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).
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
We develop a functional analytical framework for a linear peridynamic model of a spring network system in any space dimension. Various properties of the peridynamic operators are examined for general micromodulus functions. These properties are utilized to establish the well-posedness of both the stationary peridynamic model and the Cauchy problem of the time dependent peridynamic model. The connections to the classical elastic models are also provided.
The swelling and shrinkage of biological tissues are modelled by a four-component mixture theory in which a deformable and charged porous medium is saturated with a fluid with dissolved ions. Four components are defined: solid, liquid, cations and anions. The aim of this paper is the construction of the Lagrangian model of the four-component system. It is shown that, with the choice of Lagrangian description of the solid skeleton, the motion of the other components can be described in terms of...
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...
We present a mesh adaptation method by node movement for two-dimensional linear elasticity problems with unilateral contact. The adaptation is based on a hierarchical estimator on finite element edges and the node displacement techniques use an analogy of the mesh topology with a spring network. We show, through numerical examples, the efficiency of the present adaptation method.
For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of ; the minimizer is and is such that vanishes at one point.
For a class of 2-D elastic energies we show that a radial equilibrium solution is the unique global minimizer in a subclass of all admissible maps. The boundary constraint is a double cover of S1; the minimizer u is C1 and is such that vanishes at one point.
A mixed formulation is given for elastic problems. Existence and uniqueness of the discretized problem are given for conformal continuous interpolations for the stress tensor components and for the components of the displacement vector. A counterpart of the problem is discussed in the case of an even-dimensional Euclidean space with an associated Hamiltonian vector field and the Poisson structure. For conformal interpolations of the same order the question remains open.
In this paper we prove that every weak and strong local minimizer of the functional where , f grows like , g grows like and 1<q<p<2, is on an open subset of Ω such that . 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 is also treated for weak local minimizers. ...
This paper is devoted to several applications of morphological analysis applied to the bounding of the overall behaviour of composite materials. In particular we focus our attention to the generalization of the Hashin-Shtrikmann variational principles to thermoelasticity.