V. I. Erofeyev, A. A. Potapov
The paper contains information about EUROMECH Colloquium «Mechanics of Generalized Continua: A handred years after the Cosserats» (Paris, France, May 1316, 2009).
The centenary in 2009 of the publication of the much cited monograph by the Cosserat brothers on the «Theory of deformable bodies» offers a timely opportunity to examine the strong influence of, and the progress and innovation in, the mechanics of so-called generalized continua., Cosserat continua providing one example of such generalized continua. The actuality of such a subject matter is enhanced by the recognized physical fact that in virtually all physical natural or man-made materials and systems, interactions exist between mechanical processes at different spatial scales.
Nowadays, generalized continua facilitate the development of new metallurgical procedures as well as the production of artificial materials with a controlled microstructure. They help predict the failure of heterogeneous brittle materials such as concrete and ice. Several non-destructive testing techniques are based on the averaged material properties predicted by the generalized continua. The rapidly advancing nano-technologies are seeking for appropriate modelling approaches of which the one based on the concept of generalized continua is considered to be very promising.
Generalized continua such as micropolar or oriented materials, micromorphic continua, strain-gradient materials, bodies with weakly or strongly nonlocal interactions are also emerging as an integral part of the multi-scale numerical techniques. These techniques aim at coupling different spatial scales in one numerical scheme. Starting from the quantum-mechanical description, the simulations proceed into the atomistic, molecular, micro and then to the continuum scale. The latter scale is often broken into two sub-scales: the generalized and the classical continuum. The latter is then considered as representative of the averaged properties of the generalized continuum.
The aim of this Colloquium was to discuss advances in the theory, experimental identification, numerical implementation and applications of the generalized continua. Particular topics were the following:
Phenomenology of generalized continua,
Derivation techniques (homogenization, crystal-lattice dynamics, etc),
Generalized continua versus discrete models,
The energy, momentum and moment of momentum in generalized continua,
Causality and waves in generalized continua,
Experimental identification of parameters of the generalized continua,
Numerical implementation of the generalized continua,
Classical and emerging applications of the generalized continua: nanomechanics, biology, life sciences, earth sciences, civil and mechanical engineering, etc,
Technological advances facilitated by the generalized continuum theories,
Non-destructive testing techniques based on the generalized continuum properties.