Finite and Infinitesimal Deformations
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This chapter contains the fundamental definitions and theorems relative to finite and infinitesimal deformations of a continuous system. Starting from the deformation gradient, the rotation tensor, right and left stretching tensors are defined making clear their use in defining the different aspects of deformation. Then, the left and right Cauchy–Green tensors are introduced with a complete analysis of their invariants. Starting from the displacement gradient, the infinitesimal deformations are defined. Finally, the compatibility conditions of a deformation are analyzed. After a section of exercises, the chapter ends with the introduction of the program Deformation, written with MathematicaⓇ .