Nonlinear Elasticity

  • Andreas Öchsner
  • Markus Merkel


Within this chapter, the case of the nonlinear elasticity, meaning strain-dependent modulus of elasticity, will be considered. The problem will be illustrated with the example of bar elements. First, the stiffness matrix or alternatively the principal finite element equation will be derived under consideration of the strain dependency. For the solving of the nonlinear system of equations three approaches will be derived, namely the direct iteration, the complete NewtonRaphson iteration and the modified NewtonRaphson iteration, and will be demonstrated with the help of multiple examples. Within the framework of the complete NewtonRaphson iteration the derivation of the tangent stiffness matrix will be discussed in detail.


Stiffness Matrix Iteration Scheme Raphson Method Displacement Boundary Condition Element Stiffness Matrix 
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Copyright information

© 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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