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A study of dynamic crack growth in elastic materials using a cohesive zone model
Abstract The problem of a semi-infinite mode III crack dynamically propagating in a two-dimensional linear elastic infinite body is considered. The crack tip is assumed to be a cohesive zone whoseExpand
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Dependence of the Frequency Spectrum of Small Amplitude Vibrations Superimposed on Finite Deformations of a Nonlinear, Cylindrical Elastic Body on Residual Stress
We model and analyze the response of nonlinear, residually stressed elastic bodies subjected to small amplitude vibrations superimposed upon large deformations. The problem derives from modeling theExpand
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On strong ellipticity for isotropic hyperelastic materials based upon logarithmic strain
Abstract This paper discusses various constitutive restrictions on the strain energy function for an isotropic hyperelastic material derived from the condition of strong ellipticity. The strainExpand
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A mathematical model of atherogenesis as an inflammatory response.
We construct a mathematical model of the early formation of an atherosclerotic lesion based on a simplification of Russell Ross' paradigm of atherosclerosis as a chronic inflammatory response.Expand
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Sufficient conditions for strong ellipticity for a class of anisotropic materials
We provide sufficient conditions for strong ellipticity for a general class of anisotropic hyperelastic materials. This general class includes as a subclass transversely isotropic materials. OurExpand
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A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale
In this paper we focus on the analysis of the partial differential equations arising from a new approach to modeling brittle fracture based on an extension of continuum mechanics to the nanoscale. ItExpand
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The Dynamic Energy Release Rate for a Steadily Propagating Mode I Crack in an Infinite, Linearly Viscoelastic Body
The material is assumed to have a constant Poisson's ratio, but the shear modulus is only assumed to be decreasing and convex. An expression for the Stress Intensity Factor is derived for veryExpand
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The Convexity Properties of a Class of Constitutive Models for Biological Soft Issues
During the last three decades, the theory of nonlinear elasticity has been used extensively to model biological soft issues. Although this research has generated many different models to describe theExpand
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Modeling fracture in the context of a strain-limiting theory of elasticity: a single anti-plane shear crack
This paper is the first part of an extended program to develop a theory of fracture in the context of strain-limiting theories of elasticity. This program exploits a novel approach to modeling theExpand
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A Theory of Fracture Based Upon an Extension of Continuum Mechanics to the Nanoscale
A theory of fracture is presented that is based upon an extension of continuum mechanics to the nanoscale through the incorporation of long-range intermolecular forces which correct bulk materialExpand
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