Finite- Element-analysis and Algorithms for Large Elastic Strains

Summary

Elastic solids with large strains are treated in the fraxne of poly convex materials so that the existence of solutions for boundary value problems can be ensured. Especially Neo-Hooke materials and a constitutive equar tion due to Ciarlet are treated both in material and spatial description.

A finite-element-algorithm is developed starting from the Fréchet-derivative of the principle of virtual work in material coordinates. Pushingforward this linearized form to the current configuration, performing the iteration process in this state yields a Newton method with reference to the current configuration. Isoparametric 8-node 3-D elements are most efficient for the numerical process and used for the following examples such as a bar, tensioned to nearly the double length and compressed to nearly the half length. Both examples were calculated in one increment with 4, respective 6 iteration steps.