Non-linear analysis of soft elastic membranes containing holes and slits

We study the stress distribution in the neighbourhood of geometric discontinuities, such as holes and slits, in soft elastic membranes subject to increasing uniaxial traction. The search for the solutions is carried out taking simultaneously into account the main sources of nonlinearity. In particular, large displacements and large deformations are considered by adopting the Green-Lagrange measure of strain, while physical non-linearity is entered via Ogden’s constitutive law. Within this context, possible phenomena of local buckling are automatically taken into account through the concept of relaxed energy proposed by Pipkin for the analysis of wrinkled membranes. Finally, a continuation procedure of the arc-length type permits the tracing of the equilibrium path. The proposed model can be usefully exploited for analysing the instantaneous response of biological tissues under increasing loads. Cases of rectangular membranes are illustrated as a numerical application.