Nonlinear Mechanics of Three-Dimensional Solids

  • Walter Lacarbonara


This chapter presents the theory of nonlinear three-dimensional solids with regard to the geometry of deformation, stress, interactions with the environment, and constitutive equations. A unique feature of this presentation is that a few key concepts such as the stretch vector or the surface stretch vector are introduced in an original fashion that paves the way for reduced structural theories of special slender (beam-like) or thin (plate-like) bodies. The presented nonlinear three-dimensional theory constitutes the theoretical framework from which reduced or constrained theories of slender or thin bodies can be deduced or within which they can be fully justified. A few examples are presented to show the richness of the implications stemming from three-dimensional theory.


Deformation gradient Stretch vector Surface stretch vector Cauchy–Green strain tensor Green–Lagrange strain tensor Infinitesimal strain tensor Euler–Almansi strain tensor Stretching tensor Spin tensor Cauchy polar decomposition Cauchy stress Piola–Kirchhoff stress tensor Nominal stress Equations of motion Constitutive equations Principle of Objectivity Nonlinearly elastic materials Thermodynamic restrictions Clausius–Duhem inequality Principle of Virtual Work Principle of Virtual Power Weak form 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Walter Lacarbonara
    • 1
  1. 1.Sapienza University of RomeRomeItaly

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