LAUSR

Abstract This paper presents a finite element formulation for the analysis of softening in plane problems. The model is not based on the non-local or gradient-dependent approaches. It is an extension of lumped damage mechanics. Lumped damage mechanics, or LDM, is a formulation that introduces ideas of fracture and damage mechanics into the concept of plastic hinge. So far, LDM was limited to the analysis of frames and arches, but within this limited framework it represents also a regularization scheme. A finite element in LDM is the assemblage of an elastic beam-column with two inelastic hinges at the ends of the element. In a plate, a plastic hinge becomes a hinge line, in a two-dimensional continuum, a localization band. The finite element proposed in this work consists on an elastic four-node element with a set of localization bands on the sides. Damage evolution laws describing the behavior of each band are then introduced. The convergence of the numerical results with the reduction of the size of the elements is shown with the example presented in graphical abstract. The final configuration of the solid is also presented.