Construction method of 3D printing alkali-activated concrete orthotropic constitutive model

Abstract

The invention discloses a method for constructing an orthotropic constitutive model of 3D printing alkali-activated concrete, comprising the following steps: determining isotropic elastic parameters and Poisson's ratio of a matrix based on modulus, alkali equivalent and water-binder ratio of an alkali-activated system; based on the printing equipment and the printing process parameters, identifying interface distribution parameters; judging whether macroscopic pores are generated or not according to the interface distribution parameters; if macroscopic pores are generated, macroscopic pore parameters and macroscopic damage variables of the 3D printing alkali-activated concrete are determined; if the macroscopic pores are not generated, determining a microscopic damage variable; obtaining a total damage tensor according to the macroscopic damage variable and the microscopic damage variable; and the damage tensor is introduced into a matrix stiffness matrix, and the 3D printing alkali-activated concrete orthotropic constitutive model is constructed. According to the method, accurate prediction of the mechanical response of the 3D printing concrete in different printing paths and loading directions can be realized.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of constitutive model construction methods, and particularly relates to a method for constructing a 3D-printed alkali-activated concrete orthotropic constitutive model. BACKGROUND

[0002] 3D-printed concrete is formed by layer-by-layer stacking, and its mechanical properties are significantly affected by the comprehensive influence of material rheological behavior, printing parameters and interlayer interface density. In order to reduce the cement dosage and realize green and low-carbon construction, alkali-activated materials are gradually applied to 3D-printed concrete. However, the alkali-activated system has fast setting, obvious thixotropic recovery and structural building effect at the early age, which is essentially different from the traditional cement-based system. The existing parameter design methods and mechanical models of 3D-printed concrete are mostly based on Portland cement systems, and generally use simplified rheological or solidification assumptions, which cannot accurately describe the time-varying thixotropic properties of alkali-activated systems and the influence of polycondensation reactions on the printing window and mechanical state. At the same time, the extrusion effect, water migration and deposition deformation in the printing process easily lead to weakly cemented interfaces and through pores, but the existing models usually assume that the interface properties are consistent with the matrix, and cannot effectively depict the multi-scale pore structure and its directionality. In addition, the current constitutive relationship for describing the mechanical behavior of printed components mostly relies on the isotropic assumption or empirical model, and cannot reflect the influence of printing-induced geometric directionality, interface defects and pore structure on the stress field, elastic modulus and damage evolution.

[0003] Therefore, the existing technology still lacks a constitutive model that can systematically characterize the multi-scale structural characteristics of alkali-activated concrete and the printing-induced anisotropy, and cannot meet the actual needs of performance prediction and design of 3D-printed low-carbon components. SUMMARY

[0004] The purpose of the present application is to overcome the deficiencies in the prior art, and to provide a method for constructing a 3D-printed alkali-activated concrete orthotropic constitutive model that can accurately predict.

[0005] Technical scheme: The method for constructing a 3D-printed alkali-activated concrete orthotropic constitutive model comprises the following steps: Step 1: based on the modulus of the alkali-activated system, the alkali equivalent and the water-binder ratio, the isotropic elastic parameters and the Poisson's ratio of the matrix are determined; based on the printing equipment and printing process parameters, the interface distribution parameters are identified; Step 2: according to the isotropic elastic parameters, the Poisson's ratio and the interface distribution parameters of the matrix, it is determined whether macroscopic pores will be generated; Step 3: if macroscopic pores are generated, the macroscopic pore parameters and the macroscopic damage variable of the 3D-printed alkali-activated concrete are determined; if no macroscopic pores are generated, the fine microscopic damage variable of the 3D-printed alkali-activated concrete is determined; Step four, get the total damage tensor according to the macro damage variable and the micro damage variable; Step five, introduce the damage tensor into the matrix stiffness matrix to build the 3D printing alkali-activated concrete orthotropic anisotropic constitutive model.

[0006] Further, in step one, the matrix isotropic elastic parameters and Poisson's ratio are measured by uniaxial compression test.

[0007] Further, in step one, the printing process parameters include extrusion nozzle diameter, strip width, strip height, printing speed, extrusion speed, vertical offset and horizontal offset, and the interface distribution parameters include the number of interlayer interfaces and the number of interstrip interfaces.

[0008] Further, in step two, when the horizontal offset < strip width ∩ vertical offset ≤ strip height, no macroscopic pore is generated, and when the horizontal offset ≥ strip width ∪ vertical offset > strip height, macroscopic pore is generated.

[0009] Further, in step three, the macroscopic pore characteristic length is greater than 1 cm, and the macroscopic pore parameters include the total pore volume fraction, the shape parameter and the concave parameter.

