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A general structure for space-time that preserves the classical notion of absolute time, and to which we refer as Proto-Galilean space-time, is presented. In this setting, space-time is modeled as a general fiber bundle over the time axis. The motion of a particle is a section of the fiber bundle. A recent framework for continuum mechanics, where configurations are represented by sections of a fiber bundle over the body manifold, is used to formulate the dynamics of a particle and the dynamics of a continuous body in a Proto-Galilean space-time. [ABSTRACT FROM AUTHOR]

In the original paper, we erroneously used the total potential energy (Helmholtz free energy of the material plus potential energy of the external forces) in the entropy inequality. [ABSTRACT FROM AUTHOR]

Inspired by the seminal works of Eshelby (Philos Trans R Soc A 244A:87–112, 1951, J Elast 5:321–335, 1975) on configurational forces and of Noll (Arch Ration Mech Anal 27:1–32, 1967) on material uniformity, we study a thermoelastic continuum undergoing volumetric growth and in a dynamical setting, in which we call the divergence of the Eshelby stress the Eshelby force. In the classical statical case, the Eshelby force coincides with the negative of the configurational force. We obtain a differential identity for the modified Eshelby stress, involving the torsion of the connection induced by the material isomorphism of a uniform body, which includes, as a particular case, that found by Epstein and Maugin (Acta Mech 83:127–133, 1990). In this identity, the divergence of the modified Eshelby stress with respect to this connection of the material isomorphism takes the name of modified Eshelby force. Moreover, we show that Eshelby's variational approach (1975) can be used to formulate not only the balance of material momentum, but also the balance of energy. In this case, we find that what we call Eshelby power is the temporal analogue of the Eshelby force, and we obtain a differential identity for the modified Eshelby power. This leads to concluding that the driving force for the process of growth–remodelling is the Mandel stress. Eventually, we find that the relation between the differential identities for the modified Eshelby force and modified Eshelby power represents the mechanical power expended in a uniform body to make the inhomogeneities evolve. [ABSTRACT FROM AUTHOR]

Walter Noll's trailblazing constitutive theory of material defects in smoothly uniform bodies is recast in the language of Lie groupoids and their associated Lie algebroids. From this vantage point the theory is extended to non-uniform bodies by introducing the notion of singular material distributions and the physically cognate idea of graded uniformity and homogeneity. [ABSTRACT FROM AUTHOR]

Self-diffusion, or the flux of mass of a single species within itself, is viewed as an independent phenomenon amenable to treatment by the introduction of an auxiliary field of diffusion velocities. The theory is shown to be heuristically derivable as a limiting case of that of an ordinary binary mixture. [ABSTRACT FROM AUTHOR]

Studies of solitary waves commonly apply the long-wave approximation, which unnecessarily rigidifies the behavior of the tube, but permits the problem to be solved using certain approximate numerical techniques. In this study, an approach was developed where approximating the contribution of the axial strain as a linear function of the radial strain reduced the system of exact governing differential equations to a single equation of a single dependent variable. The approximated solution was found to agree with the exact solution to within 3%. This approach would be useful for considering more complex problems where the exact solution technique may not be reasonably applied. [ABSTRACT FROM AUTHOR]

For evolutionary processes of material remodelling and growth, a comparison is drawn between a conventional formulation and one that postulates the existence of additional balance laws for the configurational forces. [ABSTRACT FROM AUTHOR]

Nonlinear waves are investigated numerically by a direct analysis of the field equations, thereby establishing the magnitude of the errors inherent in the commonly used reductive perturbation technique. The method is also applied beyond the long-wave approximation and a comparative assessment of the results obtained is presented. [ABSTRACT FROM AUTHOR]

The existence and uniqueness of a relaxed energy function for anisotropic elastic membranes is established. It is shown that the extra strains during wrinkling abide by a normality rule akin to that of metal plasticity, and that throughout such wrinkling processes both the strain energy and the Piola-Kirchhoff stresses remain constant. [ABSTRACT FROM AUTHOR]

The problem of the propagation and decay of acceleration waves in nonlinear hyperelastic rods, subject to a general class of constraints, is treated herein. The growth-decay equation, clearly showing the effect of the constraints, is derived for all waves which can propagate in the rod. For a certain class of constraints, general enough to include most of the practical applications, the wave decay equation is found to have the same form as for a rod without constraints, provided the rod is initially at rest. [ABSTRACT FROM AUTHOR]