Elastic-plastic tip field for a stationary crack in a reinforced thin sheet

A class of plane stress problems for incompressible materials is studied. The class concerns problems for unidirectionally reinforced thin sheets under quasi-static loading conditions. An incremental theory of plasticity and an isotropic yield condition is assumed. It is demonstrated how a corresponding antiplane strain problem can be identified. Thus solutions are readily found to a variety of problems. A stationary crack in a perfectly plastic material is chosen for demonstration. Small-scale yielding is assumed but solutions for e.g., large-scale of yielding or hardening materials are also easity obtained.