A Time Integration Algorithm for Nonlinear Viscoelastic Behaviors of Orthotropic Media

Abstract

This study develops a recursive-iterative algorithm for analyzing nonlinear viscoelastic responses of orthotropic materials. The algorithm is derived based on implicit stress integration solutions within a general displacement based finite element (FE) framework for small deformations and uncoupled thermo-mechanical problems. The Schapery's nonlinear single integral model is generalized for stress-temperature-time dependent responses of an orthotropic medium. The time-dependent compliance follows material symmetry, which leads to nine independent time integral equations. A recursive method is used to solve the time-dependent integral model. An incremental iterative algorithm is added in order to minimize error arising from the linearized strain formulation in the recursive method. Furthermore, a consistent tangent stiffness matrix is formulated to enhance equilibrium and avoid divergence. The recursive-iterative numerical formulation is implemented within the ABAQUS general purpose FE code. Available experimental data on nonlinear viscoelastic responses of orthotropic laminated composite materials are used to verify the above numerical algorithm.