An explicit finite element approach with patch projection technique for strain gradient plasticity formulations

Implicit and explicit finite element approaches are frequently applied in real problems. Explicit finite element approaches exhibit several advantages over implicit method for problems which include dynamic effects and instability. Such problems also arise for materials and structures at small length scales and here length scales at the micro and sub-micron scales are considered. At these length scales size effects can be present which are often treated with strain gradient plasticity formulations. Numerical treatments for strain gradient plasticity applying the explicit finite element approach appear however to be absent in the scientific literature. Here such a numerical approach is suggested which is based on patch recovery techniques which have their origin in error indication procedures and adaptive finite element approaches. Along with the proposed explicit finite element procedure for a strain gradient plasticity formulation some numerical examples are discussed to assess the suggested approach.