Research On Data-driven Hyperelastic Modeling

Accurately predicting the mechanical response of rubber-like materials under arbitrary de-formation modes has always been a frontier problem in the study of constitutive relations.In order to describe the highly nonlinear mechanical behavior,essentially complete recoverability,and approximate incompressibility exhibited by rubber-like materials,the existence of a strain energy function is usually assumed,and the analytical form of the strain energy function is then determined by experimental observations and phenomenological or statistical methods to con-struct a hyperelastic constitutive model.Although numerous constitutive models have been pro-posed in the literature,these models are often in a dilemma where reducing the material param-eters reduces the predictive capability of the model,while increasing the material parameters makes the model too complicated.In recent years,a new computational paradigm,"data-driven computational mechanics",that directly using experimental data to solve the boundary value problems has been proposed in order to get rid of the dependence of traditional constitutive models on empirical facts and the arbitrariness of their material parameters.In this work,after testing the performance of several classical constitutive models in real experiments,a data-driven approach is proposed for the analysis of the boundary value prob-lem of hyperelastic materials.This approach directly using the experimental data of uniaxial and equibiaxial tension,avoiding constructing the analytical form of the strain energy function.The original experimental data is reconstructed into a new data form,and combined with data search techniques the approach can efficiently accomplish stress update in finite element anal-ysis.Unlike traditional constitutive models,this approach does not presuppose the material to be completely incompressible,and is therefore applicable to compressible and approximately incompressible materials.Numerical experiments using the reference models are conducted to generate the required data,and examples with different deformation modes and complexities are designed to test the predictive capability of the proposed approach.Results show that the ap-proach is consistent with the reference models at either the overall or element level.Furthermore,classical experimental data of Treloar and Kawabata on rubber are used to test the prediction abil-ity of the proposed approach in real experiments.Results show that the approach can accurately predict the results of Treloar experiments and a part of Kawabata experiments despite the lack of a priori quantity.This approach provides a new path for accurately predicting the mechanical response of nonlinear elastic materials under arbitrary deformation modes.