The large deformation of nonlinearly elastic shells in axisymmetric flows
The method of fictitious domains in the Signorini problem.
The null condition and global existence of nonlinear elsastic waves.
The Numerical Computation of Compressed States of Nonlinearly Elastic Anisotropic Plates.
The problem of dynamic cavitation in nonlinear elasticity
The notion of singular limiting induced from continuum solutions (slic-solutions) is applied to the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of entropic weak solutions (with polyconvex energy) due to a forming cavity.
The relaxation of the Signorini problem for polyconvex functionals with linear growth at infinity
The aim of this paper is to study the unilateral contact condition (Signorini problem) for polyconvex functionals with linear growth at infinity. We find the lower semicontinuous relaxation of the original functional (defined over a subset of the space of bounded variations BV(Ω)) and we prove the existence theorem. Moreover, we discuss the Winkler unilateral contact condition. As an application, we show a few examples of elastic-plastic potentials for finite displacements.
The solution of inverse nonlinear elasticity problems that arise when locating breast tumours.
Time-dependent invariant regions for parabolic systems related to one- dimensional nonlinear elasticity
A parabolic system arisng as a viscosity regularization of the quasilinear one-dimensional telegraph equation is considered. The existence of - a priori estimates, independent of viscosity, is shown. The results are achieved by means of generalized invariant regions.
Un problema di ostacolo elastico non lineare per la piastra incastrata
Si formula il problema della piastra su mezzo elastico con riferimento ad una particolare modellazione del comportamento di tale mezzo. Si ipotizza infatti una natura unilaterale del contatto tra la piastra, supposta sottile e linearmente elastica, ed il mezzo di fondazione (od ostacolo), per il quale si ipotizza un legame cubico tra spostamenti e reazioni. Tale modello costituisce una generalizzazione di quello ben noto di Winkler e si presta alla descrizione approssimata di numerosi casi della...
Una caratterizzazione variazionale della vorticità
Une justification d'un modèle non linéaire en théorie des plaques
Une méthode numérique pour les problèmes d'équilibre de corps hyperélastiques compressibles en grandes déformations.
Unexpected solutions of first and second order partial differential equations.
Unilateral elastic subsoil of Winkler's type: Semi-coercive beam problem
The mathematical model of a beam on a unilateral elastic subsoil of Winkler's type and with free ends is considered. Such a problem is non-linear and semi-coercive. The additional assumptions on the beam load ensuring the problem solvability are formulated and the existence, the uniqueness of the solution and the continuous dependence on the data are proved. The cases for which the solutions need not be stable with respect to the small changes of the load are described. The problem is approximated...
Unique global solvability of 1D Fried-Gurtin model
We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified assumptions...
Variational-hemivariational inequalities in nonlinear elasticity. The coercive case
Existence of a solution of the problem of nonlinear elasticity with non-classical boundary conditions, when the relationship between the corresponding dual quantities is given in terms of a nonmonotone and generally multivalued relation. The mathematical formulation leads to a problem of non-smooth and nonconvex optimization, and in its weak form to hemivariational inequalities and to the determination of the so called substationary points of the given potential.
Von Kármán equations. III. Solvability of the von Kármán equations with conditions for geometry of the boundary of the domain
Solvability of the general boundary value problem for von Kármán system of nonlinear equations is studied. The problem is reduced to an operator equation. It is shown that the corresponding functional of energy is coercive and weakly lower semicontinuous. Then the functional of energy attains absolute minimum which is a variational solution of the problem.
Деформирование структурно- неоднородного упругого полупространства
Исследование разрешимости задачи о сильном изгибе цилиндрической оболочки
Конечномерность аттрактора в некоторых задачах нелинейной теории оболочек