Element-Embedded Localization Band Based on Regularized Displacement Discontinuity

Abstract

The paper describes a new finite element, derived from the classical constant strain element, in the context of localization analysis of elastic-plastic materials. The formulation is based on the “enhanced strain” concept, which is extended to include regularized displacement discontinuities. As a result, the localization band is embedded within the element and the conventional displacement topology is preserved. The major advantage, as compared to the interelement representation, is that advanced mesh (re)alignment strategies are totally avoided and unstructured meshes are sufficient. An interesting feature of the element is that the condition for existence of an internal element discontinuity is identical to the classical condition for band-shaped localization. The element is combined with a cohesive crack model that is based on the Rankine criterion and a well-established calibration technique to achieve an objective response in the post peak softening range in terms of the dissipated (fracture) energy. Results from finite-element analyses of a notched concrete plate are provided.