A thermo-mechanical viscoelastic analysis of orthotropic materials

Abstract

Abstract This study introduces a numerical algorithm for nonlinear thermo-mechanical viscoelastic analyses of orthotropic composite materials and structures that follow thermo-rheologically complex behaviors. 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 form is generalized for modeling viscoelastic responses of an orthotropic medium. The effects of stress and temperature are incorporated in the elastic and time-dependent material properties, which allow prediction of time-dependent responses under general stress and temperature histories. A recursive–iterative method is developed to calculate the current stress state from the given strains and temperature, and the history variables stored at the previous time step. Furthermore, a consistent tangent stiffness matrix is formulated to enhance equilibrium and avoid divergence at the structural level. Available experimental data of nonlinear viscoelastic responses of orthotropic composite materials are used to verify the above numerical algorithm. An integrated recursive–iterative algorithm with FE structural analysis is also presented for creep responses of orthotropic composite plate with a hole.