The mistaken notion that consistency with fading memory should require uniqueness is refuted by citation of the sources. Indeed, insistence on uniqueness would exclude many examples from non-linear elasticity and would exclude materials capable of exhibiting hysteresis.

In this paper we investigate the equivalence of the sequential weak lower semicontinuity of the total energy functional and the quasiconvexity of the stored energy function of the nonlinear micropolar elasticity. Based on techniques of Acerbi and Fusco [Arch. Rational Mech. Anal.86 (1984) 125–145] we extend the result from Tambača and Velčić [ESAIM: COCV (2008) DOI: 10.1051/cocv:2008065] for energies that satisfy the growth of order p≥ 1. This result is the main step towards the general existence...

The paper deals with the approximation of optimal shape of elastic bodies, unilaterally supported by a rigid, frictionless foundation. Original state inequality, describing the behaviour of such a body is replaced by a family of penalized state problems. The relation between optimal shapes for the original state inequality and those for penalized state equations is established.

The singularities occurring in any sort of ordering are known in physics as defects. In an organized fluid defects may occur both at microscopic (molecular) and at macroscopic scales when hydrodynamic ordered structures are developed. Such a fluid system serves as a model for the study of the evolution towards a strong disorder (chaos) and it is found that the singularities play an important role in the nature of the chaos. Moreover both types of defects become coupled at the onset of turbulence....

This paper presents the main concept and several key features of the user-defined interface of COMSOL Java API for the solution of mechanical problems in fractured rock. This commercial computational system based on FEM has yet to incorporate fractures in mechanical problems. Our aim is to solve a 2D mechanical problem with a fracture which is defined separately from finite-element discretization and the fracture properties are included through the constitutive laws. This will be performed based...

A problem of unilateral contact between an elasto-plastic body and a rigid frictionless foundation is solved within the range of the so called deformation theory of plasticity. The weak solution is defined by means of a variational inequality. Then the so called secant module (Kačanov's) iterative method is introduced, each step of which corresponds to a Signorini's problem of elastoplastics. The convergence of the method is proved on an abstract level.

Si considerano due spazi $S_{\mu }$ e $S_{\nu }^{\ast }$, Riemanniani e a metrica eventualmente indefinita, riferiti a sistemi di co-ordinate $\mathrm{\varnothing }$ e ${\mathrm{\varnothing }}_{\nu }^{\ast }$; e inoltre un doppio tensore $T_{\mathrm{\cdots }}^{\mathrm{\cdots }}$ associato ai punti ${\mathrm{\varnothing }}^{-1}(x)\in S_{\mu }$ e ${\mathrm{\varnothing }}^{\ast -1}(y)\in S^{\ast }$. Si pensa $T_{\mathrm{\cdots }}^{\mathrm{\cdots }}$ dato da una funzione ${\tilde{T}}_{\mathrm{\cdots }}^{\mathrm{\cdots }}$ di $m$ altri tali doppi tensori e di variabili puntuali $x(\in {\mathrm{\Re }}^{\mu })$, $t\in \mathrm{\Re }$ e $y(\in {\mathrm{\Re }}^{\nu })$; poi si considera la funzione composta $${\widehat{T}}_{\mathrm{\cdots }}^{\mathrm{\cdots }}(x,t,y)={\tilde{T}}_{\mathrm{\cdots }}^{\mathrm{\cdots }}[\underset{1,\mathrm{\dots },m}{\underbrace{{\breve{H}}_{\mathrm{\cdots }}^{\mathrm{\cdots }}(x,t,y),\mathrm{\dots },{\breve{H}}_{\mathrm{\cdots }}^{\mathrm{\cdots }}(x,t,y)}},x,t,y].$$ Nella Parte I si scrivono due regole per eseguire la derivazione totale di questa, connessa con una mappa $\widehat{ℰ}$

In this paper we study the linear thermodynamical problem of mixtures of thermoelastic solids. We use some results of the semigroup theory to obtain an existence theorem for the initial value problem with homogeneous Dirichlet boundary conditions. Continuous dependence of solutions upon the initial data and body forces is also established. We finish with a study of the asymptotic behavior of solutions of the homogeneous problem.

This paper outlines recent developments and prospects in the application of the continuum mechanics expressed intrinsically on the material manifold itself. This includes applications to materially inhomogeneous materials, physical effects which, in this vision, manifest themselves as quasi-inhomogeneities, and the notion of thermodynamical driving force of the dissipative progress of singular point sets on the material manifold with special emphasis on fracture, shock waves and phase-transition...