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Journals and Conferences
where ν denotes the outer unit normal to ∂Ω. So far, many papers have been written on the existence and multiplicity of solutions for second order elliptic problems with Dirichlet boundary conditions, especially by means of variational methods. In particular, if Ω ⊂ R (n 3) is a smooth bounded domain, φ ∈ L(Ω) and 2 < σ < 2n n−2 , the following model… (More)
It is well-known that the modelization of interactions in Continuum Physics deals with set functions associated with physical quantities rather than with functions evaluated at single points (see e.g. ). Very important examples of these are the stress and the heat flux. This, in turn, implies that the concept of subbody of a material body B has to be… (More)
An approach to weak balance laws in Continuum Mechanics is presented, involving densities with only divergence measure, which relies on the balance of power. An equivalence theorem between Cauchy powers and Cauchy fluxes is proved. As an application of this method, the construction of the stress tensor when the body is an orientable differential manifold is… (More)
Abstract. By means of balanced virtual powers, an axiomatic approach is developed, in the spirit of Noll, to second-gradient continua. The measure-theoretical formulation allows a considerable simplification since the existence of an edge stress density is regarded as a special case of a surface stress which is a singular measure with respect to the area.… (More)
In this paper we reconsider the standard formulation of the Second Law of Thermodynamics in the general framework of fields with divergence measure, using Geometric Measure Theory and some recent results on Cauchy interactions. To our knowledge, the first attempt to put the Second Law of Thermodynamics within the framework of Geometric Measure Theory is… (More)
A weak formulation of the stress boundary conditions in Continuum Mechanics is proposed. This condition has the form of a balance law, allows also singular measure data and is consistent with the regular case. An application to the Flamant solution in linear elasticity is shown. Mathematics Subject Classifications (2000): 74A10, 74G70.
In this paper we deal with the study of limits of solutions of a class of fully nonlinear elliptic problems at nearly critical growth. By means of P.L. Lions’ concentrationcompactness principle, we prove an alternative result for the existence of non-trivial solutions of the limit problem.
The Cauchy Stress Theorem is proved for bodies which has finite perimeter, without extra topological assumptions, and the notions of Cauchy flux and Cauchy interaction are extended to this case. Also bodies with an empty interior can be considered.
We present a continuum model for the mechanical behavior of the skeletal muscle tissue when its functionality is reduced due to aging. The loss of ability of activating is typical of the geriatric syndrome called sarcopenia. The material is described by a hyperelastic, polyconvex, transverse isotropic strain energy function. The three material parameters… (More)