Si dimostra che ci sono valide ragioni per considerare la teoria standard dei vincoli interni, nella meccanica dei continui, insufficientemente generale. In particolare, con l’unica eccezione dell’iperelasticità, l’extra-stress dovrebbe dipendere anche dai moltiplicatori di Lagrange, cioè, dallo stress che non effettua lavoro (virtuale).

The paper deals with approximations and the numerical realization of a class of hemivariational inequalities used for modeling of delamination and nonmonotone friction problems. Assumptions guaranteeing convergence of discrete models are verified and numerical results of several model examples computed by a nonsmooth variant of Newton method are presented.

Rock bolts as construction elements are often used in underground civil engineering projects. This work deals with their numerical modelling. Aydan special finite elements for the description of rock bolts and hexahedral quadratic finite elements for the description of rock massif were used. A code for the computation of stiffness matrices and right hand sides of these elements was developed. The code was tested on several simple test examples and their results were compared with the analytical...

The main goal of the paper is to describe a reinforcement consisting of fully grouted bolts, which is applied to stabilizing underground openings and tunnels. After a variational formulation is given, the existence and uniqueness is proved. Some asymptotic results that make it possible to replace the real system with a continuous one more suitable for discretization are presented. Some other types of reinforcements and properties are studied.

In this paper we prove existence, uniqueness, and continuous dependence for a one-dimensional time-dependent problem related to a thermo-mechanical model of structural phase transitions in solids. This model assumes the free energy depending on temperature, macroscopic deformation and also on the proportions of the phases. Here we neglect regularizing terms in the momentum balance equation and in the constitutive laws for the phase proportions.

In this paper we prove that every weak and strong local minimizer $u\in W^{1,2}(\Omega ,{ℝ}^3)$ of the functional $I\left(u\right)={\int }_{\Omega }{\left|Du\right|}^2+f\left(\mathrm{Adj}Du\right)+g\left(\det Du\right),$ where $u:\Omega \subset {ℝ}^3\to {ℝ}^3$, f grows like ${\left|\mathrm{Adj}Du\right|}^p$, g grows like ${\left|\det Du\right|}^q$ and 1<q<p<2, is $C^{1,\alpha }$ on an open subset ${\Omega }_0$ of Ω such that $\mathrm{𝑚𝑒𝑎𝑠}(\Omega \setminus {\Omega }_0)=0$. Such functionals naturally arise from nonlinear elasticity problems. The key point in order to obtain the partial regularity result is to establish an energy estimate of Caccioppoli type, which is based on an appropriate choice of the test functions. The limit case $p=q\le 2$ is also treated for weak local minimizers. ...

Si affronta il problema del calcolo dello stato tensionale in strutture costituite da materiale non resistente a trazione ed elastico lineare a compressione. Si formula la legge costitutiva e se ne fornisce l'espressione esplicita nel caso di stati tensionali monoassiali, biassiali e triassiali. Si imposta quindi il problema dell'equilibrio elastico e si discute sulla condizione da imporre ai carichi affinché venga assicurata l'esistenza della soluzione. Si sviluppa la formulazione agli elementi...

This paper is a survey of articles [5, 6, 8, 9, 13, 17, 18]. We are interested in the influence of small geometrical perturbations on the solution of elliptic problems. The cases of a single inclusion or several well-separated inclusions have been deeply studied. We recall here techniques to construct an asymptotic expansion. Then we consider moderately close inclusions, i.e. the distance between the inclusions tends to zero more slowly than their characteristic size. We provide a complete asymptotic...