An Abaqus user subroutine solving convergence problems of nonlinear viscoelastic models with thermorheologically simple temperature dependence

The temperature dependence of viscoelastic materials is usually modeled assuming thermorheologically simple behavior. In the commercial finite element software Abaqus, this feature is available for both linear and nonlinear viscoelastic models. The nonlinear implementation of viscoelasticity enables to use more sophisticated creep models, but also to formulate the material behavior dependent on an additional field variable, e.g. a variable describing ageing. Convergence problems or a prohibitive large number of small increments can occur if a significant change of temperature is simulated using the nonlinear approach with implicit time integration.

This technical note presents a user subroutine avoiding the convergence problem. The solution is explained and demonstrated in a test case of bonded plates under stresses induced by thermal cycling. In this test, the solution using the user subroutine agrees with the linear reference solution and shows similarly good convergence, while the nonlinear simulation without the user subroutine shows convergence problems. User subroutine and test input files are provided in the supplementary material.