Classical Continuum Mechanics – Limitations and New Developments
Holm Altenbach
Institute of Mechanics, Otto von Guericke University, Magdeburg Germany
ABSTRACT: Continuum mechanics is a branch of mechanics that deals with the analysis of the mechanical behavior of materials modeled as a continuous manifold. Continuum mechanics models begin by introduction of three-dimensional (or less dimensional) Euclidean space. The points within this region are defined as material points with prescribed properties. Each material point is characterized by a position vector that is continuous in time. Thus, the body changes in a way that is realistic—globally invertible at all times and orientation preserving, so that the body cannot intersect itself as transformations which produce mirror reflections are not possible in nature. For the mathematical formulation, the model is also assumed to be twice continuously differentiable, so that differential equations describing the motion may be formulated. Finally, the kinematical relations, the balance equations, the constitutive equations, and the boundary and/or initial conditions have to be defined. Altenbach discusses some examples of solid deformable continua with regard to the basics and introduces advanced models of continuum mechanics.
