By Y. C. Fung
Revision of a vintage textual content via a wonderful writer. Emphasis is on challenge formula and derivation of governing equations. re-creation gains elevated emphasis on functions. New bankruptcy covers long term alterations in fabrics less than rigidity.
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Extra info for A first course in continuum mechanics: for physical and biological engineers and scientists
Thus the elastic strain is the difference between the total strain and eigenstrain: eij ϭ ij Ϫ ij*. 5) eij ϭ ij Ϫ *ij ϭ Mijklkl. 5) is that the stress in a linear elastic material is caused only by elastic strain. If there is no elastic strain, there would be no stress. For this reason, we do not introduce the concept of eigenstress in this book. 5), let us consider the uniaxial tension of a metal bar. 1. The eigenstrain in this case is the plastic strain p while the elastic strain is e.
G ϭ Ϫ sT Ϫ ii. 4 CONSTITUTIVE LAWS Constitutive laws are used to describe material behavior when subjected to applied thermomechanical loads. One of the major areas of micromechanics is to develop constitutive laws for heterogeneous materials under various thermomechanical loading conditions. For real materials, their thermomechanical behavior can be rather complex. It is usually not feasible to write down one or a set of equations to describe the entire range of material behavior. Instead, we formulate separately constitutive equations describing various kinds of idealized material response, each of which is a mathematical formulation designed to approximate physical observations of a real material’s response over a suitably restricted range.
8) are over the entire threedimensional space, while dx and d are volume elements in the x space and the space, respectively. 6 INTEGRAL REPRESENTATIONS OF ELASTICITY SOLUTIONS 1 (2)3 ͵ ϱ Ϫϱ Ѩg(x) Ϫi⅐x e dx ϭ ijgˆ (). 8) by eϪi⅐x /(2)3 and integrate: Lijkl ͭ 1 (2)3 ͵ ϱ Ϫϱ ͮ uk,lj(x)eϪi⅐x dx ϩ 1 (2)3 ͵ ϱ Ϫϱ ƒi(x)eϪi⅐x dx ϭ 0. 12) where uˆ k and ƒˆ i are the Fourier transforms of and uk and ƒi, respectively. 13) where the dependence of uˆ k and ƒˆ i on is implied without writing it out explicitly as an argument, and Kik ϭ Kik() ϭ Lijkllj.