Nonlinear Elasticity

• Andreas Öchsner
• Markus Merkel
Chapter

Abstract

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.

Keywords

Stiffness Matrix Iteration Scheme Raphson Method Displacement Boundary Condition Element Stiffness Matrix
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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