Optimal kinematics for finite elements with smeared-embedded discontinuity

Abstract

In this paper an optimal kinematics for finite elements with smeared non-uniform discontinuity/crack is proposed to eliminate the spurious stress transfer across a fully softened crack (i.e. stress locking). We first present the optimal kinematics of the finite elements with embedded non-uniform displacement jumps. It is found that, if the regularization bandwidth of the strong discontinuity reaches a critical value, i.e. the so-called consistent characteristic length of an element, the concept of classical smeared crack model is recovered. The optimal definition of the smeared cracking (inelastic) strain is then established such that the stress locking is completely removed. Finally, a constant stress triangle with a non-uniform discontinuity is analytically solved. The prediction shows that finite elements with the proposed kinematics can capture the expected stress and strain states even if a smeared crack model is used.