Session: 12-03-01: Minisymposium on Peridynamic Modeling of Materials’ Behavior

Paper Number: 70793

Start Time: Monday, 11:25 AM

70793 - Peridynamics for Quasistatic Fracture Modeling 

 

Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the perspective of mechanics fracture should appear as an emergent phenomena generated by a continuum field theory eliminating the need for a supplemental kinetic relation describing crack growth.

We develop a new fast quasi-static fracture modeling using peridynamics. We apply fixed point theory and model stable crack evolution for hard loading. For soft loading we successfully recover unstable fracture. We demonstrate the efficient numerical method for several illustrative  examples. Our method uses an analytic stiffness matrix for fast numerical Implementation. A rigorus mathematical analysis shows that the method convergeges for load paths associated with a hard device. For soft devices the crack becomes unstable as soon as the crack tip stress exceeds the critical stress intensity for a material.

This is done for a class of peridynamic models with nonlocal forces derived from double well potentials. The term double well describes the force potential between two points. One of the wells is degenerate and appears at infinity while the other is at zero strain. For small strains the nonlocal force is linearly elastic but for larger strains the force begins to soften and then approaches zero after reaching a critical strain. This type of nonlocal model is called a cohesive model. Fracture energies of this type have been defined earlier for displacement gradients with the goal of understanding fracture as a phase transition.

Peridynamic modeling implicitly couples the dynamics of the un-cracked elastic material to crack tip growth. Here it is of natural interest to explicitly recover the coupling between the length of the crack and the dynamics of the elastic field. One answer lies in deriving an explicit formula relating the time rate of change of kinetic energy and stress work inside a neighborhood surrounding the crack tip to the external elastic power applied to the neighborhood. This is done for the case at hand.

We use this formula and provide a numerical simulation using the cohesive dynamics to show that a crack moving at constant speed satisfies energy balance. The numerical computation also shows that the stress work flux is nearly equal to the energy release rate as anticipated by the theory. The peridynamic fracture energy is compared to the classic fracture energy and is found to be nearly identical

Presenting Author: Robert Lipton Louisiana State University

Authors:

Debdeep Bhatacharya Louisiana State University
Patrick Diehl Louisiana State University
Robert P. Lipton Louisiana State University