The analysis of incompressible hyperelastic bodies by the finite element method

Abstract A method is developed for the finite element analysis of problems involving incompressible hyperelastic bodies; the constitutive relation is based on a class of strain-energy functions due to Ogden [4], which involve sums of real powers of principal stretches. Incremental equilibrium equations are derived from a rate form of the principle of virtual work and an additional set of equations which express the condition of incompressibility in an average manner, is appended to the equilibrium equations. Examples of solutions are given and compared either with closed-form solutions or with numerical solutions found using conventional approaches.