Multiple scale meshfree methods for damage fracture and localization

Liu, Wing Kam; Hao, Su; Belytschko, Ted; Li, Shao Fan; Chang, C. T.

doi:10.1016/s0927-0256(99)00062-2

Cited by 72 publications

(31 citation statements)

References 30 publications

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“…These include, but are not limited to, the Diffuse Element Method of Nayroles et al [65], the Element Free Galerkin method of Belytschko et al [10], the Reproducing Kernel Particle Method of Liu and Chen [56], and the Meshless Local Petrov-Galerkin method of Atluri and Zhu [4]. A number of overviews and reviews have appeared regarding these methods [9,59,58,60,61], though the interested reader will find no shortage of new developments.…”

Section: Application Of Meshfree Methods To Modeling Fracturementioning

confidence: 99%

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Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Klein

Foulk

Chen

et al. 2001

Theoretical and Applied Fracture Mechanics

149

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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.

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Section: Application Of Meshfree Methods To Modeling Fracturementioning

confidence: 99%

“…However, certain representations of the displacement field are more susceptible to introducing these errors in the mapping from the reference to the deformed configuration. Due to the more diffuse, or non-local, character of the meshfree shape functions, they display a higher resistance against errors of this type [17,60].…”

Section: Introductionmentioning

confidence: 99%

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Klein

Foulk

Chen

et al. 2001

Theoretical and Applied Fracture Mechanics

149

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“…13 and 15 because ®nite element volume must remain positive. One way to address this problem is to implement the strong discontinuity plasticity model within the framework of a mesh-free method (Belytschko et al, 1996;Liu et al, 1999), thus abandoning the AES method. Such an implementation is presently being considered.…”

Section: Plane Strain Slope Stabilitymentioning

confidence: 99%

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

Regueiro

Borja

2001

International Journal of Solids and Structures

114

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Numerical simulations of localized deformation in solids should capture the structural phenomenon of localization and associated loss of material body strength in a manner independent of spatial discretization. Many regularization techniques have been proposed to address the ill posedness associated with rate-independent softening plasticity that leads to mesh-dependent numerical simulations. One approach to alleviating mesh dependence is the strong discontinuity approach, which represents localized deformation as a slip surface within a plasticity model; a strong discontinuity is a discontinuous displacement ®eld. This approach is used in this paper to formulate a plane strain, pressure sensitive, nonassociative plasticity model with strong discontinuity and to implement the model, along with an enhanced bilinear quadrilateral element, via an assumed enhanced strain method. Numerical examples demonstrate mesh independence of the method for pressure sensitive materials. Ó

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“…This assumes that the constitutive model leads to a well-posed system of governing partial differential equations (elastodynamic or coupled elastodynamicheat conduction). There are new numerical methods (Hughes et Liu et al 1999) capable of capturing the "fine scale'' effects of the physics (in this case the adiabatic shear band) at the "coarse scale" within the finite element or nodal influence region. These are powerful methods because the spatial discretization would not need to be refined to the physical length scale of the shear band (possibly on the order of 10 pm) in order to represent its effect in a convergent manner with respect to spatial discretization.…”

Section: Discussionmentioning

confidence: 99%

High-Rate Shear Deformation and Failure in Structural Alloys

Dawson¹

2002

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Experiments were conducted to determine the dynamic shear behavior of a wide range of aluminum, titanium, and steel alloys. Principal experimental techniques were the torsional Kolsky bar and the Shear Compression Specimen (SCS) geometry. For the purpose of determining adiabatic shear susceptibility in this range of alloys, it was found that both techniques were unable to induce adiabatic shear in alloys resistant to that failure mode. The SCS geometry has demonstrated a capability for characterizing shear deformation behavior over a wide range of strain rates. For modeling and simulation of adiabatic shear phenomena, an improved adiabatic temperature evolution equation has been implemented. Finite element simulations of the torsional Kolsky and SCS geometries were conducted to evaluate the influence of pre-existing geometric inhomogeneities on adiabatic shear band initiation. 3

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Multiple scale meshfree methods for damage fracture and localization

Cited by 72 publications

References 30 publications

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods

Plane strain finite element analysis of pressure sensitive plasticity with strong discontinuity

High-Rate Shear Deformation and Failure in Structural Alloys

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