Asymptotically-Accurate Nonlinear Hyperelastic Shell Constitutive Model Using Variational Asymptotic Method
01 Jan 2019-pp 135-156
TL;DR: In this paper, the authors developed a nonlinear hyperelastic constitutive model for thin shell structures using Variational Asymptotic Method (VAM) for both geometric and material nonlinearities.
Abstract: The focus of this work is on the development of asymptotically-accurate nonlinear hyperelastic constitutive model for thin shell structures using Variational Asymptotic Method (VAM). In this work, these structures are analyzed for both geometric and material nonlinearities. The geometric nonlinearity is handled by allowing finite deformations and generalized warping functions through Green strain, while the material nonlinearity is incorporated through strain energy density function of hyperelastic material model. Using the inherent small parameters (moderate strains, very small thickness-to-wavelength ratio and very small thickness-to-initial radius of curvature) for the application of VAM, the process begins with three-dimensional nonlinear hyperelasticity and it weakly decouples the analysis into a one-dimensional through-the-thickness nonlinear analysis and a two-dimensional nonlinear shell analysis. Through-the-thickness analysis is analytical work, providing 3-D warping functions and two-dimensional nonlinear constitutive relation for Nonlinear Finite Element Analysis of shells. Current theory and code are demonstrated through standard test cases and validated with literature.
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TL;DR: In this paper, the nonlinear vibration of a hyperelastic moderately thick cylindrical shell with 2:1 internal resonance in a temperature field is investigated based on the third-order shear deformation theory.
Abstract: The nonlinear vibration of a hyperelastic moderately thick cylindrical shell with 2:1 internal resonance in a temperature field is investigated based on the third-order shear deformation theory. A ...
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TL;DR: Bonet and Wood as discussed by the authors provide a complete, clear, and unified treatment of nonlinear continuum analysis and finite element techniques under one roof, providing an essential resource for postgraduates studying non-linear continuum mechanics and ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
Abstract: Designing engineering components that make optimal use of materials requires consideration of the nonlinear characteristics associated with both manufacturing and working environments. The modeling of these characteristics can only be done through numerical formulation and simulation, and this requires an understanding of both the theoretical background and associated computer solution techniques. By presenting both nonlinear continuum analysis and associated finite element techniques under one roof, Bonet and Wood provide, in this edition of this successful text, a complete, clear, and unified treatment of these important subjects. New chapters dealing with hyperelastic plastic behavior are included, and the authors have thoroughly updated the FLagSHyP program, freely accessible at www.flagshyp.com. Worked examples and exercises complete each chapter, making the text an essential resource for postgraduates studying nonlinear continuum mechanics. It is also ideal for those in industry requiring an appreciation of the way in which their computer simulation programs work.
1,763 citations
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TL;DR: In this paper, a set of kinematical and intrinsic equilibrium equations for plates undergoing large deflection and rotation but with small strain was derived for the case of large deformation and rotation.
Abstract: A set of kinematical and intrinsic equilibrium equations are derived for plates undergoing large deflection and rotation but with small strain
94 citations
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TL;DR: In this paper, a rigorous and systematic dimensional reduction of a shell-like structure is undertaken, which is carried out using the variational asymptotic method and splits the 3D problem into a linear, one-dimensional, through-the-thickness analysis and a nonlinear, two-dimensional (2-D), shell analysis.
Abstract: A rigorous and systematic dimensional reduction of a shell-like structure is undertaken. It starts with geometrically nonlinear, three-dimensional (3-D), anisotropic elasticity theory and takes advantage of small parameters associated with the geometry. This reduction is carried out using the variational asymptotic method and splits the 3-D problem into a linear, one-dimensional (1-D), through-the-thickness analysis and a nonlinear, two-dimensional (2-D), shell analysis. The 2-D equations are put into the form of a nonlinear Reissner–Mindlin shell theory, details of which are dealt with in a separate paper. The focus of this paper is on the through-the-thickness analysis, which is solved by a 1-D finite element method and which provides two useful pieces of information: a generalized 2-D constitutive law for the shell equations, and a set of recovery relations that can be used to express the 3-D field variables through the thickness in terms of 2-D shell variables calculated in the shell analysis. The resulting analysis can be incorporated into standard Reissner–Mindlin shell finite element codes. Numerical results are compared with the exact solution, and the excellent agreement validates the fidelity of this modeling approach.
63 citations