scispace - formally typeset
Search or ask a question
Topic

Continuum mechanics

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


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, a set of constitutive equations for nonlocal thermoelastic solids is developed by means of the nonlocal thermodynamics and the axiom of objectivity.

181 citations

Journal ArticleDOI
TL;DR: In this paper, the applicability of the proposed nonlocal elastic shell theory is explored and analyzed based on the differences between the wave solutions from local and nonlocal theories in numerical simulations.
Abstract: Wave propagation in carbon nanotubes (CNTs) is studied based on the proposed nonlocal elastic shell theory. Both theoretical analyses and numerical simulations have explicitly revealed the small-scale effect on wave dispersion relations for different CNT wavenumbers in the longitudinal and circumferential directions and for different wavelengths in the circumferential direction. The applicability of the proposed nonlocal elastic shell theory is especially explored and analyzed based on the differences between the wave solutions from local and nonlocal theories in numerical simulations. It is found that the newly proposed nonlocal shell theory is indispensable in predicting CNT phonon dispersion relations at larger longitudinal and circumferential wavenumbers and smaller wavelength in the circumferential direction when the small-scale effect becomes dominant and hence noteworthy. In addition, the asymptotic frequency, phase velocities and cut-off frequencies are also derived from the nonlocal shell theory. Moreover, an estimation of the scale coefficient is provided based on the derived asymptotic frequency. The research findings not only demonstrate great potential of the proposed nonlocal shell theory in studying vibration and phonon dispersion relations of CNTs but also signify limitations of local continuum mechanics in analysis of small-scale effects, and thus are of significance in promoting the development of nonlocal continuum mechanics in the design of nanostructures.

180 citations

Journal ArticleDOI
TL;DR: In this paper, a nonlocal plate model was developed to study the vibrational characteristics of multi-layered graphene sheets with different boundary conditions embedded in an elastic medium, and the results obtained from the present numerical solution have been compared with the existing data from the literature and good agreement has been found.

179 citations

Book
16 Nov 2010
TL;DR: In this paper, the phase diagram of Ising systems with Kac potentials and the phase transitions in the LMP model are discussed. But the phase transition is not considered in this paper.
Abstract: Statistical Mechanics of Ising systems.- Thermodynamic limit in the Ising model.- The phase diagram of Ising systems.- Mean field, Kac potentials and the Lebowitz-Penrose limit.- Stochastic Dynamics.- Mesoscopic Theory, non-local functionals.- Non-local, free energy functionals.- Surface tension, Gamma convergence, Wulff shape.- One dimensional interfaces.- Phase transitions in systems with Kac potentials.- Ising systems with Kac potentials.- The LMP model and the Pirogov-Sinai strategy.- Phase transitions in the LMP model.- DLR measures and the ergodic decomposition.

179 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered Hill's condition of stability and diffuse modes of failure in geomaterials in a dual framework: continuum mechanics and discrete mechanics, and concluded that the second order work criterion (under its dual form: continuous and discrete) can be a proper tool to analyse diffuse mode of failure.

178 citations


Network Information
Related Topics (5)
Boundary value problem
145.3K papers, 2.7M citations
86% related
Finite element method
178.6K papers, 3M citations
86% related
Partial differential equation
70.8K papers, 1.6M citations
84% related
Nonlinear system
208.1K papers, 4M citations
82% related
Differential equation
88K papers, 2M citations
81% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202363
2022136
2021150
2020176
2019181
2018185