A study of characteristic element length for higher-order finite elements

Abstract

Abstract. The utilization of a fracture energy regularization technique, based on the crack band model, can effectively resolve the issue of mesh-size dependency in the finite element modelling of quasi-brittle structures. However, achieving accurate results requires proper estimation of the characteristic element length in the finite element method. This study presents practical calculation methods for the characteristic element length, particularly for higher-order finite elements based on the Carrera Unified Formulation (CUF). Additionally, a modified Mazars damage model that incorporates fracture energy regularization is employed for damage analysis in quasi-brittle materials. An experimental benchmark is adopted then for validation, and the result shows that the proposed methods ensure accurate regularization of fracture energy and provide mesh-independent structural behaviors.