Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach

Abstract

A new approach to simulating fracture, in which toughness is partitioned between the crack tip and, optionally, a process zone, is applied to dynamic fracture processes. In this approach, classical fracture mechanics determines crack tip propagation, and cohesive laws characterize process zone response and determine crack root and process zone propagation. The approach is implemented in the Material Point Method, a particle method in which the fracture path is unconstrained by a body-fitted mesh. The approach is found suitable for modeling a range of dynamic fracture processes, from brittle fracture to fracture with crack bridging. A variety of ways of partitioning toughness are explored with the aim of distinguishing model parameters via experimental measurements, particularly R curves. While no unique relationship exists, R curves, or effective R curves, on a suite of materials would provide substantial insight into model parameters. Advantages to the approach are identified, both in S. G. versatility and in regards to practical matters associated with implementing numerical fracture algorithms. It is found to perform well in dynamic fracture scenarios.

Phase-Field Material Point Method for dynamic brittle fracture with isotropic and anisotropic surface energy

“…To this point, few research has been conducted in damage simulation utilizing MPM using either discrete [38,39], cohesive [40,41], or continuum damage models [42,43]. Taking advantage of the good qualities of phase field modelling in naturally resolving complex crack paths, a Phase Field Material Point Method According to Griffith's theory [47] the stored energy Ψ s of the body Ω can be expressed as…”

Animation of crack propagation by means of an extended multi-body solver for the material point method

“…The crack is explicitly represented as a Lagrangian mesh of massless particles, which in 2D constitutes of connected line segments and in 3D a polygon mesh. CRAMP is primarily used for engineering applications to investigate the stress response of a specimen with a non-propagating crack, but was recently extended by Bardenhagen et al (2011) to allow for dynamically propagating cracks. The authors, however, also say that their dynamic crack propagation algorithm "...…”

“…The removal of the line crossing algorithm is the main computational speedup that this work provides over CRAMP, together with the fact that no crack release rates are calculated for crack propagation, as done in e.g., Bardenhagen et al (2011). For real materials, a propagating crack tip is normally followed by a plastic deformation in the crack region, that absorbs some of the potential energy released when the crack forms.…”

Coupled Fluid-Solid Geomechanical Modeling of Multiple Hydraulic Fractures Interacting with Natural Fractures and the Resulting Proppant Distribution

“…This is possible due to developments of the original MPM method allowing fractures to be included in the discretization scheme. The initial development, known as CRAcks in the Material Points, or CRAMP (Nairn 2003, Bardenhagen et al 2011, enables the calculation of stresses and strains in the presence of a fracture and also allows the dynamic behavior of fractures, such as opening and propagation, to be simulated. A recent extension of the CRAMP algorithm allowing fractures interacting has been used to simulate the interaction of hydraulic and natural fractures to solve multiple completion optimization problems (Aimene & Ouenes, 2015, Ouenes et al 2015a, Ouenes et al 2015b, Ouenes et al 2015c.…”