Edvige Pucci

A Note on the Gent Model for Rubber-Like Materials

Abstract We consider the strain energy recently proposed, on a phenomenological basis by Alan Gent to take into account limiting chain extensibility in rubber-like materials. We show that this mode...

On the reduction methods for ordinary differential equations

As tandard method based on the use of differential invariants of a Lie group, G ,e nables us to reduce any ordinary differential equation invariant under the action of G .W e show that this method is applicable to vector fields more general than those associated with Lie symmetries. We characterize all such vector fields and study their relationship with nonlocal symmetries and λsymmetries (Govinder K S and Leach P G L 1995 J. Phys. A: Math. Gen. 28 5349–59, Muriel C and Romero L 2001 IMA J. Appl. Math. 66 111–25).

Evolution equations, invariant surface conditions and functional separation of variables

Abstract This paper is devoted to a discussion of the reduction methods for evolution equations based on invariant surface conditions related to functional separation of variables. The relationship of these methods with nonclassical and weak point symmetries is stressed. Applications to diffusion equations with an inhomogeneous reaction term or with saturating dissipation are provided.

On the weak symmetry groups of partial differential equations

Abstract We define an algorithm to characterize all weak symmetry groups of a partial differential equation. New invariant solutions to the Fokker-Planck equation are found.

Group properties of a class of semilinear hyperbolic equations

Abstract We present the results of a systematical investigation of invariance properties of a semilinear hyperbolic equation u xt = ƒ(u) , under a one-parameter Lie group of transformations, for arbitrary ƒ(u). The infinitesimals, resulting generators of the Lie algebra, and ordinary differential equations determining invariant solutions, are determined.

Universal Relations in Constrained Elasticity

New universal relations for nonlinear isotropic materials with internal isotropic constraints are found. It is also shown that two families of nonhomogeneous deformations, with constant principal invariants, are universal solutions for all materials in the above-mentioned class.

Symmetries and conservation laws in micropolar elasticity

Abstract In this paper, following the lines of a Noethers theorem, is established the complete set of generators of conservation laws related to geometric symmetries for linear theory of isotropic micropolar elastostatic.

On a Special Class of Nonlinear Viscoelastic Solids

We investigate some possible nonlinear generalizations of the Kelvin—Voigt viscoelastic models. We use the usual idealization of creep and recovery experiments to discuss the mechanical significance of some constitutive requirements and we show that in the case of a shear-rate dependent viscosity localization of the solution is possible under a simple constitutive characterization.

On the controllable states of elastic dielectrics and magnetoelastic solids

Abstract We prove that the controllable states for the models of Elastic Dielectrics and Magnetoelastic Solids proposed by Eringen and Maugin can be derived from the catalog of controllable states of the Singh and Pipkin theory of Elastic Dielectrics.

Universal motions for constrained simple materials

Abstract The problem of universal motions of a uniform and isotropic simple material subject to a generic isotropic internal constraint is studied. Complete results are achieved for motions with space-dependent strain invariants. As an application, free oscillations of an elastic Bell-constrained spherical shell are investigated.