A Cosserat Point Element (CPE) for the Numerical Solution of Problems in Finite Elasticity

The theory of a Cosserat Point is a special continuum theory that characterizes the motion of a small material region which can be modeled as a point with finite volume. This theory has been used to develop a 3-D eight-noded brick Cosserat Point Element (CPE) to formulate the numerical solution of dynamical problems in finite elasticity. The kinematics of the CPE are characterized by eight director vectors which are functions of time only. Also, the kinetics of the CPE are characterized by balance laws which include: conservation of mass, balances of linear and angular momentum, as well as balances of director momentum. The main difference between the standard Bubnov Galerkin and the Cosserat approaches is the way that they each develop constitutive equations. In the direct Cosserat approach, the kinetic quantities are given by derivatives of a strain energy function that models the CPE as a structure and that characterizes resistance to all models of deformation. A generalized strain energy function has been developed which yields a CPE that is truly a robust user friendly element for nonlinear elasticity that can be used with confidence for 3-D problems as well as for problems of thin shells and rods.