# Robust Algorithm for Brittle Fracture based on Energy Minimization

2006-03-31
The paper outlines a variational formulation of brittle fracture in solids and considers its numerical implementation by adistinct ﬁnite element method. The starting point is a variational setting of fracture mechanics that recasts a monotonicquasistatic fracture process into a sequence of incremental minimization problems. The proposed implementation introducesdiscretized crack patterns with material-force-driven incremental crack-segment releases. These releases of crack segmentsconstitute a sequence of positive deﬁnite subproblems with successively decreasing overall stiffness, providing an extremelyrobust algorithmic setting in the postcritical range. The formulation is embedded into accompanying r-adaptive crack-patternreorientation procedures with material-force-based indicators, providing reorientations of elements at the crack-tip.
77th Annual Meeting of Gesellschaft für Angewandte Mathematik und Mechanik (GAMM) (27 - 31 Mart 2006)

# 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...
 Numerical Modeling of Electromagnetic Scattering from Periodic Structures by Transformation Electromagnetics ÖZGÜN, ÖZLEM; Kuzuoğlu, Mustafa (2016-09-22) The transformation electromagnetics is applied to the modeling of electromagnetic scattering from periodic structures in conjunction with the finite element method with periodic boundary conditions. In a unit cell of periodic structure, a uniform mesh is used over a flat surface and the arbitrary periodic surface is modeled by a coordinate transformation. The major advantage of this approach is that arbitrary geometries can be handled by using a single and simple mesh. Therefore, repeated computations (such...
 Hybrid finite element for analysis of functionally graded beams Sarıtaş, Afşin; Soydas, Ozan (2017-01-01) A hybrid finite element model is presented, where stiffness and mass distributions over a beam with functionally graded material (FGM) are accurately modeled for both elastic and inelastic material responses. Von Mises and Drucker-Prager plasticity models are implemented for metallic and ceramic parts of FGM, respectively. Three-dimensional stress-strain relations are solved by a general closest point projection algorithm, and then condensed to the dimensions of the beam element. Numerical examples and veri...
 Progressive structural and electronic properties of nano-structured carbon atomic chains Usanmaz, D.; Srivastava, G. P. (AIP Publishing, 2013-05-21) Ab initio calculations, based on the planewave pseudopotential method and the density functional theory, have been reported on the changes in the electronic and structural properties of short carbon atomic chains held rigidly between hydrogenated thin armchair graphene nanoribbons (N-a-AGNR) of dimer line numbers N-a = 4 and 5. We have considered chains of several lengths (n = 4-9 atoms) and with different forms of attachment with the AGNRs. It is found that odd-numbered chains are metallic in nature, with ...
 Theoretical investigation of quercetin and its radical isomers Erkoc, E; Erkoc, F; Keskin, N (Elsevier BV, 2003-08-01) The structural and electronic properties of quercetin and its five radical isomers have been investigated theoretically by performing semi-empirical molecular orbital theory calculations. The geometry of the systems have been optimized and the electronic properties of the systems considered have been calculated by semi-empirical self-consistend-field molecular orbital theory at the level AM1 within UHF formalism in their ground state. Conclusions have been drawn by comparing with experimental results.
Citation Formats
E. Gürses, “Robust Algorithm for Brittle Fracture based on Energy Minimization,” Berlin, Germany, 2006, vol. 6, p. 167, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/78141.