[0010] Further, in step three, the calculation formula of the micro damage variable is: Wherein, D is the total damage tensor, I is the unit tensor, is the mesoscopic damage variable, is the micro damage variable.

[0011] Further, the mesoscopic damage variable is obtained by the porosity and half-axis length statistics extracted by X-ray CT.

[0012] Further, the micro damage variable is based on uniaxial mechanical test, which describes the micro damage by Weibull distribution, and the micro damage variable is determined by fitting the uniaxial peak strain and peak stress.

[0013] Further, in step four, the calculation formula of the total damage tensor is: Wherein, D is the total damage tensor, I is the unit tensor, is the macro damage variable, is the mesoscopic damage variable, is the micro damage variable.

[0014] Further, in step five, the 3D printing alkali-activated concrete orthotropic anisotropic constitutive model is: wherein, is the stress, C0 is the matrix isotropic elastic stiffness matrix, is the total damage tensor, is the unit tensor, is the strain.

[0015] Beneficial effects: compared with the prior art, the present application has the following remarkable features: 1. The mechanical response of 3D printing alkali-activated concrete under different printing paths and loading directions can be accurately predicted. 2. A multi-scale orthotropic damage constitutive model capable of simultaneously representing the matrix, interface and pore effect is proposed to address the problems of weak interface and pore structure in 3D printing low-carbon alkali-activated concrete. The model is constrained by the strip structure and through pores formed during printing, and the influence of micro-pore on elastic degradation and strength evolution is introduced into the constitutive analysis and calculation by assuming that the micro-pore can be equivalent to an ellipsoid or a hyper-ellipsoid inclusion, thereby accurately describing the printing-induced anisotropy and significantly improving the accuracy and applicability of the mechanical property prediction of 3D printing low-carbon alkali-activated concrete. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is a flowchart of the present application; Figure 2 is a pore structure classification diagram of 3D printing alkali-activated concrete in the present application; Figure 3 is a schematic diagram of strain equivalence principle; Figure 4 is a schematic diagram of printing parameter definition in the present application; Figure 5 is a schematic diagram of macro-pore parameters in the present application; Figure 6 is a schematic diagram of micro-pore parameters in the present application; Figure 7 is a schematic diagram of the structure of 3D printing concrete specimen in the present application; Figure 8 is a comparison diagram of constitutive model calculation results and test results, wherein a is the stress-strain curve of 3D printing alkali-activated concrete in three directions measured by test, b is the comparison of predicted curve and test curve in X direction, c is the comparison of predicted curve and test curve in Y direction, and d is the comparison of predicted curve and test curve in Z direction. DETAILED DESCRIPTION

[0017] As Figure 1 A method for constructing an orthotropic anisotropic constitutive model of 3D printing alkali-activated concrete, comprising the following steps: Step S1, determine the isotropic elastic parameters of the matrix based on the modulus of alkali-activated system, alkali equivalent and water-binder ratio.

[0018] Step S1.1, according to the requirements of printability and structural performance, determine the mix proportion of alkali-activated system, including modulus of alkali-activated system Ms=SiO2 / Na2O=1.1, alkali equivalent Na2O%=7% (based on the mass fraction of cementitious materials), water-binder ratio w / b=0.3, type and dosage of admixture, and according to GB / T 50081-2019 "Standard for Testing Methods of Mechanical Properties of Ordinary Concrete", obtain the isotropic elastic modulus (32GPa) and Poisson's ratio (0.2) of the matrix as initial input through uniaxial compression test.

[0019] Step S1.2, according to the requirements of printing process and material performance, determine the process parameters such as extrusion nozzle diameter d, strip width W and height H, printing speed V, extrusion speed E, vertical offset VO and horizontal offset HO. On this basis, further identify the interface distribution parameters, wherein: represents the number of interlayer interfaces; represents the number of interstrip interfaces.

[0020] According to the strain equivalence principle, as shown in Figure 3 , the total stress acting on the damaged material causes strain , and the effective stress acting on the undamaged material causes strain , which are equivalent, then: where, is the strain of 3D printed alkali-activated concrete under external load considering macroscopic, mesoscopic and microscopic pores, , and are the strains of 3D printed alkali-activated concrete after considering only macroscopic, mesoscopic and microscopic damage, is the strain of undamaged 3D printed alkali-activated concrete. Correspondingly, the damage variable caused by macroscopic pores is , the damage variable caused by mesoscopic pores is , and the damage variable caused by microscopic pores is , and the coupling damage variable is .

