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This essay is dedicated with gratitude and esteem to Mike Hayes who introduced me to the wonderful and powerful world of bivectors. Abstract: A homogeneous isotropic incompressible viscoelastic material of [...]

Structure evolution during deformation of isotropic auxetic foams is investigated by simple compression experiments. It is shown that the main feature observed in the experimental data can be accurately described by an isotropic hyperelastic model with an Ogden-type strain energy function. The model can be easily implemented in a finite element code and, hence, can be used to simulate foams undergoing complex structural deformations. [ABSTRACT FROM AUTHOR]

We re-examine the Love equation , which forms the first historical attempt at improving on the classical wave equation to encompass for dispersion of longitudinal waves in rods. Dispersion is introduced by accounting for lateral inertia through the Love hypothesis. Our aim is to provide a rigorous justification of the Love hypothesis , which may be generalized to other contexts. We show that the procedure by which the Love equation is traditionally derived is misleading: indeed, proper variational dealing of the Love hypothesis in a two-modal kinematics (the Mindlin–Herrmann system) leads to the Bishop–Love equation instead. The latter is not asymptotically equivalent to the Love equation, which is in fact a long wave low frequency approximation of the Pochhammer–Chree solution. However, the Love hypothesis may still be retrieved from the Mindlin–Herrmann system, by a slow-time perturbation process. In so doing, the linear KdV equation is retrieved. Besides, consistent approximation demands that a correction term be added to the classical Love hypothesis. Surprisingly, in the case of isotropic linear elasticity, this correction term produces no effect in the correction term of the Lagrangian, so that, to first order, the same Bishop–Love equation is the Euler–Lagrange equation corresponding to a family of Love-like hypotheses, all being different by the correction term. Besides, ill-posedness coming from non-standard (namely non static) natural boundary conditions is now amended. • Variational derivation through the Love hypothesis leads to the Bishop–Love equation. • This is not asymptotically equivalent to the Love equation. • The Love hypothesis naturally emerges from a two-modal kinematics by multiscale analysis. • This approach provides a correction term of the same order as that in the Love equation. • The traditional ill-posedness coming from nonstandard boundary conditions is remedied. [ABSTRACT FROM AUTHOR]

A new modelling approach is employed in this work for application to the rate-dependent mechanical behaviour of the brain tissue, as an incompressible isotropic material. Extant datasets encompassing single- and multi-mode compression, tension and simple shear deformation(s) are considered, across a wide range of deformation rates from quasi-static to rates akin to blast loading conditions, in the order of 1000 s−1. With a simple functional form and a reduced number of parameters, the model is shown to capture the considered rate-dependent behaviours favourably, including in both single- and multi-mode deformation fits, and over all range of deformation rates. The provided modelling results here are obtained from either first fitting the model to the quasi-static data, or/and predicting the behaviour at a different rate than those used for calibrating the model parameters. Given its simplicity, versatility, predictive capability and accuracy, the application of the utilised modelling framework in this work to the rate-dependent mechanical behaviour of the brain tissue is proposed. [ABSTRACT FROM AUTHOR]

We consider nonclassical symmetries of partial differential equations (PDEs) in 1+1 dimensions. Given a nth‐order ordinary differential equation G=0 in the unknown w=w(z) we are able to find the most general scalar PDE of a given order which can be reduced via a nonclassical symmetry to G=0. [ABSTRACT FROM AUTHOR]

The propagation of localised (in space-time) waves is analysed in the context of the dynamic theory of incompressible hyperelastic solids subject to body forces corresponding to a dual power-law substrate potential. A broad class of exact solutions is obtained which, under the assumption of slow modulation, incorporates Helmholtz-type solitary waves. The linear stability of these solutions is studied under the assumption that the speed of propagation of the wave is small enough compared to the speed at which transverse waves travel in the linear regime and in the absence of external actions. [ABSTRACT FROM AUTHOR]

In the framework of linear transversely isotropic elasticity, we study the deformation of a circular infinite hollow cylinder, whose inner face is fixed, while its outer surface is subject to a constant axial surface traction. In isotropic linear elasticity, the solution of this problem is just a state of anti-plane axial shear. In the case of a transversely isotropic material with a chosen arrangement of fibers, the corresponding deformation field becomes more complex and the coupling of axial anti-plane shear with an in-plane deformation may occur. Therefore, it is possible to use an axial tension field to generate, for example, an azimuthal shear deformation. This fact suggests to use anisotropy to design some elastic machines which can combine different deformation modes. [ABSTRACT FROM AUTHOR]