A discrete nonlocal damage mechanics approach

In this paper the authors develop the governing equations for a finite element model of micro-cracking based on a novel approach, eschewing differential equations and continuum mechanics. Instead of first stating the continuum balance laws and constitutive relations followed by discretization, the body is discretized first and then the equations of equilibrium are directly stated for the discretized body. It is shown that, as a result, the balance laws and constitutive relations can be entirely stated in terms of edge forces and lengths rather than strains. Furthermore, by ensuring that microcracks always propagate along the dual mesh which represents the possible fracture microplanes in the element, the need for creating additional nodes, gap elements or cohesive zones is avoided. Finally, the notion of the survival probability of a fracture microplane is introduced and the transition probability evolution is described by using probabilistic notions from population models. Thus the resulting governing equations can be solved by a conventional elastic predictor, followed by a nonlocal fracture corrector, making this convenient to augment conventional elements with fracture abilities.

Automated summary

In this paper, the authors develop a finite element model of micro-cracking using a novel approach that avoids differential equations and continuum mechanics. The body is discretized first, followed by the direct statement of equilibrium equations. The balance laws and constitutive relations are expressed in terms of edge forces and lengths instead of strains. By ensuring that microcracks propagate along the dual mesh and introducing the concept of survival probability, additional nodes, gap elements, and cohesive zones are not needed. The resulting governing equations can be solved using an elastic predictor and a nonlocal fracture corrector.