A Research On Data-Driven Elastic And Elastoplastic Constitutive Modeling Method Based On Prior Knowledge Of Mechanics

The design of modern advanced industrial equipment is inseparable from the simulation of solid mechanics,and the simulation of solid mechanics is inseparable from the constitutive models of materials.With the development of materials science,a large number of new materials with excellent properties have appeared.However,without constitutive models to describe these new materials,it is difficult to fully use these materials in the advanced industrial equipment.Rich experiences and rigorous mathematical derivations,which are complicated and time-consuming,are often required in the progress of building the traditional constitutive models.Sometimes even if the existing constitutive models can be used for some new materials,it is not easy to select an appropriate constitutive model from the many existing models to describe the mechanical behavior of the new material.All these difficulties restrict the application and development of new materials.In recent years,many scholars tried to overcome the difficulties by using machine learning technology.Many new constitutive modeling methods have been developed,which can automatically establish the constitutive model based on experimental data.However,most of the existing methods do not make full use of mechanism of mechanics as the prior knowledge.As a result,these methods require a large amount of data,which restricts the application and development of these methods.In order to solve these difficulties,this thesis proposes four novel data-driven constitutive modeling methods,in which the prior knowledge of mechanics and machine learning technology(i.e.ANN)is fully utilized.The priorly known and universal inner mechanisms are directly incorporated into the data-driven model,so that the machine learning model can learn the“knowledge”which is unknown instead of what priorly known from the precious data.The research in this thesis is carried out in two general directions: one is to describe more complex mechanical behavior of materials,and the other is to establish constitutive models with fewer and more accessible data.The main research contents and achievements of this thesis are as follows:(1)An ANN based data-driven constitutive modeling method is proposed for isotropic nonlinear elastic materials.The basic idea of this method is to establish the mapping of principal strain to principal stress by ANN.In order to ensure the strict isotropy of the constitutive model,a special ANN structure is proposed to make sure that the ANN’s output is independent of its input sequence.In order to ensure the strict symmetry of the tangent modulus matrix,a new ANN with strict symmetrical Jacobian matrix is proposed.The tangent modulus expressed by analytical form based on ANN is derived.Numerical examples show that the method has good stability and convergence when used in finite element simulation,and a numerical example is given to demonstrate the effectiveness of this method in predicting the overall properties of elastic composites.(2)An ANN based data-driven constitutive modeling method is proposed for isotropic elastoplastic materials.The yield function in traditional plasticity theory is adopted.The ANN is used to learn yield function instead of strain-stress mapping directly.So,the data requirement is greatly reduced in the learning of elastoplastic material constitutive model.The elastoplastic modulus expressed by analytical form through ANN is derived.Numerical examples are given to demonstrate that the method has good stability and convergence when used in finite element simulation.(3)A data-driven method based on displacement field data is proposed for building the constitutive models of nonlinear elastic materials.An ANN parameter initialization algorithm is proposed to avoid the gradient disappearing problem.Compared with stress-strain data,the displacement field data is easier to be obtained,so this method is more practical than other methods which require stress-strain data.(4)A constitutive modeling method driven by the small amount of data for nonlinear elastic materials is proposed.Based on the three hypotheses proposed in this paper,the spherical component and the deviatoric component of the stress are calculated separately.Only uniaxial tension/compression data of materials are required to establish the constitutive model in this method.And the model can be fully extended and utilized if there are more data available.The accuracy of the model also can be improved with more data.The tangent modulus expressed by analytical form based on the data is derived.Examples show that the method has good stability and convergence when used in finite element simulation.All the methods presented in this thesis can be implemented in commercial structural finite element analysis software through user-defined material interface,to help researchers and engineers in related fields apply them conveniently.