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We obtain the minimal energy solution of the Plateau problem with elastic boundary as a variational limit of the minima of the Kirchhoff-Plateau problems with a rod boundary when the cross-section of the rod vanishes. The limit boundary is a framed curve that can sustain bending and twisting.

We present a continuum hyperelastic model which describes the mechanical response of a skeletal muscle tissue when its strength and mass are reduced by aging. Such a reduction is typical of a geriatric syndrome called sarcopenia. The passive behavior of the material is described by a hyperelastic, polyconvex, transversely isotropic strain energy function, and the activation of the muscle is modeled by the so called active strain approach. The loss of ability of activating of an elder muscle is then obtained by lowering of some percentage the active part of the stress, while the loss of mass is modeled through a multiplicative decomposition of the deformation gradient. The obtained stress-strain relations are graphically represented and discussed in order to study some of the effects of sarcopenia.

We study a simplified version of a class of constitutive relations used to describe large deformations of soft tissues, where the elastic energy density involves an exponential term. The class was originally introduced by Y.C. Fung as a model of many biological soft tissues in a series of papers during the Seventies. We prove existence and uniqueness of the equilibrium solution for a general measure-valued external load, under quite general boundary conditions, and study the validity of the associated Euler–Lagrange equation in the sense of distributions.

Lake Garda, the largest lake in Italy at the southern front of the central Alps, provides a unique opportunity to reconstruct Quaternary geological processes related to the interplay between deglaciation driven sedimentation and tectonic activity. In fact, the topographic depression presently occupied by the lake was site of a major glacial tongue during the LGM, and is located close to the epicentral areas of two of the largest magnitude historical earthquakes recorded in the Po Plain, the Verona (Jan. 13, 1117) and Brescia, (Dec. 25, 1222) seismic events, characterized by Io IX-X MCS, respectively. Despite this peculiarity, geophysical surveys of the lake are scant. We present results of a waterborne geophysical survey of Lake Garda, leading to the acquisition of a densely-spaced grid of high-resolution seismic reflection profiles which image the lake floor and uppermost sedimentary sequence. These data enabled us to compile thematic maps which provide insights on active geologic processes in different sectors of the basin. We focused our work on a prominent seismic reflector (H1), correlated over the entire lake surface, to estimate the sediment deposition rate at the scale of the last 10 ka, and to evaluate the variability of seismic facies and geological processes in different sectors of the basin. Based on available stratigraphic data, we discuss whether H1 could mark the diachronic glacial/fluvio-glacial transition after the Last Glacial Maximum, when the ice tongues south of the Alps started to melt and collapse. We observed that sediments of the southern Lake Garda are affected by incipient tectonic deformation, and two major seismoturbidite-homogenite beds might represent over 50% of the Holocene sedimentary record in the lake depocenter, making the study of the Lake Garda stratigraphy an interesting tool for assessing earthquake hazards at the southern front of the Alpine chain.

We study the equilibrium problem of a system consisting of several Kirchhoff rods linked in an arbitrary way and tied by a soap film, using techniques of the Calculus of Variations. We prove the existence of a solution with minimum energy, which may be quite irregular, and perform experiments confirming the kind of surface predicted by the model.

We introduce a model of fluid which has four main features: it readily emerges by a general continuum mechanical framework; it is a generalization maintaining most of the physical features of incompressible Newtonian fluids; it can model adherence interactions with one-dimensional structures surrounded by the fluid; the associated initial boundary-value problem is well-posed on three-dimensional domains. © 2010 Springer-Verlag.

We give a general formulation of the Principle of virtual powers in Continuum Mechanics from a distributional point of view, and study some of its relevant consequences in the field of balance equations. Keywords: Virtual Powers, Contact Interactions, Balance Equations Mathematics Subject Classification (2000): 74A10, 74G70, 74A30, 74A60

A weak formulation of the stress boundary conditions in Continuum Mechanics is pro- posed. 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.

Balance laws of the type of entropy are treated in the framework of geometric measure theory, and a weak version, although conceptually simple, of the Second Law of Thermodynamics is introduced, allowing extensions to measure-valued entropy productions and to sets of finite perimeter as subbodies.

In this paper we study the long time behaviour of dynamical systems acting in topological spaces. We give suitable definitions of attractivity and prove some properties of limit sets, as well as theorems on existence of attractors in the class of regular spaces.

In this paper we investigate the asymptotic behavior, as time tends to infinity, of the solutions of an non-autonomous integro-partial differential equation describing the heat flow in a rigid heat conductor with memory. Existence and uniqueness of solutions is provided. Moreover, under proper assumptions on the heat flux memory kernel and on the magnitude of nonlinearity, the existence of uniform absorbing sets and of a global uniform attractor is achieved. In case of quasiperiodic dependence of time of the external heat supply, the above attractor is shown to have finite Hausdorff dimension.

We consider the free fall of slender rigid bodies in a viscous incompressible fluid. We show that the dimensional reduction (DR), performed by substituting the slender bodies with one-dimensional rigid objects, together with a hyperviscous regularization (HR) of the Navier--Stokes equation for the three-dimensional fluid lead to a well-posed fluid-structure interaction problem. In contrast to what can be achieved within a classical framework, the hyperviscous term permits a sound definition of the viscous force acting on the one-dimensional immersed body. Those results show that the DR/HR procedure can be effectively employed for the mathematical modeling of the free fall problem in the slender-body limit., Comment: arXiv admin note: substantial text overlap with arXiv:1305.0707

A “saddle point” (or maximum-minimum) principle is set up for the quasi-static boundary-value problem in linear viscoelasticity. The appropriate class of convolution-type functionals for it is taken in terms of bilinear forms with a weight function involving the Fourier transform. The “minimax” property is shown to hold as a direct consequence of thermodynamic restrictions on the relaxation function. This approach can be extended to further linear evolution problems where initial data are not prescribed.

1 Dipartimento di Matematica e Fisica, Universita Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy m.degiovanni@dmf.unicatt.it 2 Dipartimento di Matematica, Universita di Brescia, Via Valotti 9, I-25133 Brescia, Italy alfredo.marzocchi@ing.unibs.it 3 Dipartimento di Matematica e Fisica, Universita Cattolica del Sacro Cuore, Via dei Musei 41, I-25121 Brescia, Italy a.musesti@dmf.unicatt.it

This paper is devoted to existence, uniqueness and asymptotic behavior, as time tends to infinity, of the solutions of an integro-partial differential equation arising from the theory of heat conduction with memory, in presence of a temperature-dependent heat supply. A linearized heat flux law involving positive instantaneous conductivity is matched with the energy balance, to generate an autonomous semilinear system subject to initial history and Dirichlet boundary conditions. Existence and uniqueness of solution is provided. Moreover, under proper assumptions on the heat flux memory kernel, the existence of absorbing sets in suitable function spaces is achieved.

Cauchy fluxes induced by locally summable tensor fields with divergence measure are characterized. The equivalence between integral formulations involving subsets of finite perimeter and much more restricted classes of subsets is proved.