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Symmetric Galerkin boundary element method for quasi-brittle-fracture and frictional contact problems. (English) Zbl 0786.73080

Summary: The analysis of elastic quasi-brittle structures containing cohesive cracks and contacts with friction is given a unitary formulation in the framework of incremental plasticity. Integral equations for displacement and tractions are enforced by a weighted-residual Galerkin approach so that symmetry is preserved in the key operators (in contrast to collocation BE approaches), and cracks (either internal or edge cracks) can be dealt with by a single-domain BE formulation. The space-discrete problem in rates is expressed as a linear complementarity problem centered on a symmetric matrix or, equivalently, as a quadratic programming problem in variables pertaining to the displacement discontinuity locus only. Criteria for overall instabilities and bifurcations are derived from this formulation. The BE approach proposed and implemented by a suitable time-stepping technique, is comparatively tested by numerical solutions of cohesive-crack propagation problems.

MSC:

74S15 Boundary element methods applied to problems in solid mechanics
74R99 Fracture and damage
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics

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