TY - JOUR
T1 - A refined dynamic finite-strain shell theory for incompressible hyperelastic materials
T2 - equations and two-dimensional shell virtual work principle
AU - Yu, Xiang
AU - Fu, Yibin
AU - Dai, Hui-Hui
PY - 2020/5
Y1 - 2020/5
N2 - Based on previous work for the static problem, in this paper, we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.
AB - Based on previous work for the static problem, in this paper, we first derive one form of dynamic finite-strain shell equations for incompressible hyperelastic materials that involve three shell constitutive relations. In order to single out the bending effect as well as to reduce the number of shell constitutive relations, a further refinement is performed, which leads to a refined dynamic finite-strain shell theory with only two shell constitutive relations (deducible from the given three-dimensional (3D) strain energy function) and some new insights are also deduced. By using the weak formulation of the shell equations and the variation of the 3D Lagrange functional, boundary conditions and the two-dimensional shell virtual work principle are derived. As a benchmark problem, we consider the extension and inflation of an arterial segment. The good agreement between the asymptotic solution based on the shell equations and that from the 3D exact one gives verification of the former. The refined shell theory is also applied to study the plane-strain vibrations of a pressurized artery, and the effects of the axial pre-stretch, pressure and fibre angle on the vibration frequencies are investigated in detail.
KW - Artery
KW - Dimension-reduction method
KW - Incompressible hyperelastic material
KW - Shell theory
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85086072000&origin=recordpage
U2 - 10.1098/rspa.2020.0031
DO - 10.1098/rspa.2020.0031
M3 - RGC 21 - Publication in refereed journal
C2 - 32523417
VL - 476
JO - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
SN - 1364-5021
IS - 2237
M1 - 20200031
ER -