# An interface cohesive zone model based on an inverse strong discontinuity formulation

**Mechanics of Material Forces; (Advances in Mechanics and Mathematics, Vol. 11) ; Steinmann, Paul; Maugin, Gérard A. (Eds.)**p. Chapter 27. (2005)

[Kapitel]

This contribution focuses on a strong discontinuity formulation of the crack kinematics that exploits the direct and inverse deformation maps of both the continuous and total deformations. As a result, unique push-forward - pull-back transformations are obtained between the material and spatial discontinuities. Similar transformations may be obtained by regularizing the strong discontinuity. Moreover, upon introducing the material (Eshelby) stress, pertinent to hyper-elastic continuum behavior, a separation of the continuous direct motion and the discontinuous inverse motion problems is obtained in the weak form of the momentum balance. Thereby, the solution of the continuos forward and the discontinuous inverse problems can be obtained simultaneously. As to the material discontinuous problem, a prototype model calibrated with respect to mode I fracture is proposed in the material (rather than the spatial or physical) traction for a fixed fracture surface. In this development, the assumption of brittle fracture is made, leading to a significant simplification of the equations. Interestingly, the dependence of a material inhomogeneity appears explicitly as a load term in the discontinuous problem, which thus acts as a driving force for the discontinuity development. The paper is concluded by a couple of numerical examples displaying the preditive capabilities of the proposed formulation.

**Nyckelord: **crack propagation, X-FEM

*Orginally presented at Mechanics of Material Forces, Euromech Colloquium 445, Kaiserslautern, May, 2003*

Denna post skapades 2005-12-03. Senast ändrad 2016-02-01.

CPL Pubid: 9183