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A major focus is ensuring that the mathematical descriptions of deformation are physically possible. University of Auckland Strain-Displacement Relations
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You're looking for a complete article on Solid Mechanics Part II by Kelly, in PDF format. I can guide you on how to find it, but I must clarify that I won't be able to provide the actual PDF file due to copyright restrictions.
: Covers both elastostatics and elastodynamics.
You might ask: Why search for a specific university PDF when I can buy a $150 textbook?