Finite and Infinitesimal Deformations

  • Antonio Romano
  • Addolorata Marasco
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


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 [69].


Infinitesimal Deformation Cauchy-Green Tensor Programme De Formation Deformation Gradient Rotation Tensor 
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    J. Marsden, T. Hughes, Mathematical Foundations of Elasticity (Dover Publications, Inc. New York, 1983)Google Scholar
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    S. Wolfram, Mathematica ®;. A System for Doing Mathematics by Computer (Addison-Wesley Redwood City, California, 1991)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Antonio Romano
    • 1
  • Addolorata Marasco
    • 1
  1. 1.Department of Mathematics and Applications “R. Caccioppoli”University of Naples Federico IINaplesItaly

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