KINEMATIC CONSTRAINTS IN NONLINEAR ELASTICITY (INCOMPRESSIBILITY, PERTURBATION, CONVERGENCE)

The constitutive equations for a material which approximately satisfies a kinematic constraint are investigated for the particular case of an elastic material.;A perturbation scheme based on the definition is given, with the constrained material as the lowest order approximation. Uniqueness for the higher order linear equations is determined.;Convergence for an almost incompressible material which is hyperelastic to that of an incompressible material is shown. The hypotheses on the strain energy needed to show convergence are compared and contrasted to penalty methods.;Kinematically constrained materials in elasticity describe materials in which certain deformations are ruled out a priori. Since a constrained material is an idealization, we give a definition of a material which is almost constrained. The definition is based on the constitutive equation for the stress, not on the strain energy. The definition is constructed so that any material satisfying the definition may deviate only slightly from the constraint. Also, the stress must give the constrained theory in the limit as the constraint is satisfied.