Constitutive Coefficients for Viscohyperelastic Materials,
ARMY LAB COMMAND WATERTOWN MA MATERIAL TECHNOLOGY LAB
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Elastic and viscous stresses in rubberlike materials can be modeled using strain energy density functions. The large strain elastic hyperelastic deformations are often modeled with the Rivlin strain invariant power series 1 . Similarly, large strain viscous deformations of rubberlike materials viscohyperelastic can be modeled using an internal solid theory with hyperelastic solids 2,3,4,5. The energy functions material coefficients are found by least square fitting to the classical tension, shear, and equibiaxial stress-stretch tests 6. These least squares fits typically produce energy functions which are not stable for deformations other than those covered by the test data. That is, when strain states not included in the test data are considered the models often suffer from the flaw that for isothermal deformations they predict a decrease in the solids internal strain energy for an increment of applied stress which does positive work on the solid. This conservation of energy statement is known as Druckers postulate on stability. Such a flaw cannot be accepted since computations for complex deformations will include strain states which are not the same as those used to determine the energy density function.