Performance of a finite element procedure for hyperelastic–viscoplastic large deformation problems

Abstract

In this paper, the details of implementation of a formulation for hyperelastic–viscoplastic solids are discussed. The formulation employs the constitutive equation based on multiplicative decomposition of deformation gradient, incrementally objective integration, and closed-form tangent operator consistent with the constitutive evaluation. The standard updated Lagrangian framework for the virtual work equation is used. Different measures, taken to make computation efficient and stable, are discussed such as the solution of scalar nonlinear equations for rate-dependent plasticity using a hybrid method. The proposed method is numerically implemented and the computational aspects are examined in detail. A number of numerical examples are presented that illustrate the excellent performance of the proposed method, even with very large strain increments. The performance of the current implementation is compared with other closed-form elasto-viscoplastic tangent operators having hypoelastic or hyperelastic assumption reported in the literature.