Simulating body deformations with initial stresses using Hooke‐like isotropic hypoelasticity models based on corotational stress rates

Abstract

We use isotropic hypoelastic models based on corotational stress rates to simulate deformations of elastic bodies with initial stresses. Four material models based on different corotational stress rates are used: the Zaremba–Jaumann, Green–Naghdi, logarithmic, and Hill models. The main result of the study are new objective algorithms for integrating stresses that provide sufficiently accurate values of stresses for large time steps. In addition, a new approach to symmetrizing tangent stiffness matrices that has a clear mechanical interpretation was used in computations. All four material models were implemented in a homemade FE system for nonlinear analysis of deforming bodies. The developed algorithms were verified and validated by solving both uniform deformation problems that have exact solutions and applied problem of plate bending with non‐equilibrated initial stresses. The performance of the developed software was assessed by comparing numerical solutions obtained using this software with similar solutions obtained using the commercial MSC.Marc nonlinear FE system. Comparative analysis of the obtained solutions shows that our software is comparable in performance with one of the leading commercial software packages for solving problems of isotropic hypoelasticity with initial stresses.