Adaptive dynamic cohesive fracture simulation using nodal perturbation and edge‐swap operators

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SUMMARY Adaptive mesh refinement and coarsening schemes are proposed for efficient computational simulation of dynamic cohesive fracture. The adaptive mesh refinement consists of a sequence of edge‐split operators, whereas the adaptive mesh coarsening is based on a sequence of vertex‐removal (or edge‐collapse) operators. Nodal perturbation and edge‐swap operators are also employed around the crack tip region to improve crack geometry representation, and cohesive surface elements are adaptively inserted whenever and wherever they are needed by means of an extrinsic cohesive zone model approach. Such adaptive mesh modification events are maintained in conjunction with a topological data structure (TopS). The so‐called PPR potential‐based cohesive model (J. Mech. Phys. Solids 2009; 57:891–908) is utilized for the constitutive relationship of the cohesive zone model. The examples investigated include mode I fracture, mixed‐mode fracture and crack branching problems. The computational results using mesh adaptivity (refinement and coarsening) are consistent with the results using uniform mesh refinement. The present approach significantly reduces computational cost while exhibiting a multiscale effect that captures both global macro‐crack and local micro‐cracks. Copyright © 2012 John Wiley & Sons, Ltd.

Section: Adaptive Mesh Refinement (Amr)mentioning

confidence: 99%

Section: Adaptive Mesh Coarsening (Amc)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Adaptive mesh refinement and coarsening for cohesive zone modeling of dynamic fracture

Park

Paulino

Celes

et al. 2012

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“…In this numerical example, the compact compression specimen tests conducted by Rittel and Maigre are numerically modeled. Various numerical methods have been used to model this problem . The geometry and the boundary conditions of the problem are shown in Figure .…”

Section: Numerical Examplesmentioning

confidence: 99%

A general mass lumping scheme for the variants of the extended finite element method

Asareh

Song

Mullen

et al. 2020

Summary A new strategy for the mass matrix lumping of enriched elements for explicit transient analysis is presented. It is shown that to satisfy the kinetic energy conservation, the use of zero or negative masses for enriched degrees of freedom of lumped mass matrix may be necessary. For a completely cracked element, by lumping the mass of each side of the interface into the finite element nodes located at the same side and assigning zero masses to the enriched degrees of freedom, the kinetic energy for rigid body translations is conserved without transferring spurious energy across the interface. The time integration is performed by adopting an explicit‐implicit technique, where the regular and enriched degrees of freedom are treated explicitly and implicitly, respectively. The proposed method can be viewed as a general mass lumping scheme for the variants of the extended finite element methods because it can be used irrespective of the enrichment method. It also preserves the optimal critical time step of an intact finite element by treating the enriched degrees of freedom implicitly. The accuracy and efficiency of the proposed mass matrix are validated with several benchmark examples.

“…Nodes and elements are explicitly represented, whereas vertices, edges, and facets are implicitly derived from the basis of element templates. Additionally, a client‐server approach is employed to maintain a consistent data structure when modification events occur …”

Section: Element Splitting Schemementioning

confidence: 99%

Removing mesh bias in mixed‐mode cohesive fracture simulation with stress recovery and domain integral

Choi

Park

2019

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Summary To remove mesh bias and provide an accurate crack path representation in mixed‐mode investigation, a novel stress recovery technique is proposed in conjunction with a domain integral and element splits. Based on a domain integral and stress recovery technique, a maximum strain energy release rate is estimated to determine a crack path direction. Then, for a given crack path direction, continuum elements are split, and a cohesive surface element is adaptively inserted. One notes that the proposed stress recovery technique provides a more accurate stress field than a standard stress evaluation procedure. The proposed computational framework is verified and validated by solving mode‐I and mixed‐mode examples. Computational results demonstrate that the domain integral with the stress recovery accurately evaluates a crack path, even with a lower‐quality mesh and under a biaxial stress state. Furthermore, the cohesive surface element approach, with the element split in conjunction with the stress recovery and the domain integral, predicts mixed‐mode fracture behaviors while removing mesh bias in the crack path representation. Additionally, the condition numbers of stiffness matrices are within the same order of magnitude during cohesive fracture simulation.