A stabilization technique to avoid hourglassing in finite elasticity.

*(English)*Zbl 0983.74070Summary: Enhanced strain element formulations are known to show an outstanding performance in many applications. The stability of these elements, however, cannot be guaranteed for general deformation states and arbitrarily shaped elements. In order to overcome this deficiency, we develop an innovative control technique based on a modal analysis on element level. The control is completely automatic in the sense that no artificial factors are introduced. The computational effort is negligible. The key to the approach is the split of the element tangent matrix into constant and hourglass parts, which is not possible for the classical enhanced strain concept in general. This motivates the use of a recently developed reduced integration method, which, since its stabilization part is derived on the basis of the enhanced strain method, shows the same performance and retains the crucial split. Using this formulation in combination with the new control technique, leads to a ‘smart’ element which is free of hourglass instabilities and generally applicable, also for strongly distorted meshes.

##### Keywords:

finite elasticity; Gauss one-point integration; hourglass stabilization; enhanced strain method; distorted mesh; plane strain state; smart element; modal analysis; reduced integration method
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\textit{S. Reese} and \textit{P. Wriggers}, Int. J. Numer. Methods Eng. 48, No. 1, 79--109 (2000; Zbl 0983.74070)

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