[0021] Under the premise of assuming that the material satisfies Hooke's law, the strain equivalence principle can be rewritten as: Similarly, based on the strain equivalence principle, we can get By combining the above formula, we have: According to the mix proportion of alkali-activated system, including the modulus of activator Ms=SiO2 / Na2O, alkali equivalent Na2O% (in the mass fraction of cementitious materials), water-binder ratio w / b, etc., and the initial isotropic elastic modulus and Poisson's ratio of the matrix are obtained as the initial input. The initial isotropic stiffness matrix C0 of the material can be obtained.

[0022] Step S2, according to the printing parameters and the deposition forming characteristics, that is, the interface distribution parameters, it is judged whether macroscopic pores will be generated. Based on the pore structure characteristics, the pore structure of 3D printing alkali-activated concrete is divided into macroscopic pores, mesoscopic pores and microscopic pores, and the scale separation is as shown in Figure 2 . Figure 2 In the middle, the pores with feature length greater than 1 cm caused by unreasonable printing parameter setting are defined as macroscopic pores, which mainly appear in the area combined by interlayer and interstrip interface. The pores with morphology significantly changed due to printing process and lack of vibration are defined as mesoscopic pores, which are mainly micron-sized pores. For smaller pores, it is considered the same as cast concrete, which are mainly sub-micron to nanometer-sized pores.

[0023] Step S3, if macroscopic pores are generated, steps S3.1-S3.3 are performed to determine the macroscopic pore parameters and macroscopic damage variables of 3D printing alkali-activated concrete. If no macroscopic pores are generated, =0, directly to step S3.4 to determine the meso-microscopic damage variables of 3D printing alkali-activated concrete.

[0024] Step S3.1, as shown in Figure 4 , according to the printing offset and the strip feature value together to determine, , there are macroscopic pores generated. As shown in Figure 5 , under parallel printing path, the strips are parallel to each other, the orientation of the macroscopic pores is consistent with the horizontal moving direction of the printing head. The hyper-elliptical cylinder is used to characterize the morphology of the macroscopic pores.

[0025]

[0026] wherein r1 is the length of the long axis of the hyper-elliptical pore, r2 is the length of the central axis of the hyper-elliptical pore, r3 is the length of the short axis of the hyper-elliptical pore, , and is the shape parameter.

[0027] As Figure 6 , for simplification, the is set to be 1 unit length, , , the above formula can be simplified as: .

[0028] Step S3.2, extract the pore parameters at the macroscopic level, including the total pore volume fraction , shape parameters and concave parameters , used to describe the forming defects in the printing process.

[0029] Step S3.3, macroscopic damage variable related to macroscopic pore shape parameters , XY plane concave factor , YZ plane concave factor and porosity , used to describe the overall stiffness degradation caused by macroscopic pores or forming defects.

[0030] According to the Mori-Tanaka homogenization method, the influence of macroscopic hyper-elliptical pores on the compliance matrix S macro is: wherein, is the compliance tensor of the matrix, is the compliance contribution tensor of the inclusion, is the compliance tensor of the inclusion, is the unit tensor.

[0031] The compliance contribution tensor of the hyper-elliptical pore is approximately solved by using the linearization method, and In the formula, is the influence of the concave parameter on the matrix, is the compliance contribution tensor of the inclusion, is the compliance tensor of the corresponding ellipsoid, which can be obtained by Eshelby tensor.

[0032]

[0033] Thus, the macroscopic damage variable of 3D printing concrete considering macroscopic hyper-elliptical pores is:

[0034] wherein, macro C is the stiffness tensor of the macroscopic hyper-elliptical pore, and C0 is the initial stiffness tensor of the 3D printing alkali-activated concrete.

[0035] Step S3.4, obtaining statistical parameters of meso-pore from X-ray CT scanning data. According to the statistical half-axis length The Eshelby tensor of the equivalent ellipsoidal pore can be obtained .

[0036] According to the porosity of the meso-ellipsoidal pore The influence of meso-pore on the stiffness matrix can be obtained: where, is the stiffness tensor of the pore, is the Hill tensor of the equivalent ellipsoidal pore, which can be obtained by the Eshelby tensor of the corresponding ellipsoidal pore and the stiffness tensor of the matrix.

[0037]

[0038] Thus, the meso-damage variable of 3D-printed alkali-activated concrete considering meso-ellipsoidal pores can be obtained is .

[0039] Step S3.5, for the micro-damage of 3D-printed alkali-activated concrete, it is considered that the strength of the micro-element obeys the Weibull probability density function: where, represents the micro-unit strength parameter, which can be represented by the strain under the strain strength theory framework, where, and are distribution parameters; and represents the percentage of damaged units in all micro-elements. It is assumed that represents the total number of all micro-units, represents the number of units that fail under a certain load, and then the micro-damage variable can be represented as:

[0040] When the strain level increases from , the number of micro-units that are damaged increases by . Therefore, when the strain increases from 0 to , the total number of micro-units that are damaged is: Substituting the formula into the formula can obtain

[0041] Micro-damage variable is determined by boundary conditions and geometric constraints of uniaxial test stress-strain curve: wherein, is the ultimate strain of the test piece and the peak stress is the ultimate stress of the test piece, and the micro-damage parameters can be obtained by simultaneously solving the above equations: .

