Generalized Continua from the Theory to Engineering Applications
September 19, 2011 — September 23, 2011
- Victor A. Eremeyev (South Federal University and South Scientific Center of RASci, Rostov on Don, Russian Federation)
- Holm Altenbach (Otto von Guericke University Magdeburg, Magdeburg, Germany)
The need of generalized continua models is coming from the practice – complex material behaviour cannot be presented in all cases by the classical Cauchy continua. Generalized Continua are in the focus of scientists from the end of the 19th century. A first summary was given in 1909 by the Cosserat brothers. After World War II a true renaissance in this field occurred with a publication of Ericksen & Truesdell in 1958. Further developments were connected with the fundamental contributions of, among others, Kröner (Germany), Aero and Palmov (Soviet Union), Nowacki (Poland), Eringen (USA), and Maugin (France). Strong Interest in the field is checked and at present the attention will be focussed on the most recent research items: new models, application of well-known models to new problems, micro-macro aspects, computational effort, and possibilities to identify the constitutive equations.
The Mechanics of Generalized Continua is an established research topic since the end of the 50s – early 60s of the last century. The starting point was the monograph of the Cosserat brothers from 1909 Théorie des corps déformables and some previous works of such famous scientists like Lord Kelvin. All these contributions were focussed on the fact that in a continuum one has to define translations and rotations independently (or in other words, one has to establish force and moment actions as it was done by Euler).
The reason for the revival of generalized continua is that some effects of the mechanical behaviour of solids and fluids could not be explained by the available classical models. Examples of this are the turbulence of a fluid or the behaviour of solids with a significant and very complex microstructure. Since the suggested models satisfy all requirements from Continuum Thermomechanics (the balance laws were formulated and the general representations of the constitutive equations were suggested) the scientific community accepted for a while but missed real applicative developments.
Indeed, for practical applications the developed models were not useful. The reason for this was a gap between the formulated constitutive equations and the possibilities to identify the material parameters. As often the case one had much more parameters compared to classical models.
During the last ten years the situation has drastically changed. More and more researches emerged, being kindled by the partly forgotten models since now one has available much more computational possibilities and very complex problems can be simulated numerically. In addition, with the increased attention paid to a large number of materials with complex microstructure and a deeper understanding of the meaning of the material parameters (scale effects) the identification becomes much more well founded. We have thus contributions describing the micro- and macro-behaviours, new existence and uniqueness theorems, the formulation of multi-scale problems, etc. In addition, generalized continua models are not included in the actual BSc or MSc programs.
KEYWORDS: Microcontinuum, Non-linear mechanics, Plastic strain, Configurational forces.