Consistent tangent stiffness for local-nonlocal damage modelling of metals

Abstract

In the present study we consider an adaptation of Nguyen’s model [G.D. Nguyen, A thermodynamic approach to constitutive modelling of concrete using damage mechanics and plasticity theory, D.Phil. Thesis, Dept. of Engng. Sci., University of Oxford, 2005] for brittle materials to the case of ductile rupture. We focus our attention on the formulation of a consistent tangent stiffness matrix which is essential for the efficiency and convergence of the implementation within a finite element framework. We demonstrate the capability of the model to generate mesh-independent results and to follow the rupture process very close to failure. Rupture analysis of thin plates of different geometry is presented (symmetric double notch-edged specimen, asymmetric double notch-edged specimen, double notch-edged specimen containing a hole). Further modifications are outlined required to simulate crack growth and paths under the conditions of creep and fatigue.