Springer Online Journal Archives 1860-2000
Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
Abstract The hyperelasticity condition imposed on a material in which the stress is given as a function of the deformation gradient requires the existence of a strain-energy density function. If the material is incompressible, the indeterminacy of the pressure field is normally an additional postulate on material behavior. However, it is shown that in the case of a material in which the strain is determined as a function of an appropriately chosen stress measure, hyperelasticity demands the existence of a complementary strain-energy density function and the incompressibility condition isequivalent to the indeterminacy of the pressure field. The dependence of the complementary strain-energy density on the pressure, necessary and sufficient for incompressibility, is presented.
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