IMCOMPRESSIBILITY AND MATERIALS WITH COMPLEMENTARY STRAIN-ENERGY DENSITY

The hyperelasticity condition imposed on a material in which the stres s is given as a function of the deformation gradient requires the exis tence of a strain-energy density function. If the material is incompre ssible, the indeterminacy of the pressure field is normally an additio nal postulate on material behavior. However, it is shown that in the c ase of a material in which the strain is determined as a function of a n appropriately chosen stress measure, hyperelasticity demands the exi stence of a complementary strain-energy density function and the incom pressibility condition is equivalent to the indeterminacy of the press ure field. The dependence of the complementary strain-energy density o n the pressure, necessary and sufficient for incompressibility, is pre sented.