Browsing Mathematics by Title
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Hyperelastic and viscoelastic properties of brain tissue in tension
(ASME, 2012)Mechanical characterization of brain tissue at high loading velocities is particularly important for modelling Traumatic Brain Injury (TBI). During severe impact conditions, brain tissue experiences a mixture of compression, ... 
Improved mathematical and numerical modelling of dispersion of a solute from a continuous source
(2011)We present a refinement of a model due to Mondal and Mazumder [7] for dispersion of fine particles in an oscillatory turbulent flow. The model is based on the timedependent advectiondiffusion equation posed on a ... 
The incompressible limit in linear anisotropic elasticity, with applications to surface waves and elastostatics
(Elsevier, 2002)[no abstract available] 
Incremental equations for soft fibrous materials
(Springer, 2015)The general theory of nonlinear anisotropic elasticity is extended to describe smallamplitude motions and static deformations that can be superimposed on large prestrains of fibrereinforced solids. The linearised ... 
Incremental magnetoelastic deformations, with application to surface instability
(Springer, 200801)In this paper the equations governing the deformations of infinitesimal (incremental) disturbances superimposed on finite static deformation fields involving magnetic and elastic interactions are presented. The coupling ... 
An inductive approach to Coxeter arrangements and Solomon's descent algebra
(Springer Verlag, 20120720)In our recent paper (Douglass et al. arXiv: 1101.2075 (2011)), we claimed that both the group algebra of a finite Coxeter group W as well as the OrlikSolomon algebra of W can be decomposed into a sum of induced onedimensional ... 
Influence of initial residual stress on growth and pattern creation for a layered aorta
(Nature Research, 20190603)Residual stress is ubiquitous and indispensable in most biological and artificial materials, where it sustains and optimizes many biological and functional mechanisms. The theory of volume growth, starting from a stressfree ... 
Influence of preservation temperature on the measured mechanical properties of brain tissue
(Elsevier, 20130426)The large variability in experimentally measured mechanical properties of brain tissue is due to many factors including heterogeneity, anisotropy, age dependence and postmortem time. Moreover, differences in test protocols ... 
Inhomogeneous "longitudinal" circularlypolarized plane waves in anisotropic elastic crystals
(S. Hirzel verlag, Ingenta Connect, 2006)Conditions on the elastic stiffnesses of anisotropic crystals are derived such that circularly polarized longitudinal inhomogeneous plane waves with an isotropic slowness bivector may propagate for any given direction of ... 
Inhomogeneous "longitudinal" plane waves in a deformed elastic material
(Springer, 200501)By definition, a homogeneous isotropic compressible Hadamard material has the property that an infinitesimal longitudinal homogeneous plane wave may propagate in every direction when the material is maintained in a state ... 
Inhomogeneous deformation of brain tissue during tension tests
(Elsevier, 2012)Mechanical characterization of brain tissue has been investigated extensively by various research groups over the past 50 years. These properties are particularly important for modeling Traumatic Brain Injury (TBI). ... 
Inhomogeneous shear of orthotropic incompressible nonlinearly elastic solids: Singular solutions and biomechanical interpretation
(Elsevier, 2009)We present a detailed study of rectilinear shear deformation in the framework of orthotropic nonlinear elasticity, under Dirichlet and mixedboundary conditions. We take a slab made of a soft matrix, reinforced with two ... 
Initial stress symmetry and its applications in elasticity
(The Royal Society, 20151028)An initial stress within a solid can arise to support external loads or from processes such as thermal expansion in inert matter or growth and remodelling in living materials. For this reason, it is useful to develop a ... 
Initial stresses in elastic solids: Constitutive laws and acoustoelasticity
(2011)On the basis of the nonlinear theory of elasticity, the general constitutive equation for an isotropic hyperelastic solid in the presence of initial stress is derived. This derivation involves invariants that couple the ... 
Instabilities in elastomers and soft tissues
(Oxford Journals, 20060915)Biological soft tissues exhibit elastic properties that can be dramatically different from rubbertype materials (elastomers). To gain a better understanding of the role of constitutive relationships in determining material ... 
The integral homology of PSL(2) of imaginary quadratic integers with nontrivial class group
(2011)We show that a cellular complex defined by Flöge allows us to determine the integral homology of the Bianchi groups PSL(2)(O[m]), where O[m] is the ring of integers of an imaginary quadratic number field Q [square root ... 
Interface waves in misoriented prestressed incompressible elastic solids
(Oxford Journals, 20041217)Some relationships, fundamental to the resolution of interface wave problems, are presented. These equations allow for the derivation of explicit secular equations for problems involving waves localized near the plane ... 
Interface waves in prestressed incompressible solids
(Springer, 2007)We study incremental wave propagation for what is seemingly the simplest boundary value problem, namely that constitued by the plane interface of a semiinfinite solid. With a view to model loaded elastomers and soft ... 
Introduction to the special issue on stability under finite deformation
(Oxford University Press, 2010)In the botanical gardens of Grenoble, France, there is small bridge, just a few metres long, made of prestressed concrete. The bridge dates back to 1855 and is thought to be the oldest manufactured prestressed structure ... 
John Todd and the development of modern numerical analysis
(2012)The purpose of this article is to mark the centenary of the birth of John Todd, a pioneer in the fields of numerical analysis and computational science. A brief account is given of his early life and career, and that of ...