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ABSTRACT
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... Many of the counterexamples displaying lack of uniqueness arise because the path of loading is not specified. But specification of this path does not rule out non-uniqueness due to instabilities such as buckling. ... We write Lin +... more
... Many of the counterexamples displaying lack of uniqueness arise because the path of loading is not specified. But specification of this path does not rule out non-uniqueness due to instabilities such as buckling. ... We write Lin + ={HeLin: detH>0}, Orth + ={QsLin+ : QrQ =i}, ...
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Research Interests: Mathematics, Applied Mathematics, Physics, Nonlinear Elasticity, Modeling, and 15 morePure Mathematics, Mathematical Analysis, SPHERE, Hyperelasticity, Surface Area, Isoperimetric Inequality, Strain Energy, Hyperelastic material, Constraint, Boolean Satisfiability, Certified Reference Material, Boundary Condition, Boundary Value Problem, Constitutive Equation, and Sobolev space
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Research Interests: Applied Mathematics, Physics, Nonlinear Elasticity, Modeling, Pure Mathematics, and 14 moreSPHERE, Hyperelasticity, Surface Area, Isoperimetric Inequality, Strain Energy, Hyperelastic material, Large classes, Constraint, Boolean Satisfiability, Certified Reference Material, Boundary Condition, Boundary Value Problem, Constitutive Equation, and Sobolev space
ABSTRACT
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In this paper the existence of minimizers in nonlinear elasticity is established under assumptions on the stored energy that permit the formation of new holes in the body. Such cavities have been observed in experiments on elastomers, and... more
In this paper the existence of minimizers in nonlinear elasticity is established under assumptions on the stored energy that permit the formation of new holes in the body. Such cavities have been observed in experiments on elastomers, and a mathematical theory for ...
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In this paper we investigate the question of uniqueness for the standard boundary-value problem of quasi-static nonlinear viscoelasticity. As our main result we show that a solution u which is Hadamard stable at all times is unique; 1 or... more
In this paper we investigate the question of uniqueness for the standard boundary-value problem of quasi-static nonlinear viscoelasticity. As our main result we show that a solution u which is Hadamard stable at all times is unique; 1 or equivalently, that this type of stability precludes bifurcation. Hadamard stability at a given time t is defined in terms of the instantaneous elasticity tensor DS(Vu t) for the history Vu t, and is, in fact, the assertion that for some tc > 0,
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A. On the modified Bessel functions of the first kind: We consider the functions v (t) t I (t) / I + 1 (t) where I are the modified Bessel functions of the first kind of order 0. We prove that v is strictly monotone and strictly convex on... more
A. On the modified Bessel functions of the first kind: We consider the functions v (t) t I (t) / I + 1 (t) where I are the modified Bessel functions of the first kind of order 0. We prove that v is strictly monotone and strictly convex on R+. These results have application in finite elasticity. B. On barrelling for a material in finite elasticity: In this paper we investigate the question of stability for a solid circular cylinder, composed of a particular homogeneous isotropic (compressible) nonlinearly elastic material, that is subjected to compressive end forces in the direction of its axis (so as to give fixed axial displacements at the ends)
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We investigate the relation between stability and continuous dependence for a nonlinearly elastic body at equilibrium. We show that solutions of the governing equations that lie in a convex, stable set of deformations depend continuously... more
We investigate the relation between stability and continuous dependence for a nonlinearly elastic body at equilibrium. We show that solutions of the governing equations that lie in a convex, stable set of deformations depend continuously on the body forces and the surface tractions. The definition of stability used is essentially due to Hadamard.