Finite- Element-analysis and Algorithms for Large Elastic Strains

E. Stein and N. Mneller-Hoeppe
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E. Stein: Universitaet Hannover
N. Mneller-Hoeppe: Universitaet Hannover

Chapter D4 in Numerical Techniques for Engineering Analysis and Design, 1987, pp 29-36 from Springer

Abstract: 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.

Keywords: Virtual Work; Elasticity Tensor; Current Configuration; Spatial Description; Material Description (search for similar items in EconPapers)
Date: 1987
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DOI: 10.1007/978-94-009-3653-9_4

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