Numerical modelling of wrinkled hyperelastic membranes with topologically complex internal boundary conditions

Several soft biological tissues and artificial materials are characterised by a mechanical behaviour described by two-dimensional structural systems sustaining in-plane forces. Within the framework of finite strain elasticity, in this paper the formulation and finite element implementation of a hyperelastic incompressible membrane is presented. Focus is placed on the behaviour of membranes presenting holes and internal cuts. A new efficient algorithm is presented to describe topologically complex internal boundaries along which dislocation-like distributions are prescribed, so as to allow a one-to-one progressive joining of boundary material points. The classical Ogden's model is modified into a relaxed version in order to accommodate the no-compression response of thin membranes due to wrinkling. Three applicative examples are presented to illustrate the potential of the method proposed.