Kinematics of Continua

Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 174)

Abstract

Let us consider a continuum \(\mathcal{B}\). Due to Axiom2, at time t=0 there is a one-to-one correspondence between every material point \(\mathcal{M}\in \mathcal{B}\)and its radius-vector \(\mathop{\mathbf{x}}^{\circ } =\overrightarrow{ O\mathcal{M}}\)in a Cartesian coordinate system \(O\bar{{\mathbf{e}}}_{i}\). Denote Cartesian coordinates of the radius-vector by \(\mathop{x}^ {\circ }{}^{i}\)(\(\mathop{\mathbf{x}}^{\circ } =\mathop{ x}^ {\circ }{}^{i}\bar{{\mathbf{e}}}_{i}\)) and introduce curvilinear coordinates X i of the same material point \(\mathcal{M}\)in the form of some differentiable one-to-one functions
$$\mathop{x}^ {\circ }{}^{i} =\mathop{ x}^ {\circ }{}^{i}({X}^{k}).$$
(2.1)

Keywords

Material Point Deformation Gradient Tensor Field Total Derivative Deformation Tensor 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  1. 1.Bauman Moscow State Technical UniversityMoscowRussia

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