation, characterized in that, include: The module for determining material parameters and test conditions determines the micro-indentation test parameters, macro-mechanical parameters, and loading stress levels of hydrated calcium silicate and cement paste. The nonlinear viscoelastic-plastic constitutive model construction module constructs a nonlinear viscoelastic-plastic constitutive model based on the parameters determined in the material parameters and experimental conditions determination module. The viscosity parameters of the nonlinear viscoelastic-plastic constitutive model are functions of the equivalent stress level. The nano-micro indentation numerical simulation and parameter inversion module establishes a nano-micro indentation finite element model based on the nonlinear viscoelastic-plastic constitutive model and uses a genetic algorithm to invert and identify the constitutive parameters of the hydrated calcium silicate and the cement paste. The macroscopic creep finite element model establishment and verification module will... The constitutive parameters obtained by the inversion identification are applied to the macroscopic creep finite element model to simulate the macroscopic creep process of cement paste. By comparing with the macroscopic creep test results, the macroscopic-microscopic consistency of the nonlinear viscoelastic-plastic constitutive model is verified. The cross-scale prediction module, based on the verified nonlinear viscoelastic-plastic constitutive model, simulates the creep response of cement paste under different stress levels, extracts the creep characteristic time and establishes a quantitative relationship between the creep characteristic time and the stress level, so as to realize the cross-scale prediction of macroscopic creep behavior based on the microscopic indentation test results.

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