Finite element analysis of hyperelastic shells without any local iterative calculations by block Newton method

• Published in: Kikai Gakkai ronbunshū = Transactions of the Japan Society of Mechanical Engineers Vol. 88; no. 912; p. 22-00150
• Main Authors: YAMAMOTO, Takeki, YAMADA, Takahiro, MATSUI, Kazumi
• Format: Journal Article
• Language: English; Japanese
• Published: The Japan Society of Mechanical Engineers 2022
• Subjects: Block Newton Method; Finite Element Analysis; Hyperelasticity; Large Strains; Plane Stress
• ISSN: 2187-9761; 2187-9761
• DOI: 10.1299/transjsme.22-00150

The simultaneously iterative procedure proposed by the authors is extended to hyperelastic shells. The weak form of the equilibrium equation and the plane stress condition at every material point are defined as a coupled problem, and a numerical procedure based on the block Newton method to solve them with simultaneous linearization is developed in this paper. In the proposed block Newton method, the tangent moduli can be constructed algebraically by eliminating the internal variables, which are also updated algebraically without any local iterative calculations. In addition, the pseudo-stress for the residuals of plane stress state is incorporated into the linearized weak form of the equilibrium equation. Hence, the proposed procedure enables us to decrease the residuals in the coupled boundary value problems simultaneously. Some numerical examples demonstrate the validity and the effectiveness of the procedures in hyperelastic shells.