Velocity-based space-time finite element method for large deformation analysis of solids incorporating arbitrary moving mesh and hypoelastic constitutive model

This study proposes a velocily-based space-time finite element method (v-ST/FEM) that enables a large deformation analysis of solids over arbitrary moving mesh (AMM) via simple and rigorous formulation in the space-time domain. The proposed method solves quasi-static problems with a hypoelastic constitutive model. The Cauchy stress convected through AMM is incrementally updated following the relative velocity between the moving mesh and the solid deformation, which results in the weak form for the primary unknown of velocity. An iterative algorithm for solving the discretized system equation is implemented, whereby geometrical nonlinearity is considered by the iterative update of the stress over the moving mesh. Numerical analyses of benchmark problems such as simple tensile deformation, rotating cylinder under compression, and non-uniform large tensile deformation have been conducted. The numerical results have shown that v-ST/FEM achieves as accurate computation over AMM as over Lagrangian mesh and have demonstrated the applicability of AMM. © 2023 by the Japan Society for Computational Engineering and Science.