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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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TL;DR: In this article, a geometric discretization of elasticity when the ambient space is Euclidean is presented, which is built on ideas from algebraic topology, exterior calculus, and the recent developments of discrete exterior calculus.
Abstract: This paper presents a geometric discretization of elasticity when the ambient space is Euclidean. This theory is built on ideas from algebraic topology, exterior calculus, and the recent developments of discrete exterior calculus. We first review some geometric ideas in continuum mechanics and show how constitutive equations of linearized elasticity, similar to those of electromagnetism, can be written in terms of a material Hodge star operator. In the discrete theory presented in this paper, instead of referring to continuum quantities, we postulate the existence of some discrete scalar-valued and vector-valued primal and dual differential forms on a discretized solid, which is assumed to be a triangulated domain. We find the discrete governing equations by requiring energy balance invariance under time-dependent rigid translations and rotations of the ambient space. There are several subtle differences between the discrete and continuous theories. For example, power of tractions in the discrete theory is written on a layer of cells with a nonzero volume. We obtain the compatibility equations of this discrete theory using tools from algebraic topology. We study a discrete Cosserat medium and obtain its governing equations. Finally, we study the geometric structure of linearized elasticity and write its governing equations in a matrix form. We show that, in addition to constitutive equations, balance of angular momentum is also metric dependent; all the other governing equations are topological.

85 citations

Journal ArticleDOI
TL;DR: In this paper, the wave propagation behavior of a size-dependent laminated composite cylindrical nanoshell in a thermal environment is analyzed based on nonlocal strain gradient theory (NSGT).
Abstract: In this article, the wave propagation behavior of a size-dependent laminated composite cylindrical nanoshell in a thermal environment is presented. The small-scale effects are analyzed based on nonlocal strain gradient theory (NSGT). The governing equations of the cylindrical laminated composite nanoshell in a thermal environment were obtained using Hamilton’s principle and solved by the analytical method. The novelty of this study is considering the effects of the composite layers and NSGT in addition to considering the thermal environment of the cylindrical composite nanoshell. Finally, the investigation was performed on the influence of temperature difference, wave number, angular velocity and the different types of laminated composite on the phase velocity using the mentioned continuum mechanics theory. The results show that wave number, ply angle, shear correction factor and thermal environment play an important role on the phase velocity of the laminated composite nanostructure. Another significant result is that, in a specific temperature difference, there is an inverse relation between the number of layers in a laminate and the dynamic behavior of the nanostructure. The outcome of the present work can be used in a structural health monitoring and ultrasonic inspection techniques.

85 citations

Journal ArticleDOI
TL;DR: The physics of the conversion of the electronic excitation energy into mechanical and chemical energy links atomic physics in a solid at low excitation densities to nanometer-scale continuum mechanics at high excitation density.
Abstract: The surprising fact that even very complex molecules can be ejected intact into the vapor phase when a material is electronically excited by incident particles provides a new probe of the behavior of condensed matter at high excitation densities. The physics of the conversion of the electronic excitation energy into mechanical and chemical energy links atomic physics in a solid at low excitation densities to nanometer‐scale continuum mechanics at high excitation densities

85 citations

Journal ArticleDOI
TL;DR: In this paper, two consistent formulations for elastic-plastic large deformation analysis are presented in which either the initial configuration or the current configuration is used for the description of static and kinematic variables.

84 citations

Journal ArticleDOI
TL;DR: In this article, the authors applied nonlocal continuum mechanics to derive a complete and asymptotic representation of the infinite higher-order governing differential equations for nano-beam and nano-plate models.

84 citations


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