A pressure projection method for nearly incompressible rubber hyperelasticity, part I: Theory

A least-squares-based pressure projection method is proposed for the nonlinear analysis of nearly incompressible hyperelastic materials. The strain energy density function is separated into distortional and dilatational parts by the use of Penn’s invariants such that the hydrostatic pressure is solely determined from the dilatational strain energy density. The hydrostatic pressure and hydrostatic pressure increment calculated from displacements are projected onto appropriate pressure fields through the least-squares method. The method is applicable to lower and higher order elements and the projection procedures can be implemented into the displacement based nonlinear finite element program. By the use of certain pressure interpolation functions and reduced integration rules in the pressure projection equations, this method can be degenerated to a nonlinear version of the selective reduced integration method.