Strain, Hooke’s Law

  • Dietmar GrossEmail author
  • Jörg Schröder
  • Javier Bonet
  • Werner Hauger
  • Wolfgang A. Wall


In Chapter 1 the deformation of a bar has been characterized by the strain and the displacement. We will now generalize these kinematic quantities to the plane and the spatial cases. For this purpose, we introduce the displacement vector and the strain tensor, the latter describing length and angle changes. In addition, we will extend the already known Hooke’s law from the uniaxial case to the two and three-dimensional cases. Finally, we will discuss the so-called strength hypotheses in order to assess the exertion of the material under multiaxial stress. The students shall learn how to calculate the stresses from the strains or displacements and vice versa.


Shear Strain Strain Tensor Equivalent Stress Principal Direction Normal Strain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Dietmar Gross
    • 1
    Email author
  • Jörg Schröder
    • 2
  • Javier Bonet
    • 3
  • Werner Hauger
    • 4
  • Wolfgang A. Wall
    • 5
  1. 1.Division of Solid MechanicsTU DarmstadtDarmstadtGermany
  2. 2.Institute of MechanicsUniversität Duisburg-EssenEssenGermany
  3. 3.School of Engineering Swansea UniversitySwanseaUnited Kingdom
  4. 4.TU DarmstadtDarmstadtGermany
  5. 5.Institute for Computational MechanicsTU MünchenGarchingGermany

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