A Modeling of Wrinkled Membranes Using a Projection Matrix: Derivation of Modified Elasticity Matrix Using a Projection Technique

A modeling of wrinkled membranes based on projection operator is presented within the classical membrane theory. The total strains in wrinkled membranes are decomposed into elastic and zero-strain energy parts. A projection matrix that extracts the elastic parts from the total strains is derived from the view point of linear algebra. The resulting modified elasticity matrix that represents the stress-strain relations in wrinkled membranes is thus obtained as product of the classical elasticity matrix and projection matrix. A qualitative comparison is conducted between the presented modified elasticity matrix and the existing modified elasticity matrices.