This paper presents a ductile damage-gradient based nonlocal and fully coupled
elastoplastic constitutive equations by adding a Helmholtz equation to regularize the
initial and boundary value problem (IBVP) exhibiting some damage induced softening. First,
a thermodynamically-consistent formulation of gradient-regularized plasticity fully
coupled with isotropic ductile damage and accounting for mixed non linear isotropic and
kinematic hardening is presented. For the sake of simplicity, only a simplified version of
this model based on von Mises isotropic yield function and accounting for the single
nonlinear isotropic hardening is studied and implemented numerically using an in house FE
code. An additional partial differential equation governing the evolution of the nonlocal
isotropic damage is added to the equilibrium equations and the associated weak forms
derived to define the IBVP (initial and boundary value problem). After the time and space
discretization, two algebraic equations: one highly nonlinear associated with the
equilibrium equation and the second purely linear associated with the damage non locality
equation are obtained. Over a typical load increment, the first equation is solved
iteratively thanks to the Newton-Raphson scheme and the second equation is solved directly
to compute the nonlocal damage \hbox{$\Bar{{D}}$}D̅ at each node. All the constitutive equations are “strongly” affected by
this nonlocal damage variable transferred to each integration point. Some applications
show the ability of the proposed approach to obtain a mesh independent solution for a
fixed value of the length scale parameter. Comparisons between fully local and nonlocal
solutions are given.