An elasto-viscoplastic constitutive model for polymers at finite strains: Formulation and computational aspects

• This work formulates an elasto-viscoplastic model at finite strains.
• A particularly efficient numerical integration algorithm is presented.
• A closed-form analytical expression is derived for the consistent tangent operator.
• The non-linear behaviour of polymers is captured in the numerical examples.
• Quadratic rate of convergence is successfully achieved.

This paper describes a finite strain elasto-viscoplastic constitutive model to predict the non-linear behaviour of polymeric based materials. The theoretical basis of the material model and the computational treatment are presented. The operator split methodology and the Newton–Raphson method are used to derive the state update algorithm and to obtain the numerical solution. The integration algorithm reduces to the solution of only one scalar non-linear equation. A closed formula for the corresponding consistent tangent operator is presented. Different aspects of the constitutive model and its integration algorithm are investigated by considering a comprehensive set of numerical examples.