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<p>The focus of a current paper is on eliminating hourglassing at the bifurcation point, particularly in simulations involving incompressible materials. Three eight-node (hexahedron) solid-shell elements that are free from the hourglassing in their tangent plane are developed for this purpose. To eliminate hourglassing, a transposition of the enhancement matrix <b>G</b> of the <i>Enhanced Assumed Deformation Gradient</i> (EADG) method is used, see Korelc and Wriggers (Eng Comput 13(1):103–123, 1996) and Glaser and Armero (Eng Comput 14(7):759–791, 1997). Several modifications are proposed to convert three existing (parent) solid-shell elements into the new ones: 1. A two-parameter enhancement (EADG2) of the deformation gradient <b>F</b> is proposed to suppress hourglassing of our <i>Hu–Washizu</i> element HW19 and the <i>Enhanced Assumed Strain</i> element EAS10. Originally neither of them uses the EADG method, so they are reformulated to embed it. 2. A new transformation rule (designated T4) is proposed for the EADG enhancement, and it involves the inverse of the current Jacobian for large deformations. T4 is an alternative to the other three transformations used in the literature. We check that T4 is objective and subject it to numerical tests in the current paper. 3. For the third parent element, which uses the standard EADG4 enhancement, we propose 3 additional modes, which are necessary to eliminate one of the large spurious eigenvalues for the nearly incompressible material and to improve its bending behavior. The improved performance of the obtained elements is demonstrated using several linear and non-linear examples for the linear elastic material and the neo-Hookean hyperelastic material. They are also compared to the best existing solid-shell elements.</p>

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Modification of solid-shell elements to suppress mesh hourglassing at bifurcation point

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  • 发表日期：

    2025年11月26日

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  • K. Wisniewski,
  • E. Turska

摘要

The focus of a current paper is on eliminating hourglassing at the bifurcation point, particularly in simulations involving incompressible materials. Three eight-node (hexahedron) solid-shell elements that are free from the hourglassing in their tangent plane are developed for this purpose. To eliminate hourglassing, a transposition of the enhancement matrix G of the Enhanced Assumed Deformation Gradient (EADG) method is used, see Korelc and Wriggers (Eng Comput 13(1):103–123, 1996) and Glaser and Armero (Eng Comput 14(7):759–791, 1997). Several modifications are proposed to convert three existing (parent) solid-shell elements into the new ones: 1. A two-parameter enhancement (EADG2) of the deformation gradient F is proposed to suppress hourglassing of our Hu–Washizu element HW19 and the Enhanced Assumed Strain element EAS10. Originally neither of them uses the EADG method, so they are reformulated to embed it. 2. A new transformation rule (designated T4) is proposed for the EADG enhancement, and it involves the inverse of the current Jacobian for large deformations. T4 is an alternative to the other three transformations used in the literature. We check that T4 is objective and subject it to numerical tests in the current paper. 3. For the third parent element, which uses the standard EADG4 enhancement, we propose 3 additional modes, which are necessary to eliminate one of the large spurious eigenvalues for the nearly incompressible material and to improve its bending behavior. The improved performance of the obtained elements is demonstrated using several linear and non-linear examples for the linear elastic material and the neo-Hookean hyperelastic material. They are also compared to the best existing solid-shell elements.