A consistent time FE-method for large strain elasto-plasto-dynamics

In the present paper energy-consistent momentum-conserving time-stepping schemes for geometrically nonlinear multiplicative elasto-plasto-dynamics – referred to as ‘ECMC-cG methods’ – are developed. In this context, the entire discretisation procedure of the global equations of motion is based on Galerkin methods in space and time, whereby special emphasis is placed on the desired conservation properties related to the approximation of time-integrals. To guarantee energy-consistency also for higher-order Finite Elements in time, a thermodynamically motivated ‘enhanced stress tensor’, which defines a non-standard quadrature rule, is derived for elasto-plastic material behaviour. Concerning the integration of the local evolution equations in time, exemplarily, a well-established first-order accurate exponential update is applied and adapted according to the global time-stepping scheme based on linear Finite Elements in time. The performance of the resulting scheme is demonstrated by means of several representative numerical examples, whereby it is shown that global energy-consistency is guaranteed exactly within the calculation accuracy by applying the proposed concepts.