[0042] Step S4: According to the macro and micro damage variables, the tensor coupling formula is used to integrate the multi-scale damage to obtain the total damage tensor D: wherein, D is the total damage tensor, I is the unit tensor, is the macro damage variable, is the micro damage variable, is the micro damage variable. The formula reflects the interaction of damage effects at different levels through nonlinear coupling.

[0043] Step S5: The damage tensor is introduced into the matrix of the base stiffness to construct the orthotropic anisotropic constitutive model of 3D printing alkali-activated concrete.

[0044]

[0045] The sampling method of the 3D printing alkali-activated concrete test piece and the definition of the three loading directions are shown in Figure 7 .

[0046] Figure 8 The comparison chart of the calculation results of the constitutive model and the test results is shown, wherein, Figure 8 a is the stress-strain curve of the 3D printing alkali-activated concrete in three directions measured by the test, which shows the mechanical anisotropy of the 3D printing alkali-activated concrete. Figure 8 b, Figure 8 c and Figure 8 d respectively show the comparison of the predicted curves and the test curves in X, Y and Z directions, the theoretical curves are highly consistent with the test results, which can accurately describe the nonlinear deformation law of the material in the whole loading process, and verify the orthotropic anisotropic damage constitutive model of 3D printing alkali-activated concrete based on the pore structure proposed in the embodiment.

Claims

1. A method for constructing an orthotropic constitutive model of alkali-activated concrete using 3D printing, characterized in that, Includes the following steps: Step 1: Based on the modulus, alkali equivalent, and water-cement ratio of the alkali-activated system, determine the isotropic elastic parameters and Poisson's ratio of the matrix; Based on printing equipment and printing process parameters, and identifying interface distribution parameters; Step 2: Determine whether macroscopic pores will be generated based on the interface distribution parameters; Step 3: If macroscopic pores are generated, determine the macroscopic pore parameters and macroscopic damage variables of the 3D-printed alkali-activated concrete; if no macroscopic pores are generated, determine the microscopic damage variables of the 3D-printed alkali-activated concrete. Step 4: Based on the macroscopic damage variables and the microscopic damage variables, obtain the total damage tensor; Step 5: Introduce the damage tensor into the matrix stiffness matrix to construct an orthotropic constitutive model of 3D-printed alkali-activated concrete.

2. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: In step one, the isotropic elastic parameters and Poisson's ratio of the matrix are measured by uniaxial compression test.

3. The method for constructing a 3D-printed orthotropic anisotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: In step one, the printing process parameters include the nozzle diameter, strip width, strip height, printing speed, extrusion speed, vertical offset, and horizontal offset, and the interface distribution parameters include the number of interlayer interfaces and the number of interstrip interfaces.

4. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 3, characterized in that: In step two, when the horizontal offset is less than the strip width and the vertical offset is less than or equal to the strip height, no macroscopic pores are generated; when the horizontal offset is greater than or equal to the strip width and the vertical offset is greater than or equal to the strip height, macroscopic pores are generated.

5. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: In step three, the macroscopic pore feature length is greater than 1 cm, and the macroscopic pore parameters include the total pore volume fraction, shape parameters, and concavity parameters.

6. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: In step three, the formula for calculating the subtle damage variable is as follows: Where D is the total damage tensor and I is the unit tensor. To examine the damage variables in detail, For microscopic damage variables.

7. A method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 6, characterized in that: The microscopic damage variables were obtained by statistical analysis of porosity and semi-axial length extracted from X-ray CT.

8. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: The micro-damage variables are based on uniaxial mechanical tests, and the micro-damage is described by the Weibull distribution. The micro-damage variables are determined by fitting the uniaxial peak strain and peak stress.

9. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: In step four, the formula for calculating the total damage tensor is: in, For the total damage tensor, For unit tensors, As a macroscopic damage variable, To examine the damage variables in detail, For microscopic damage variables.

10. The method for constructing a 3D-printed orthotropic constitutive model of alkali-activated concrete according to claim 1, characterized in that: In step five, the orthotropic constitutive model of 3D-printed alkali-activated concrete is as follows: Where s is the stress, and C0 is the isotropic elastic stiffness matrix of the matrix. For the total damage tensor, For unit tensors, In response to the situation.

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