TY - JOUR
T1 - Embedded shell finite elements
T2 - Solid–shell interaction, surface locking, and application to image-based bio-structures
AU - Schillinger, Dominik
AU - Gangwar, Tarun
AU - Gilmanov, Anvar
AU - Heuschele, Jo D.
AU - Stolarski, Henryk K.
N1 - Publisher Copyright:
© 2018 Elsevier B.V.
PY - 2018/6/15
Y1 - 2018/6/15
N2 - In this article, we explore an embedded shell finite element method for the unfitted discretization of solid–shell interaction problems. Its core component is a variationally consistent approach that couples a shell discretization on the surface of an embedded solid domain to its unfitted discretization with hexahedral solid elements. Derived via an augmented Lagrangian formulation and the formal elimination of interface Lagrange multipliers, our method depends only on displacement variables, facilitated by a shift of the displacement-dependent traction vector entirely to the solid structure. We demonstrate that the weighted least squares term required for stability of the formulation triggers severe surface locking due to a mismatch in the polynomial spaces of the shell element and the embedding solid element. We show that reduced quadrature of the stabilization term that evaluates the kinematic constraint at the nodes of the embedded shell elements completely mitigates surface locking. For coarse discretizations, our variationally consistent method achieves superior accuracy with respect to a locking-free nodal penalty method. We illustrate the versatility of embedded shell finite elements for image-based analysis, including patient-specific stress prediction in a vertebra and local rind buckling in a plant structure.
AB - In this article, we explore an embedded shell finite element method for the unfitted discretization of solid–shell interaction problems. Its core component is a variationally consistent approach that couples a shell discretization on the surface of an embedded solid domain to its unfitted discretization with hexahedral solid elements. Derived via an augmented Lagrangian formulation and the formal elimination of interface Lagrange multipliers, our method depends only on displacement variables, facilitated by a shift of the displacement-dependent traction vector entirely to the solid structure. We demonstrate that the weighted least squares term required for stability of the formulation triggers severe surface locking due to a mismatch in the polynomial spaces of the shell element and the embedding solid element. We show that reduced quadrature of the stabilization term that evaluates the kinematic constraint at the nodes of the embedded shell elements completely mitigates surface locking. For coarse discretizations, our variationally consistent method achieves superior accuracy with respect to a locking-free nodal penalty method. We illustrate the versatility of embedded shell finite elements for image-based analysis, including patient-specific stress prediction in a vertebra and local rind buckling in a plant structure.
KW - Embedded shell finite elements
KW - Reduced quadrature
KW - Rotation-free shell formulation
KW - Solid–shell interaction
KW - Surface locking
KW - Voxel finite elements
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U2 - 10.1016/j.cma.2018.02.029
DO - 10.1016/j.cma.2018.02.029
M3 - Article
AN - SCOPUS:85043995010
SN - 0045-7825
VL - 335
SP - 298
EP - 326
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -