Research On Elastoplastic Constitutive Modeling Method Driven By The Small Sample Data

With the rapid development of material science and industrial technology,the demand for high-performance new materials in aerospace,household appliances,medical devices,automobiles,construction and other fields is increasing with each passing day.At the same time,it also brings more severe challenges to the solid mechanics simulation required for cutting-edge manufacturing and safety evaluation of new materials and structures.Solid mechanics simulation is inseparable from the constitutive model of materials.Accurately establishing the constitutive model of new materials and putting forward the numerical implementation method are the key to solve these challenges.However,the establishment of traditional constitutive model requires high intelligence and time cost.For example,the famous Neo-Hookean,Ogden,Hill,DrukerPrager and other models often take scientists many years.Therefore,these models are often named after scientists,reflecting their outstanding contributions.In addition,the traditional constitutive model can only describe the mechanical properties of a certain kind of materials,and the scope of application is small.It often takes more time to calibrate the parameters of the traditional constitutive model,and it is difficult to meet all the experimental data at the same time.The computational method based on the traditional constitutive model is difficult to keep up with the update speed of new materials,and it is difficult to achieve the goal of shortening the product R & D(research and development)cycle,evaluating the product safety performance and providing solutions.Therefore,it is time to develop the data-driven computational methods for new materials and structures.In recent years,many scholars have proposed the data-driven constitutive modeling methods to overcome the difficulties of traditional constitutive modeling.These methods directly uses experimental data to automatically establish the constitutive model of materials without functional expression.However,most of the proposed data-driven constitutive modeling methods are obtained by training the stress-strain data under different loading paths through machine learning methods,or optimized and solved iteratively in the experimental data through the conservation law.Due to the lack of fusion or insufficient fusion of the prior knowledge and mechanism of mechanics,these methods require a large amount of data,and certain data are difficult to be measured through physical experiments,which limits the popularization and application of data-driven computational methods.Facing the above difficulties,aiming at elastoplastic materials,this thesis makes full use of the prior knowledge and mechanism of mechanics to explore invariants that meet the constraints of physical properties and mechanical mechanism,and develops the small sample data-driven elastoplastic constitutive modeling methods based on invariants to reduce the demand of data.The specific research contents and achievements of this thesis include:(1)A constitutive modeling method driven by the small sample data for elastoplastic materials is proposed at the small deformation regime.Only need to collect uniaxial experimental data,through the coaxial relationship between stress and trial strain,a mathematical format of stress updating with uniaxial data is constructed,and a numerical algorithm is proposed to obtain the tangent stiffness matrix.This method avoids the complicated process of constitutive analysis modeling.Several numerical examples based on traditional plastic constitutive models(e.g.J2 plastic model with isotropic hardening and nonlinear hardening,Drucker-Prager model)and experimental results of Al-Cu alloy structural samples show the accuracy and computational stability of this method.(2)A constitutive modeling method driven by the small sample data for isotropic tensioncompression asymmetric elastoplastic materials is proposed at the small deformation regime.This method constructs a mathematical format for stress updating using uniaxial tension and compression data at the same time,which can simultaneously treat tension-and compressiondominated stress states,in the elastic and plastic ranges,while respecting the different yield and hardening behaviors of each.In order to obtain accurate one-dimensional data set from physical experiments,a homogenization data generation and processing method based on digital image correlation is proposed,especially for the data processing in cylindrical sample compression experiment.Two representative tension compression asymmetric materials(e.g.TC4 ELI and HDPE)are selected.The accuracy and computational stability of this method are illustrated by a variety of structural experiments and numerical examples.(3)A constitutive modeling method driven by the small sample data for elastoplastic materials is proposed at the finite deformation regime.Through the coaxial relationship between stress and trial strain,a stress updating algorithm based on uniaxial experimental data is constructed,and a numerical algorithm is proposed to obtain the tangent stiffness matrix.In this method,the logarithmic strain and true stress whose stress and strain meet the work conjugate requirements are selected as the data source,which avoids the selection of objective stress rate under the finite deformation computational framework in the finite element software,and makes the numerical implementation more simplified.The accuracy and stability of the method are proved by some numerical examples and experimental results of titanium alloy structural samples.