Research On Data-Driven Nonlinear Thermo-Elastic Constitutive Modeling And Computational Methods

Thermo-elastic problems exist widely in engineering applications.The simulation of these problems is inseparable from accurate heat transfer and mechanical constitutive models.With the continuous development of materials science,new materials with high performance or special functions are emerging.However,the properties of various new materials vary widely,and the existing constitutive models may not reflect the actual thermo-mechanical behavior of materials.Therefore,it is urgent to construct thermo-mechanical constitutive models for various new materials to carry out corresponding thermo-mechanical numerical simulations and accelerate the application of new materials.However,thermo-mechanical constitutive modeling by traditional methods often requires a deep understanding of the intrinsic deformation and heat transfer mechanisms of materials and complex mathematical derivation,thus the long model development cycle.Especially for constitutive modeling of composite materials,microstructural features and interactions between components need to be considered.This undoubtedly further increases the difficulty of establishing thermo-mechanical constitutive models with explicit function expressions.In addition,numerical simulation of composite materials requires sufficiently fine meshes to identify their microstructural geometry,resulting in excessive computational complexity,making it challenging to perform thermal-mechanical coupling computations for complex engineering structures.The above difficulties limit the application and promotion of new materials.In recent years,data-driven computational mechanics has thrived,providing new ideas for constitutive modeling and computation.This dissertation aims at the difficulties in constitutive modeling and computation for isotropic and orthotropic nonlinear elasticity.Corresponding data-driven thermo-elastic constitutive modeling and calculation approaches are proposed.A thermo-mechanical constitutive model identification approach based on displacement field and temperature field data is proposed.The main research contents and achievements of this thesis are as follows:(1)A data-driven thermo-mechanical constitutive modeling approach based on artificial neural network(ANN)is proposed for isotropic hyperelastic materials.Two independent ANNs are designed to describe a stress-strain law and a heat-conduction law with temperature dependence.The proposed approach is used for multi-scale thermal-mechanically coupled analysis under finite deformation by combining it with computational homogenization.In the offline stage,the data are generated by finite element(FE)computation of thermal/mechanical response of meso-scale representative volume element(RVE).Then,the ANNs are trained with this RVE data.In the online stage,the trained ANNs model is embedded in the FE software through the UMAT and UMATHT user subroutines,to serve as a reliable replacement of the meso-scale thermal-mechanical FE computation,thereby significantly improving the online computation efficiency.The proposed approach systematically bypasses the complex modeling process and avoids errors introduced in selecting and correcting constitutive models.Thermo-mechanical response computations for homogeneous and composite structures are discussed separately by numerical examples.The efficiency and accuracy of the proposed approach are demonstrated by comparing the computation results with these by the direct numerical simulation method.(2)A data-driven constitutive modeling approach for orthotropic nonlinear elastic materials(DDONE)is proposed.The proposed approach can use a small amount of low-cost data for constitutive modeling,which effectively deals with the large demand and high acquisition cost of data.Three uniaxial tensile experiments are designed to obtain stress-strain data,and the data-driven constitutive model is constructed using the approximate superposition principle.The DDONE approach is then embedded into FE analysis framework to solve boundary-value problems.Illustrative examples(e.g.,structures with an orthotropic nonlinear elastic material)are presented,demonstrating the effectiveness of the approach.The error distribution and causes of the DDONE approach are also analyzed.The DDONE approach is further strengthened by a mapping function,which is verified by additional numerical examples that demonstrate the effectiveness of the modified approach.Moreover,ANN are employed to further improve the computational efficiency and stability of the proposed DDONE approach.The DDONE approach has also been extended to temperature-dependent constitutive modeling for orthotropic materials.(3)The data(biaxial and triaxial stress,heat flux,etc.)required by existing data-driven methods are often difficult and costly to obtain.Therefore,a data-driven approach for identifying heat transfer and thermo-elastic constitutive models is developed based on the relatively easy-to-obtain displacement field and temperature field data.The interpolation function is used to convert the displacement and temperature data of the full-field measurement into strain and temperature gradient data,which as the input data of ANNs.The heat flux and stress output by the untrained ANNs do not satisfy the heat conduction and equilibrium equations.Therefore,the objective function is constructed by combining the control equations and a part of boundary conditions(stress and heat flux).The particle swarm optimization algorithm is used to minimize the objective function to achieve the unsupervised learning of ANNs.The constitutive identification methodology and numerical implementation in steady-state heat conduction,transient heat conduction and thermo-elasticity are discussed,respectively.The effectiveness of the proposed approach is demonstrated by comparing the FE computation using the reference material constitutive model with the results predicted by ANNs.