Open Access

ARTICLE

Quadrilateral Finite Element with Embedded Strong Discontinuity for Failure Analysis of Solids

J. Dujc^1,3, B. Brank^1,2, A. Ibrahimbegovic³

1 University of Ljubljana, Faculty of Civil and Geodetic Engineering, Ljubljana, Slovenia
2 Corresponding author, E-mail: bbrank@fgg.uni-lj.si, fax: +386 1 425 06 93
3 Ecole Normale Supérieure de Cachan, Cachan, France

Computer Modeling in Engineering & Sciences 2010, 69(3), 223-260. https://doi.org/10.3970/cmes.2010.069.223

Abstract

We present a quadrilateral finite element with discontinuous displacement fields that can be used to model material failure in 2d brittle and ductile solids. The element provides mesh-objective results. The element's kinematics can represent linear displacement jumps along the discontinuity line in both normal and tangential directions to the line. The cohesive law in the discontinuity line is based on rigid-plasticity model with softening. The material of the bulk of the element is described by hardening plasticity model. Static condensation of the jump-in-displacements kinematic parameters is made, which provides standard form of the element stiffness matrix. However, in order to make the discontinuity growth algorithm more robust, the continuity of the failure line between the elements is enforced. Several numerical tests show that the element can describe constant and linear separation modes without spurious transfer of the stresses. Other numerical examples represent failure of pure concrete, composite and metal 2d solids.

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