Distance minimizing based data‐driven computational method for the finite deformation of hyperelastic materials

Abstract The distance minimizing based data‐driven solvers are developed for the finite deformation analysis of three‐dimensional (3D) compressible and nearly incompressible hyperelastic materials in this work. The data‐driven solvers bypass the construction of a constitutive equation for the hyperelastic materials by considering a dataset of Green‐Lagrange strain‐second Piola–Kirchhoff stress pairs. They recast the boundary‐value problems into the distance minimization problems with basic kinematical and mechanical constraints. Moreover, the deviatoric/volumetric split of stress and the additional incompressible constraint are further introduced into the solver for the nearly incompressible hyperelastic materials. Several representative three‐dimensional examples are presented and the results demonstrate the good capability and robustness of the proposed data‐driven solvers.