• Andreas Öchsner
  • Markus Merkel


The continuum mechanics basics for the one-dimensional bar will be compiled at the beginning of this chapter. The yield condition, the flow rule, the hardening law and the elasto-plastic modulus will be introduced for uniaxial, monotonic loading conditions. Within the scope of the hardening law, the description is limited to isotropic hardening, which occurs for example for the uniaxial tensile test with monotonic loading. For the integration of the elasto-plastic constitutive equation, the incremental predictor-corrector method is generally introduced and derived for the fully implicit and semi-implicit backward-Euler algorithm. On crucial points the difference between one- and three-dimensional descriptions will be pointed out, to guarantee a simple transfer of the derived methods to general problems. Calculated examples and supplementary problems with short solutions serve as an introduction for the theoretical description.


Yield Surface Strain Increment Flow Rule Displacement Increment Back Projection 
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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Faculty of Mechanical Engineering, Department of Applied MechanicsUniversity of Technology Malaysia—UTMSkudaiMalaysia
  2. 2.Department of Mechanical EngineeringAalen University of Applied SciencesAalenGermany

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