Stress-concentration in a partly wrinkled elastic membrane

Soft elastic membranes are typically unable to sustain compressive stresses, so that an accurate estimation of the stress distribution cannot disregard the occurrence of wrinkling and buckling phenomena. This is particularly true for those regions surrounding geometrical or structural discontinuities. To assess the stress distribution in these cases, we propose a general nonlinear membrane model able to automatically account for the effects of the above stated forms of local instability. The set of nonlinear equilibrium equations is derived via the principle of stationary total potential energy and solved in a finite element context. The load-deflection response of the membrane under increasing loads is monitored by the aid of an arc-length path-tracing procedure. Application cases concern rectangular membranes endowed with circular or straight defects (holes or rigid inclusions).