FRONT TRACKING FOR SHEAR BANDS IN AN ANTIPLANE SHEAR MODEL

In this paper we describe a numerical algorithm for the study of shear band, formation and growth in two-dimensional antiplane shear. The co nstitutive model uses a non-associative flow rule. The numerical schem e is based on a Godunov method for updating the velocity, while the st ress is updated via integration along particle paths. The scheme is co upled with a front tracking algorithm for careful evolution of the she ar bands. The main challenges are the non-hyperbolicity of the shear b and formation and growth (front tracking avoids the catastrophic effec ts of the loss of the hyperbolicity in the Godunov-type numerical sche me), the existence of endpoints for the shear band (the tracked front does not separate the computational domain into disconnected regions), and the non-hyperbolic rate of growth of the shear band. We give exam ples of the success of the algorithm and show convergence tests. (C) 1 997 Academic Press.