Finite deformation formulation for embedded frictional crack with the extended finite element method

We introduce a phase-field method for continuous modeling of cracks with frictional contacts. Compared with standard discrete methods for frictional contacts, the phase-field method has two attractive features: (1) it can represent arbitrary crack geometry without an explicit function or basis enrichment, and (2) it does not require an algorithm for imposing contact constraints. The first feature, which is common in phase-field models of fracture, is attained by regularizing a sharp interface geometry using a surface density functional. The second feature, which is a unique advantage for contact problems, is achieved by a new approach that calculates the stress tensor in the regularized interface region depending on the contact condition of the interface. Particularly, under a slip condition, this approach updates stress components in the slip direction using a standard contact constitutive law, while making other stress components compatible with stress in the bulk region to ensure non-penetrating deformation in other directions. We verify the proposed phase-field method using stationary interface problems simulated by discrete methods in the literature. Subsequently, by allowing the phase field to evolve according to brittle fracture theory, we demonstrate the proposed method's capability for modeling crack growth with frictional contact.

Section: Introductionmentioning

confidence: 99%

A phase‐field method for modeling cracks with frictional contact

Fei

Choo

2019

“…They noted the superior rates of convergence for the penalty method compared to the LATIN method. The approach has been extended to problems with bulk plasticity (Khoei et al, 2006;Liu and Borja, 2009) and large sliding contact (Khoei and Mousavi, 2010;Liu and Borja, 2010a). It should be noted that these approaches still represent a regularization of a discrete formulation that is unstable, and involve a free penalty parameter.…”

Section: Introductionmentioning

confidence: 99%

An efficient finite element method for embedded interface problems

Dolbow

Harari

2008

219

223

We focus on developing a computationally efficient finite element method for interface problems. Finite element methods are severely constrained in their ability to resolve interfaces. Many of these limitations stem from their inability in independently representing interface geometry from the underlying discretization. We propose an approach that facilitates such an independent representation by embedding interfaces in the underlying finite element mesh. This embedding, however, raises stability concerns for existing algorithms used to enforce interfacial kinematic constraints. To address these stability concerns, we develop robust methods to enforce interfacial kinematics over embedded interafces.We begin by examining embedded Dirichlet problems -a simpler class of embedded constraints. We develop both stable methods, based on Lagrange multipliers, and stabilized methods, based on Nitsche's approach, for enforcing Dirichlet constraints over three-dimensional embedded surfaces and compare and contrast their performance. We then extend these methods to enforce perfectly-tied kinematics for elastodynamics with explicit time integration. In particular, we examine the coupled aspects of spatial and temporal stability for Nitsche's approach. We address the incompatibility of Nitsche's method for explicit time integration by (a) proposing a modified weighted stress variational form, and (b) proposing a novel mass-lumping procedure.We revisit Nitsche's method and inspect the effect of this modified variational iv form on the interfacial quantities of interest. We establish that the performance of this method, with respect to recovery of interfacial quantities, is governed significantly by the choice for the various method parameters viz. stabilization and weighting. We establish a relationship between these parameters and propose an optimal choice for the weighting. We further extend this approach to handle non-linear, frictional sliding constraints at the interface. The naturally non-symmetric nature of these problems motivates us to omit the symmetry term arising in Nitsche's method.We contrast the performance of the proposed approach with the more commonly used penalty method. Through several numerical examples, we show that with the proposed choice of weighting and stabilization parameters, Nitsche's method achieves the right balance between accurate constraint enforcement and flux recovery -a balance hard to achieve with existing methods. Finally, we extend the proposed approach to intersecting interfaces and conduct numerical studies on problems with junctions and complex topologies.v To Amma (mom) and Nannagaru (dad), vi

“…The discontinuous displacement fields in nonlinear contact usually lead to local stress concentration or serious structural damage. 1,2 In cases that the discontinuities are well pre-defined, the finite element method (FEM) can provide an efficient tool to analyze contact problems. However, if a large number of discontinuities are involved and are expected to evolve in an unknown pattern during the simulation, the FEM would require an enormous computational cost to remesh the computational domain.…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear contact behaviors are often encountered in various engineering problems. The discontinuous displacement fields in nonlinear contact usually lead to local stress concentration or serious structural damage 1,2 . In cases that the discontinuities are well pre‐defined, the finite element method (FEM) can provide an efficient tool to analyze contact problems.…”

Section: Introductionmentioning

confidence: 99%

A virtual interface‐coupled extended finite element method for three‐dimensional contact problems

Fang

Zhang

Zhou

et al. 2020

In this article, we propose a virtual interface-coupled technique to model the arbitrary discontinuous interface based on the three-field dual mortar method. The computational domain is divided into several subdomains and the enriched nodes are individually introduced to construct the approximation of the displacement field. This method provides a flexible way to describe the multiple-body contact with nonconforming mesh in the extended finite element method (XFEM). An independent virtual interface is employed to replace the XFEM discontinuous interface. The connect condition between the virtual interface and discontinuous interface is imposed using the dual Lagrange multiplier method. Due to the bi-orthogonality condition, the Lagrange multipliers can be locally eliminated at a very low computational cost. The resulting system matrix is symmetric positive definite and well-conditioned. Furthermore, the contact and natural boundary conditions can be directly imposed on the virtual interface. Several numerical experiments are performed and the results show that the proposed method provides an effective, robust, and fast way to simulate three-dimensional contact behaviors of nonconforming interfaces.