A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization

2007-06-01
MIEHE, CHRISTIAN
Gürses, Ercan
BIRKLE, MANUEL
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 associated with the classical Griffith criterion is the direction of the material configurational force which maximizes the local dissipation at the crack tip. On the numerical side, we first consider a standard finite element discretization in the two-dimensional space which yields a discrete formulation of the global dissipation in terms of configurational nodal forces. Next, consistent with the node-based setting, the discretization of the evolving crack discontinuity for two-dimensional problems is performed by the doubling of critical nodes and interface segments of the mesh. A crucial step for the success of this procedure is its embedding into a r-adaptive crack-segment re-orientation algorithm governed by configurational force-based directional indicators. Here, successive crack propagation is performed by a staggered loading release algorithm of energy minimization at frozen crack state followed by nodal releases at frozen deformation. We compare results obtained by the proposed formulation with other crack propagation criteria. The computational method proposed is extremely robust and shows an excellent performance for representative numerical simulations.
INTERNATIONAL JOURNAL OF FRACTURE

Suggestions

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 quasi-incompressible and quasi-inextensible finite element analysis of fibrous soft biological tissues
Gultekin, Osman; Rodoplu, Burak; Dal, Hüsnü (Springer Science and Business Media LLC, 2020-06-01)
The contribution presents anextensionandapplicationof a recently proposed finite element formulation for quasi-inextensible and quasi-incompressible finite hyperelasticity to fibrous soft biological tissues and touches in particular upon computational aspects thereof. In line with theoretical framework presented by Dal (Int J Numer Methods Eng 117:118-140, 2019), the mixed variational formulation is extended to two families of fibers as often encountered while dealing with fibrous tissues. Apart from that, ...
A density functional theory study on the structures and energetics of CdmTen clusters (m + n <= 6)
Pekoz, Rengin; Erkoç, Şakir (Elsevier BV, 2009-06-01)
Density functional method has been used to study the structural features and energetics of CdmTen clusters (m + n <= 6). The results presented include the geometric structures, binding energies, Mulliken charges on atoms, vibrational frequencies and the corresponding non-zero infrared intensities, HOMO-LUMO energies and the frontier molecular orbital energy gaps, the most possible dissociation channels and their corresponding energies of the clusters.
The DRBEM solution of incompressible MHD flow equations
Bozkaya, Nuray; Tezer, Münevver (Wiley, 2011-12-10)
This paper presents a dual reciprocity boundary element method (DRBEM) formulation coupled with an implicit backward difference time integration scheme for the solution of the incompressible magnetohydrodynamic (MHD) flow equations. The governing equations are the coupled system of Navier-Stokes equations and Maxwell's equations of electromagnetics through Ohm's law. We are concerned with a stream function-vorticity-magnetic induction-current density formulation of the full MHD equations in 2D. The stream f...
The finite element method for MHD flow at high Hartmann numbers
Nesliturk, AI; Tezer, Münevver (Elsevier BV, 2005-01-01)
A stabilized finite element method using the residual-free bubble functions (RFB) is proposed for solving the governing equations of steady magnetohydrodynamic duct flow. A distinguished feature of the RFB method is the resolving capability of high gradients near the layer rep-ions without refining mesh. We show that the RFB method is stable by proving that the numerical method is coercive even not only at low values but also at moderate and high values of the Hartmann number. Numerical results confirming t...
Citation Formats
C. MIEHE, E. Gürses, and M. BIRKLE, “A computational framework of configurational-force-driven brittle fracture based on incremental energy minimization,” INTERNATIONAL JOURNAL OF FRACTURE, pp. 245–259, 2007, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/49139.