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In this paper we are interested in developing constitutive equations for fiber-reinforced nonlinearly viscoelastic solids. It has been shown that constitutive equations for such bodies can be expressed in terms of a complete minimal set of 18 classical invariants associated with deformation and fiber orientation. In this paper, we give an alternative formulation using a set of spectral invariants. It is shown via the use of spectral invariants that only 11 of the 18 classical invariants are independent. We analyze the spectral invariants for two illustrative deformation gradients: (i) simple tension, and (ii) simple shear. [ABSTRACT FROM AUTHOR]

In this work a new set of principal axis invariants is proposed in order to study the problem of considering large magneto-elastic deformations, for bodies that are isotropic in the un-deformed configuration when no external magnetic induction is applied. The new set of invariants has clear physical meanings and may have an experimental advantage over the standard invariants used in many previous works in this area. The principal axis invariant formulation is also shown to be more general. Some simple boundary value problems are solved, such as the simple shear, and the biaxial extension of a slab, where with the use of these new invariants, it is possible to study in a much simpler manner the effect of different types of deformations on the response of the material. An illustrated simple specific constitutive equation is proposed which compares well with experiment. [ABSTRACT FROM AUTHOR]

Abstract: A variational formulation for an electro-elastic body surrounded by free space in the context of large and nonlinear elastic deformations is developed. The functional depends on the deformation function and the electric scalar potential. The approach presented here introduces an alternative expression for the energy stored by the exterior free space, which is intended to facilitate the (in general troublesome) calculations of the first and the second variations of the functional. [Copyright &y& Elsevier]

Abstract: A constitutive framework for electro-sensitive materials in the context of non-linear elasticity is analyzed. Constitutive equations are given in terms of energy functions that depend on several invariants. The study includes both the analysis of the invariants, which are present in the energy functions, and the analysis of constitutive restrictions that have to be obeyed by the constitutive functions. Isotropic as well as non-isotropic electro-sensitive elastomers are studied. The set of invariants that describe each material model is analyzed under two homogeneous deformations: (i) an uniaxial elongation and (ii) a simple shear deformation. These deformations are chosen since they are relevant to specific experiments, from which one may try to fit constitutive equations. The constitutive restrictions developed are based on classical ones used for isotropic non-linear elastic materials, in particular, are based on the Baker–Ericksen inequality and the ellipticity condition. [Copyright &y& Elsevier]

Abstract: This paper provides examples of the numerical solution of boundary-value problems in nonlinear magnetoelasticity involving finite geometry based on the theoretical framework developed by Dorfmann and co-workers. Specifically, using a prototype constitutive model for isotropic magnetoelasticity, we consider two two-dimensional problems for a block with rectangular cross-section and of infinite extent in the third direction. In the first problem the deformation induced in the block by the application of a uniform magnetic field far from the block and normal to its larger faces without mechanical load is examined, while in the second problem the same magnetic field is applied in conjunction with a shearing deformation produced by in-plane shear stresses on its larger faces. For each problem the distribution of the magnetic field throughout the block and the surrounding space is illustrated graphically, along with the corresponding deformation of the block. The rapidly (in space) changing magnitude of the magnetic field in the neighbourhood of the faces of the block is highlighted. [Copyright &y& Elsevier]

Abstract: Some simple boundary value problems are studied, for a new class of elastic materials, wherein deformations are expressed as non-linear functions of the stresses. Problems involving ‘homogeneous’ stress distributions and one-dimensional stress distributions are considered. For such problems, deformations are calculated corresponding to the assumed stress distributions. In some of the situations, it is found that non-unique solutions are possible. Interestingly, non-monotonic response of the deformation is possible corresponding to monotonic increase in loading. For a subclass of models, the strain–stress relationship leads to a pronounced strain-gradient concentration domain in the body in that the strains increase tremendously with the stress for small range of the stress (or put differently, the gradient of the strain with respect to the stress is very large in a narrow domain), and they remain practically constant as the stress increases further. Most importantly, we find that for a large subclass of the models considered, the strain remains bounded as the stresses become arbitrarily large, an impossibility in the case of the classical linearized elastic model. This last result has relevance to important problems in which singularities in stresses develop, such as fracture mechanics and other problems involving the application of concentrated loads. [ABSTRACT FROM AUTHOR]