Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically-based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of material, meaning that a finite material strength and work to fracture are included in the material description. In this study, we present both surface and bulk cohesive formulations for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well-suited to modeling fracture behavior. We describe the application of meshfree methods to both bulk and surface approaches to cohesive modeling. We present numerical examples highlighting the capabilities and shortcomings of the methods in order to identify which approaches are best-suited to modeling different types of fracture phenomena.
Simulation of generalized fracture and fragmentation remains an ongoing challenge in computational fracture mechanics. There are difficulties associated not only with the formulation of physically-based models of material failure, but also with the numerical methods required to treat geometries that change in time. The issue of fracture criteria is addressed in this work through a cohesive view of material, meaning that a finite material strength and work to fracture are included in the material description. In this study, we present both surface and bulk cohesive formulations for modeling brittle fracture, detailing the derivation of the formulations, fitting relations, and providing a critical assessment of their capabilities in numerical simulations of fracture. Due to their inherent adaptivity and robustness under severe deformation, meshfree methods are especially well-suited to modeling fracture behavior. We describe the application of meshfree methods to both bulk and surface approaches to cohesive modeling. We present numerical examples highlighting the capabilities and shortcomings of the methods in order to identify which approaches are best-suited to modeling different types of fracture phenomena.
Some effects of material degradation on failure mechanisms of brittle damage materials are investigated. Conditions for the localization of deformation within a shear band are established for rate independent damage materials. In contrast with previous work on shear band initiation that relied on plasticity and flow theory formulation, the present study finds it sufficient for the shear band to emerge in the regime of infinitesimal strain for brittle damage materials. Bifurcations from the homogeneous deformation mode in the form of shear bands are captured for loading conditions of plane strain compression and uniaxial compression using conventional continuum damage mechanics formulations. The inclination angle and critical strain for shear band initiation are calculated using well-established mathematical theory. A finite element simulation of shear band initiation for a rectangular mesh deformed in plane strain compression is also presented.
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