Two three-dimensional eight-node brick continuum finite elements are presented which are based on volume averaging techniques. For both elements, the point of departure is the additive split of the strain energy function into a homogeneous and an inhomogeneous part. The first element, called MEI, can be applied for robust computations of incompressibly materials. It is based on a split into a substructure consisting of eight sub-elements inside each finite element, further referred to as macro-element. For each sub-element, the deformation is averaged. The resulting sub-element response is assembled and projected onto the nodes of the macro-element. The second element, called Q1/EI9 (Q1/EI12), uses an enhancement of the inhomogeneous part of the deformation only. For the inhomogeneous part, linear elasticity is assumed, while a compressible Neo-Hooke material is used for the homogeneous part. Thus, an element which is locking and hourglassing free as well as insensitive to initial element distortion is developed. In several examples, the performance of the elements is tested.
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Wriggers, P., Mueller-Hoeppe, D.S., Loehnert, S. (2009). Brick Elements for Finite Deformations Based on Macro-concepts and on Inhomogeneous Mode Enhancement. In: Eberhardsteiner, J., Hellmich, C., Mang, H.A., Périaux, J. (eds) ECCOMAS Multidisciplinary Jubilee Symposium. Computational Methods in Applied Sciences, vol 14. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9231-2_3
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