A Novel Stress Tensor-Based Failure Criterion for Peridynamics

Abstract

Peridynamic theory has recently shown to be a versatile tool for simulating complex phenomena related to the fracture and fragmentation of structural and composite materials. We introduce a novel failure criterion based on the classic stress tensor which takes inspiration from an approach proposed in the literature. Differently from the classic critical stretch-based failure criterion used in peridynamics, our approach takes into account the total elastic energy stored in the bond allowing to predict with more accuracy problems that involve mixed-mode I-II fracture. In order to show the effectiveness of the proposed failure criterion, a benchmark fracture problem is analyzed showing a good agreement with the experimental results and the numerical results obtained with other numerical methods.

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

“…Once the force between the two points goes to zero it stays zero. It is noted that there are several other definitions for the damage function μ using strain-based criteria [38,42], as well as stress-based [43], or energy-based damage criteria [44,45], see Fig. 4.…”

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

“…where the scalar function µ : [0, T ] × R n × R n → R indicates if the bond between X and X at time t is broken (µ = 0) or active (µ = 1). There are several definitions for the function µ [11,[15][16][17]. To summarize, the damage variable is the density given by the proportion of intact bonds at time t relative to the total number of bonds inside the neighborhood.…”