A time-integration algorithm for thermo-rheologically complex polymers

This study presents nonlinear thermo-viscoelastic analyses of isotropic polymers that belong to a class of thermo-rheologically complex materials (TCM). The nonlinear viscoelastic constitutive model is expressed with an integral form of a creep function, whose initial, long-term, and transient properties change with stresses and temperatures. A combined recursive–iterative method is formulated to solve the viscoelastic integral equation. The recurrence formula allows bypassing the need to store entire strain histories. Two types of iterative procedures, fixed point (FP) and Newton–Raphson (NR), are examined within the recursive algorithm. Furthermore, a consistent tangent stiffness matrix is formulated to accelerate convergence and avoid divergence. The algorithm is compatible with displacement based finite element (FE) structural analyses for small deformation gradients and uncoupled thermo-mechanical problems. Verification of the numerical algorithm is performed using the thermo-viscoelastic experimental data available in the literature. The influences of temperature dependent material properties on the material’s viscoelastic responses are discussed for general thermo-mechanical loadings. The capability of the algorithm in predicting multi-axial viscoelastic responses is then verified using creep data of adhesive bonded joints at various temperatures. Finally, numerical simulations of time-dependent crack propagations in adhesive bonded joints are presented for the opening and shearing modes.