Stress distributions around discontinuities in soft elastic membranes

The paper is concerned with the determination of the stress distribution in the regions of a soft elastic membrane surrounding geometrical or structural discontinuities, such as holes, slits, inclusions or local stiffeners. The severity of the stress concentration is assessed through a general non-linear model that considers large displacements, large deformations and a non-linear elastic material law. Inability of the membrane of sustaining any compressive stress, highlighted by the occurrence of wrinkling and local buckling, is automatically accounted for by recourse to the concept of relaxed strain energy. Solution of the stated problem is obtained within a FEM framework, where an arc-length path-tracing procedure allows to follow the evolution of the phenomenon. Applications present the case of a rectangular membrane endowed with a circular or straight central defect – a void or a rigid inclusion. Numerical results show that when wrinkling is taken into account the stressconcentration differs significantly from that predicted by the standard membrane theory, being in some cases less severe.