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.

几种软生物组织和人造材料的特点是机械行为由维持平面内力的二维结构系统描述。在有限应变弹性的框架内，本文提出了超弹性不可压缩膜的公式和有限元实现。重点放在呈现孔洞和内部切口的膜的行为上。提出了一种新的有效算法来描述拓扑复杂的内部边界，沿着这些边界规定了位错状分布，从而允许边界材料点的一对一渐进连接。经典的 Ogden 模型被修改为松弛版本，以适应薄膜由于起皱而产生的无压缩响应。