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Orientation-preservation conditions on an iso-parametric FEM in cavitation computation

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Abstract

The orientation-preservation condition, i.e., the Jacobian determinant of the deformation gradient det ∇u being required to be positive, is a natural physical constraint in elasticity as well as in many other fields. It is well known that the constraint can often cause serious difficulties in both theoretical analysis and numerical computation, especially when the material is subject to large deformations. We derive a set of necessary and sufficient conditions for the quadratic iso-parametric finite element interpolation functions of cavity solutions to be orientation preserving on a class of radially symmetric large expansion accommodating triangulations. The result provides a practical quantitative guide for meshing in the neighborhood of a cavity and shows that the orientation-preservation can be achieved with a reasonable number of total degrees of freedom by the quadratic iso-parametric finite element method.

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Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant Nos. 11171008 and 11571022).

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Authors and Affiliations

  1. LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, China

    ChunMei Su & ZhiPing Li

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  1. ChunMei Su
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  2. ZhiPing Li
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Correspondence to ZhiPing Li.

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Su, C., Li, Z. Orientation-preservation conditions on an iso-parametric FEM in cavitation computation. Sci. China Math. 60, 719–734 (2017). https://doi.org/10.1007/s11425-016-0019-0

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