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Universal deformations

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The Universal Program of Nonlinear Hyperelasticity

For a given class of materials, universal deformations are those that can be maintained in the absence of body forces by applying only boundary tractions.  Universal deformations play a crucial role in nonlinear elasticity. To date, their classification has been accomplished for homogeneous isotropic solids following Ericksen's seminal work, and  homogeneous anisotropic solids and inhomogeneous isotropic solids in our recent works. In this paper we study universal deformations for inhomogeneous anisotropic solids defined as materials whose energy function depends on position.

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Universal Deformations in Inhomogeneous Isotropic Nonlinear Elastic Solids

Universal (controllable) deformations of an elastic solid are those deformations that can be maintained for all possible strain-energy density functions and suitable boundary tractions. Universal deformations have played a central role in nonlinear elasticity and anelasticity. However, their classification has been mostly established for homogeneous isotropic solids following the seminal works of Ericksen. In this paper, we extend Ericksen's analysis of universal deformations to inhomogeneous compressible and incompressible isotropic solids.

arash_yavari's picture

Universal Deformations in Anisotropic Nonlinear Elastic Solids

Universal deformations of an elastic solid are deformations that can be achieved for all possible strain-energy density functions and suitable boundary conditions. They play a central role in nonlinear elasticity and their classification has been mostly accomplished for isotropic solids following Ericksen's seminal work. Here, we address the same problem for transversely isotropic, orthotropic, and monoclinic solids.

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