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Continuum mechanics

About: Continuum mechanics is a research topic. Over the lifetime, 5042 publications have been published within this topic receiving 181027 citations.


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Journal ArticleDOI
TL;DR: In this article, a constitutive relation for single-walled carbon nanotubes (SWCNTs) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of CNT's during tensile deformation.
Abstract: In this paper, by capturing the atomic informa- tion and reflecting the behaviour governed by the nonlin- ear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single- walled carbon nanotubes (SWCNT's) is established to describe the nonlinear stress-strain curve of SWCNT's and to predict both the elastic properties and breaking strain of SWCNT's during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT's. of CNT's. The Young's modulus of CNT's was found to be about 1 TPa (2-5). Many theories of mechanics have also been proposed to study the mechanical properties of CNT's. Zhang et al. (6) developed a continuum mechanics approach to model elastic properties of single-walled carbon nanotubes (SWCNT's), and the Young's modulus of SWCNT's was pre- dicted to be 0.705 TPa. Li and Chou (7) presented a structural mechanics approach to model the deformation of CNT's, and calculated the Young's moduli for CNT's with different radii. A similar approach was presented by Chang and Gao (8), and the chirality- and size-dependent elastic properties such as Young's modulus, Poisson's ratio and shear modulus were predicted (9,10). Moreover, the nonlinear effect of SWCNT's was taken into account (11) recently. In view of the unrealistic demand of computational power to study materials of practical size, atomistic simulations are deemed unsuitable for the study of large scaled nanometer materials in large time spans. Therefore, various attempts have been made by researchers to introduce atomic character- istics into the mechanical theory. For example, the molecular mechanics originally developed by chemical scientists (12) can be considered one of the successful attempts. According to the definition of Burkert and Allinger (12), the total potential energy, U , is constitutive of several individual energy terms corresponding to bond stretching, angle bend- ing, torsion, and van der Waals interactions, respectively: U = � Ustretch + � Ubend

193 citations

Journal ArticleDOI
TL;DR: In this paper, a non-local elastic beam and shell model was developed and applied to investigate the small scale effect on buckling analysis of carbon nanotubes (CNTs) under compression.

192 citations

Book
01 Jan 1990
TL;DR: In this article, the authors present a review of plasticity in geotechnical engineering, focusing on nonlinear stress analyses in soil mechanics, and present a model based on the Cauchy elastic model.
Abstract: Part I. FUNDAMENTALS. 1. Introduction. Characteristics of soil behavior.Idealizations and material modeling. Historical review of plasticity in soil mechanics. Nonlinear stress analyses in geotechnical engineering. Need, objectives and scope. References. 2. Basic Concept of Continuum Mechanics. Introduction. Notations. Stresses in three dimensions. Definitions and notations. Cauchy's formulas, index notation, and summation convention. Principal axes of stresses. Deviatoric stress. Geometrical representation of stresses. Strains in three dimensions. Definitions and notations. Deviatoric strain. Octahedral strains and principal shear strains. Equations of solid mechanics. Equations of equilibrium (or motion). Geometric (compatibility) conditions. Constitutive relations. Summary. References. Part II. MATERIAL MODELING-BASIC CONCEPTS. 3. Elasticity and Modeling . Introduction. Elastic models in geotechnical engineering. Linear elastic model (generalized Hooke's law). Cauchy elastic model. Hyperelastic model. Hypoelastic model. Uniqueness, stability, normality, and convexity for elastic materials. Uniqueness. Drucker's stability postulate. Existence of W and v. Restrictions - normality and convexity. Linear elastic stress-strain relations. Generalized Hooke's law. A plane of symmetry. Two planes of symmetry (orthotropic symmetry). Transverse and cubic isotropies. Full isotropy. Isotropic linear elastic stress-strain relations. Tensor forms. Three-dimensional matrix forms. Plane stress case. Plane strain case. Axisymmetric case. Isotropic nonlinear elastic stress-strain relations based on total formulation. Nonlinear elastic model with secant moduli. Cauchy elastic model. Hyperelastic (green) model. Isotropic nonlinear elastic stress-strain relations based on incremental formulation. Nonlinear elastic model with secant muduli. Cauchy elastic model. Hyerelastic model. Hypoelastic model. Summary. References. 4. Perfect Plasticity and Modeling. Introduction. Deformation theory. An illustrative example. Variable moduli models. Flow theory. Yield criteria. Flow rule. Basic requirements. Perfect plasticity models. Tresca and von Mises models. Coulomb model. Drucker-Prager model. Prandtl-Reuss stress-strain relations. Generalized stress-strain relations. Stiffness formulation. General description. Stiffness coefficients. Summary. References. 5. Hardening Plasticity and Modeling. Introduction. Flow theory. Loading function. Hardening rule. Flow rule. Drucker's postulate. Hardening plasticity models. Lade-Duncan model. Lade model. Nested yield surface models. Generalized multi-surface models. Bounding surface models. Prandtl-Reuss stress-strain relations. Prandtl-Reuss equations. Matrix form of Prandtl-Reuss equations. Generalized stress-strain relations. Incremental stress-strain relations. Isotropic hardening. Kinematic hardening. Mixed hardening. Stiffness formulation. General description. Stiffness coefficients. Summary. References. PART III.

191 citations

Journal ArticleDOI
TL;DR: In this article, the resonant frequency and sensitivity of atomic force microscope (AFM) microcantilevers are studied using the modified couple stress theory, which employs additional material parameters besides those appearing in classical continuum theory to treat the size-dependent behavior.

190 citations

Journal ArticleDOI
TL;DR: A simple three-coefficient exponential constitutive law provides an accurate prediction of stress-stretch behavior over a wide range of deformations and could provide substantial improvement in the evaluation and treatment of valvular disease, surgery, and replacement.
Abstract: Biaxial mechanical testing and theoretical continuum mechanics analysis are employed to formulate a constitutive law for cardiac mitral valve anterior and posterior leaflets. A strain energy description is formulated based on the fibrous architecture of the tissue, accurately describing the large deformation, highly nonlinear transversely isotropic material behavior. The results show that a simple three-coefficient exponential constitutive law provides an accurate prediction of stress-stretch behavior over a wide range of deformations. Regional heterogenity may be accommodated by spatially varying a single coefficient and incorporating collagen fiber angle. The application of this quantitative information to mechanical models and bioprosthetic development could provide substantial improvement in the evaluation and treatment of valvular disease, surgery, and replacement.

188 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202363
2022136
2021150
2020176
2019181
2018185