State of art in regularization methods for numerical analysis of structures with softening

Abstract

This paper provides an extensive review of popular regularization methods utilized in numerical models to stabilize the structural response of materials exhibiting significant softening. The necessity for regularization is highlighted in cases of material softening, which is attributed to the loss of ellipticity in the governing differential equations. It discusses the advantages and disadvantages of the regularization methods most commonly employed in the scientific community. Furthermore, the paper highlights recent advancements, particularly in defining internal length within nonlocal models and characteristic element length in fracture energy regularization methods, as alternative solutions to address the limitations inherent in traditional approaches.