A computational framework of three-dimensional configurational-force-driven brittle crack propagation

Date

2009-01-01

Author

Gürses, Ercan

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

342
views

0
downloads

We consider a variational formulation of quasi-static brittle fracture and develop a new finite-element-based computational framework for propagation of cracks in three-dimensional bodies We outline a consistent thermodynamical framework for crack propagation in elastic solids and show that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius-Planck inequality in the sense of Coleman's method. Consequently, the crack propagation direction associated with the classical Griffith criterion is identified by the material configurational force which maximizes the local dissipation at the crack front. The variational formulation is realized numerically by a standard spatial discretization with finite elements which yields a discrete formulation of the global dissipation in terms configurational nodal forces. Therefore, the constitutive setting of crack propagation in the space-discretized finite element context is naturally related to discrete nodes of a typical finite element mesh. In a consistent way with the node-based setting, the discretization of the evolving crack discontinuity is performed by the doubling of critical nodes and interface facets of the mesh. The crucial step for the success of this procedure is its embedding into an r-adaptive crack-facet reorientation procedure based on configurational-force-based indicators in conjunction with crack front constraints. We propose a staggered solution procedure that results in a sequence of positive definite discrete subproblems with successively decreasing overall stiffness, providing a robust algorithmic setting in the postcritical range. The predictive capabilitiy of the proposed formulation is demonstrated by means of representative numerical simulations.

Subject Keywords

Brittle fracture, Configurational forces, Variational formulation, r-Adaptivity, Finite elements, 3D crack propagation

URI

https://hdl.handle.net/11511/47930

Journal

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

DOI

https://doi.org/10.1016/j.cma.2008.12.028

Collections

Department of Aerospace Engineering, Article

Suggestions

OpenMETU
Core

A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment MIEHE, CHRISTIAN; Gürses, Ercan (2007-10-08) The paper considers a variational formulation of brittle fracture in elastic solids and proposes a numerical implementation by a finite element method. On the theoretical side, we outline a consistent thermodynamic framework for crack propagation in an elastic solid. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius-Planck inequality in the sense of Coleman's method. Here, the canonical direction of the...
A modified applied element model for the simulation of plain concrete behaviour Soysal, Berat Feyza; Arıcı, Yalın; Tuncay, Kağan (2022-08-01) A modified applied element model to simulate the behaviour of plain concrete continuum structures including discrete cracking is proposed in this study. In the classical applied element model, Poisson effects are fully ignored. To remediate this issue, diagonal elements are introduced to include the Poisson effect, and the constitutive parameters are rigorously determined using the Cauchy-Born rule and the hyper-elastic theory. The formulation is validated for linear elastic problems and the consistency and...
A new time-domain boundary element formulation for generalized models of viscoelasticity Akay, Ahmet Arda; Gürses, Ercan; Göktepe, Serdar (2023-05-01) The contribution is concerned with the novel algorithmic formulation for generalized models of viscoelasticity under quasi-static conditions within the framework of the boundary element method (BEM). The proposed update algorithm is constructed for a generic rheological model of linear viscoelasticity that can either be straightforwardly simplified to recover the basic Kelvin and Maxwell models or readily furthered towards the generalized models of viscoelasticity through the serial or parallel extensions. ...
A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization MIEHE, CHRISTIAN; Gürses, Ercan; BIRKLE, MANUEL (Springer Science and Business Media LLC, 2007-06-01) A variational formulation of quasi-static brittle fracture in elastic solids at small strains is proposed and an associated finite element implementation is presented. On the theoretical side, a consistent thermodynamic framework for brittle crack propagation is outlined. It is shown that both the elastic equilibrium response as well as the local crack evolution follow in a natural format by exploitation of a global Clausius-Planck inequality. Here, the canonical direction of the crack propagation associate...
On evolving deformation microstructures in non-convex partially damaged solids Gürses, Ercan (2011-06-01) The paper outlines a relaxation method based on a particular isotropic microstructure evolution and applies it to the model problem of rate independent, partially damaged solids. The method uses an incremental variational formulation for standard dissipative materials. In an incremental setting at finite time steps, the formulation defines a quasi-hyperelastic stress potential. The existence of this potential allows a typical incremental boundary value problem of damage mechanics to be expressed in terms of...

Citation Formats

E. Gürses, “A computational framework of three-dimensional configurational-force-driven brittle crack propagation,” COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, pp. 1413–1428, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/47930.