  It is well known that the use of a consistent tangent stiffness matrix is
critical to obtain quadratic convergence of the global Newton iterations in the
finite element simulations of problems involving elasto-plastic deformation of
metals, especially for large scale metallic structure problems. In this paper
we derive an exact consistent stiffness matrix for a porous material model, the
GLPD model developed by Gologanu, Leblond, Perrin, and Devaux for ductile
fracture for porous metals based on generalized continuum mechanics
assumptions. Full expressions for the derivatives of the Cauchy stress tensor
and the generalized moments stress tensor the model involved are provided. The
effectiveness and robustness of the proposed tangent stiffness moduli are
assessed by applying the formulation in the finite element simulations of
ductile fracture problems. Comparisons between the performance our stiffness
matrix and the standard ones are also provided.
