Nonlinear Solid Mechanics
01 Jan 2009-
About: The article was published on 2009-01-01. It has received 1036 citations till now. The article focuses on the topics: Analytical dynamics & Solid mechanics.
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TL;DR: In this article, a nonlinear Kirchhoff-love shell element is developed on the basis of the isogeometric approach, which is discretized by displacement degrees of freedom only.
847 citations
01 Jan 2011
509 citations
TL;DR: In this article, a new formulation of the field theory of dielectric solids is proposed, which does not start with Newton's laws of mechanics and Maxwell-Faraday theory of electrostatics, but produces them as consequences.
Abstract: Two difficulties have long troubled the field theory of dielectric solids. First, when two electric charges are placed inside a dielectric solid, the force between them is not a measurable quantity. Second, when a dielectric solid deforms, the true electric field and true electric displacement are not work conjugates. These difficulties are circumvented in a new formulation of the theory in this paper. Imagine that each material particle in a dielectric is attached with a weight and a battery, and prescribe a field of virtual displacement and a field of virtual voltage. Associated with the virtual work done by the weights and inertia, define the nominal stress as the conjugate to the gradient of the virtual displacement. Associated with the virtual work done by the batteries, define the nominal electric displacement as the conjugate to the gradient of virtual voltage. The approach does not start with Newton's laws of mechanics and Maxwell–Faraday theory of electrostatics, but produces them as consequences. The definitions lead to familiar and decoupled field equations. Electromechanical coupling enters the theory through material laws. In the limiting case of a fluid dielectric, the theory recovers the Maxwell stress. The approach is developed for finite deformation, and is applicable to both elastic and inelastic dielectrics. As applications of the theory, we discuss material laws for elastic dielectrics, and study infinitesimal fields superimposed upon a given field, including phenomena such as vibration, wave propagation, and bifurcation.
485 citations
Cites background from "Nonlinear Solid Mechanics"
...The fields in material and spatial descriptions relate in usual ways (e.g., Truesdell and Noll, 2003; Kuang, 2002, Holzapfel, 2000; Huang, 2003)....
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...Furthermore, if the material is isotropic, ( )L0W is a function of the three invariants of the strain tensor, as reviewed by, e.g., Holzapfel (2000)....
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TL;DR: In this article, a review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries, focusing primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties.
Abstract: This review article is concerned with the mathematical modelling of the mechanical properties of the soft biological tissues that constitute the walls of arteries. Many important aspects of the mechanical behaviour of arterial tissue can be treated on the basis of elasticity theory, and the focus of the article is therefore on the constitutive modelling of the anisotropic and highly nonlinear elastic properties of the artery wall. The discussion focuses primarily on developments over the last decade based on the theory of deformation invariants, in particular invariants that in part capture structural aspects of the tissue, specifically the orientation of collagen fibres, the dispersion in the orientation, and the associated anisotropy of the material properties. The main features of the relevant theory are summarized briefly and particular forms of the elastic strain-energy function are discussed and then applied to an artery considered as a thick-walled circular cylindrical tube in order to illustrate its extension–inflation behaviour. The wide range of applications of the constitutive modelling framework to artery walls in both health and disease and to the other fibrous soft tissues is discussed in detail. Since the main modelling effort in the literature has been on the passive response of arteries, this is also the concern of the major part of this article. A section is nevertheless devoted to reviewing the limited literature within the continuum mechanics framework on the active response of artery walls, i.e. the mechanical behaviour associated with the activation of smooth muscle, a very important but also very challenging topic that requires substantial further development. A final section provides a brief summary of the current state of arterial wall mechanical modelling and points to key areas that need further modelling effort in order to improve understanding of the biomechanics and mechanobiology of arteries and other soft tissues, from the molecular, to the cellular, tissue and organ levels.
474 citations
TL;DR: This work performs a sequence of experimental tests on the same brain specimen to characterize the regional and directional behavior, and supplements these tests with DTI and histology to explore to which extent the macrostructural response is a result of the underlying microstructure.
388 citations
Cites methods from "Nonlinear Solid Mechanics"
...is given by l 1⁄4 1=2Pni1⁄41li ai [52]....
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...To describe the macroscopic deformation of each tested tissue cube, we used the nonlinear equations of continuum mechanics and introduced the deformation mapuðXÞwhich maps tissue from the undeformed, unloaded configuration to the deformed, loaded configuration [52]....
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...We can express the first Piola–Kirchhoff stress tensor P as the derivative of the strain-energy function W with respect to the deformation gradient F [52]....
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