Cohesive zone models are widely used in the simulation of fracture. For the traditional finite element based approach, additional elements are required to represent the strong discontinuity across the crack. In the intrinsic cohesive zone method \[1\], cohesive zone elements are inserted on every bulk element’s surface at the beginning of the simulation, which changes materials’ elastic behavior by increasing compliance, and greatly increases the number of the system’s degree of freedom. Even though the extrinsic cohesive zone method \[2\] only employs elements where the crack is initiating and propagating, this adds to the global degrees of freedom dynamically and causes complication in implementation.

Previously, a reproducing kernel finite volume method (RKFM) for elasticity has been proposed \[3\]. In this approach, meshfree shape functions are employed in order to compute stresses and strains on cell boundaries, which in turn are used to compute tractions (fluxes). When viewed from a Galerkin weak-form point of view, it can be shown that the method is variationally consistent inherently up to second-order, with low order quadrature. In addition, the method requires no spatial stabilization, despite being node-based. Essential boundary conditions are also treated effortlessly, since the method can also be viewed as a collocation approach. Thus the method has several intrinsic benefits over traditional Bubnov-Galerkin based meshfree methods.

In this work, a cohesive zone RKFM is introduced. The traction over the cohesive zone is naturally applied as a flux term in the finite volume framework. A kernel support updating algorithm is proposed such that the strong discontinuity can be obtained naturally under the flexible meshfree framework. Therefore, no additional degrees of freedom are required in this method, which reduces the computational complexity compared to finite-element based approaches, and no additional compliance is introduced. Several benchmark examples are presented to show the sufficiency of this method in yielding mesh-independent results, and crack initiation and dynamic branching. Validation of the method is also provided.

 

References:

1\.        Xu, X. P., & Needleman, A. (1994). Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids, 42(9), 1397-1434.

2\.        Camacho, G. T., & Ortiz, M. (1996). Computational modelling of impact damage in brittle materials. International Journal of solids and structures, 33(20-22), 2899-2938.

3\.        Hillman, M. & Yang, S. (2018). A conforming reproducing kernel particle finite volume method. *International Mechanical Engineering Congress and Exposition 2018*, Pittsburgh, Nov 9-15.  

 

 

Keywords: Finite volume method; Cohesive zone method; Brittle fracture; Meshfree methods;


A Cohesive Reproducing Kernel Finite Volume Method for Brittle Fracture Simulation

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Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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