Kinematic Constraints in Nonlinear Elasticity (Incompressibility, Perturbation, Convergence)
Reed, John Keith
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https://hdl.handle.net/2142/71684
Description
Title
Kinematic Constraints in Nonlinear Elasticity (Incompressibility, Perturbation, Convergence)
Author(s)
Reed, John Keith
Issue Date
1985
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Abstract
The constitutive equations for a material which approximately satisfies a kinematic constraint are investigated for the particular case of an elastic material.
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.
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.
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