This work presents a setting for the formulation of the mechanics of growing bodies. By the mechanics of growing bodies we mean a theory in which the material structure of the body does not remain fixed. Material points may be added or removed from the body.

The plane strain elastic analysis of a homogeneous and isotropic layer of constant thickness, is formulated using Fourier series expansions in the direction parallel to the layer and suitable Green's functions in the transversal direction. For each frequency the unknown distributions of the Fourier coefficients relevant to the symmetric or skew-symmetric problems are governed by one-dimensional equations which can be solved exactly. The proposed method is used to critically discuss the "transfer"...

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....

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 $\widehat{ℰ}$

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...

A homogeneous solid subject to quasi-static loading in the small strain range is considered. The material model assumed is rate-independent, non-associative and incrementally bilinear. The strain localization conditions are analytically solved using a geometric method. The expressions of the critical hardening moduli, their domains of validity and the form of the strain rate discontinuity are obtained. Finally these results, and in particular the role of hydrostatic and deviatoric non-normality,...