CONDITIONS ON THE ELASTIC STRAIN-ENERGY FUNCTION

An intuitive idea of physically realistic or stable response in one-di mensional deformation-that stress be a positive increasing function of strain-is brought to bear on general three-dimensional response of is otropic elastic materials by consideration of a special class of one-p arameter deformation paths called proportional extensions. An appropri ate strain measure is defined along such paths and an effective stress is identified. The condition that the effective stress must be a posi tive, strictly increasing function of the strain measure along any pat h of proportional extension imposes restrictions on the strain-energy function. The resulting inequalities are found for both compressible a nd incompressible materials.