2005•Chinese journal of rock mechanics and engineeringRequires access

NUMERICAL SIMULATION OF A BODY WITH CRACKS

Tiantang Yu

Abstract

Numerical simulation of arbitrary discontinuities is a hot and difficult problem;especially for tracking the dynamic cracks,it has important practical meaning.A new numerical method,extended finite element method(XFEM),which may conveniently simulate static and dynamic cracks,was introduced several years ago.The numerical method for modeling strong(displacement) as well as weak(strain localization) discontinuities with a standard finite element framework is presented.In the XFEM,in order to model the discontinuities of displacements,the jump function and asymptotic crack-tip displacement fields are added to the finite element approximation for the local enrichment by using the framework of partition of unity.Thus,the discontinuities are independent of the mesh.The principles of XFEM are given;and some formulas are derived.The integral scheme of discontinuous function is presented;and the evaluation of stress intensity factor is discussed.Numerical simulations illustrate that XFEM can effectively model the discontinuities;and it has wonderful practical merits.

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Key concepts: Classification of discontinuities, Extended finite element method, Finite element method, Jump, Partition of unity, Displacement (psychology), Discontinuity (linguistics), Mixed finite element method