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Zbl 1194.74536
Rabczuk, T.; Areias, P.M.A.; Belytschko, T.
A simplified mesh-free method for shear bands with cohesive surfaces. (English)
[J] Int. J. Numer. Methods Eng. 69, No. 5, 993-1021 (2007). ISSN 0029-5981

Summary: A simple methodology to model shear bands as strong displacement discontinuities in a mesh-free particle method is presented. The shear band is represented as a set of sheared particles. A sheared particle is developed through enrichment by tangential displacement discontinuities. The representation of the shear band as set of cohesive segments provides a simple and versatile model of shear bands. The loss of material stability is used as the criterion for switching from a classical continuum description of the constitutive behaviour to a traction-separation law acting on the discontinuity surface. The method is implemented for two and three dimensions. Examples of shear band progression in rate-dependent and rate-independent materials are presented, including the Kalthoff problem, where the transition from brittle fracture to shear banding is studied.

MSC 2000:: *74S30 Other numerical methods
74R99 Fracture and damage

Keywords: mesh-free methods; shear bands; loss of hyperbolicity; traction-separation laws

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