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- W3100258712 abstract "Abstract The form of kinematics to be used for the description of a deformation process is largely determined by the kind of mechanical response that is being described. To describe the mechanical response of purely viscous fluids it is convenient to use coordinates, which are fixed in space, since purely viscous fluids have no past memory and therefore remain in the deformed state when loads are removed. In other words, the mechanical response of purely viscous fluids is determined solely by the instantaneous values of the time rate of deformation. However, in order to describe the deformation of a viscoelastic fluid it is necessary to follow a given material element with time as it moves to define a suitable measure of deformation that always refers to the same material element as time varies. The reason is that when a material element undergoes a finite deformation the coordinate positions of the given material element (with respect to a fixed origin) will vary. Hence, any measure of deformation defined in terms of infinitesimal deformation of fixed coordinate positions loses its physical significance since it will not always be associated with the same material element. In this chapter, we introduce some basic concepts of the kinematics and stresses of a deformable body from the point of view of continuum mechanics, and discuss various representations of a deformation process in terms of the deformation (or strain) tensor and the rate-of-deformation (or rate-of-strain) tensor. In order to help the readers follow the material in the text, the elementary properties of second-order tensors are presented in Appendix 2A. In this section, we briefly describe the motion of a body, which consists of a set of particles (or “elements”), sometimes called “material points” (or “material elements”) (Jaunzemis 1967). Let X(Xi ; i = 1, 2, 3) be the particles P of the body B in some reference configuration κ at time t = 0 (i.e., undeformed state) and then we have. . . X = κ(P). . .in which κ describes the shape of the body B in the undeformed state, which in general is known to an observer." @default.
- W3100258712 created "2020-11-23" @default.
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- W3100258712 date "2007-01-25" @default.
- W3100258712 modified "2023-10-18" @default.
- W3100258712 title "Kinematics and Stresses of Deformable Bodies" @default.
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- W3100258712 doi "https://doi.org/10.1093/oso/9780195187823.003.0007" @default.
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