Finite Element Analysis of Damage in Ductile Structures Using a Nonlocal Model Combined with a Three-field Formulation

Solving finite element problems involving elasto-plasticity coupled with damage softening faces two major difficulties: mesh dependence and volumetric locking. In this study, a specific finite element is proposed which allows to solve simultaneously both problems within the small strain framework. It combines a mixed treatment based on a three-field formulation (displacements, assumed pressure, and assumed dilatation) to solve the volumetric locking and a nonlocal implicit gradient-enhanced formulation to avoid localization of damage. Simulations on a double-notched specimen are presented which allow to compare the nonlocal formulation and the mixed nonlocal formulation. Triangular elements with quadratic shape functions for the displacements and linear shape functions for the assumed dilatation, assumed pressure, and nonlocal variable are used. First results show that the mixed nonlocal method regularizes the problem and allows to obtain smoother stress fields than the nonlocal method at the same time.