Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

Abstract

Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 m/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999[( ) Science 284:1337[( -1340. The simulations are capable of handling crack growth with cracktip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between √ 2c S (c S is the shear wave speed)

A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations

“…The generalized interpolation material point (GIMP) method [3] is a generalization of the MPM that accounts for finite spatial extent occupied by each particle. MPM and GIMP have been successfully used in simulation of a range of complicated engineering problems including finite deformation plasticity, thin membranes, cracks and fracture, sea ice dynamics, granular materials, multiscale problems, hypervelocity impact, and dynamic analysis of saturated porous media among others [4][5][6][7][8][9][10][11][12][13][14][15][16]. Also, their basic algorithms and formulations have been studied by a number of authors such as [17][18][19][20][21][22][23][24][25][26][27][28][29].…”

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

“…Our goal is a crack algorithm capable of simulating realistic looking crack propagation, with lower computational requirements more suitable for computer graphics. Daphalapurkar et al (2007) have also developed a scheme for crack growth in generalized interpolation MPM (GIMP) which targets engineering applications. They simulate a crack along a pre-defined cohesive zone in a 2D specimen, where particles from opposite sides of the crack interface interact.…”

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

“…Simulations spanning many of the possible algorithmic parameters were explored, requiring substantial computational effort even for two-dimensional calculations. Additionally, plane strain calculations will allow for comparison with previous simulations of dynamic mode II fracture experiments, which also assumed plane strain (Needleman 1999;Daphalapurkar et al 2007), the next phase in this investigation. Similarly, attention was restricted to simple material response (small deformation, linearly elastic) and simple fracture propagation scenarios (mode I).…”

“…A small value of δ c results in a small process zone, and corresponds to brittle fracture response, often of interest in applications. The parameters used here are typical in terms of ratio of critical separation length to element size (Needleman 1999;Daphalapurkar et al 2007), here the ratio is 0.08. For small values of δ c very few cohesive elements are active (not separated) except for those immediately behind the fracture tip.…”

“…However another important consideration arises in numerical simulation work and that is computational efficiency. Dynamic fracture modeling using decohesion laws relies on extensive mesh refinement near the decohesion zones to adequately resolve the stress field (Needleman 1999) and provide convergence (Daphalapurkar et al 2007). The J-integrals may be calculated using contours away from the crack tip, obviating the need to extensively resolve the calculation near the crack tip, and providing for substantial computational savings.…”