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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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Book ChapterDOI
01 Jan 2000
TL;DR: This chapter presents basic continuum mechanics in the presence of geometric non-linearities, namely finite strains, displacements and rotations.
Abstract: In all previous chapters, we have worked within the small perturbation hypothesis (SPH) As a consequence, we wrote (and solved for) equilibrium and boundary condition equations on the initial, undeformed (thus known) configuration of a body The only exception was the study of possible buckling modes in Chap 10 In this chapter, we present basic continuum mechanics in the presence of geometric non-linearities, namely finite strains, displacements and rotations Practical examples are metal forming problems or large displacements of slender beams and thin shells

99 citations

Journal ArticleDOI
TL;DR: Ottinger's recent incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat transfer which support the view that revisions to the Navier-Stokes-Fourier (N-S-F) momentum/energy equation set are necessary.
Abstract: Ottinger's recent nontraditional incorporation of fluctuations into the formulation of the friction matrix appearing in the phenomenological GENERIC theory of nonequilibrium irreversible processes is shown to furnish transport equations for single-component gases and liquids undergoing heat transfer which support the view that revisions to the Navier–Stokes–Fourier (N–S–F) momentum/energy equation set are necessary, as empirically proposed by the author on the basis of an experimentally supported theory of diffuse volume transport. The hypothesis that the conventional N–S–F equations prevail without modification only in the case of “incompressible” fluids, where the density ρ of the fluid is uniform throughout, serves to determine the new phenomenological parameter α ′ appearing in the GENERIC friction matrix. In the case of ideal gases the consequences of this constitutive hypothesis are shown to yield results identical to those derived theoretically by Ottinger on the basis of a “proper” coarse-graining of Boltzmann's kinetic equation. A major consequence of the present work is that the fluid's specific momentum density v is equal to its volume velocity v v , rather than to its mass velocity v m , contrary to current views dating back 250 years to Euler. In the case of rarefied gases the proposed modifications are also observed to agree with those resulting from Klimontovich's molecularly based, albeit ad hoc, self-diffusion addendum to Boltzmann's collision integral. Despite the differences in their respective physical models—molecular vs. phenomenological—the role played by Klimontovich's collisional addition to Boltzmann's equation in modifying the N–S–F equations is noted to constitute a molecular counterpart of Ottinger's phenomenological fluctuation addition to the GENERIC friction matrix. Together, these two theories collectively recognize the need to address multiple - rather than single - encounter collisions between a test molecule and its neighbors when formulating physically satisfactory statistical–mechanical theories of irreversible transport processes in gases. Overall, the results of the present work implicitly support the unorthodox view, implicit in the GENERIC scheme, that the translation of Newton's discrete mass-point molecular mechanics into continuum mechanics, the latter as embodied in the Cauchy linear momentum equation of fluid mechanics, cannot be correctly effected independently of the laws of thermodynamics. While Ottinger's modification of GENERIC necessitates fundamental changes in the foundations of fluid mechanics in regard to momentum transport, no basic changes are required in the foundations of linear irreversible thermodynamics (LIT) beyond recognizing the need to add volume to the usual list of extensive physical properties undergoing transport in single-species fluid continua, namely mass, momentum and energy. An alternative, nonGENERICally based approach to LIT, derived from our findings, is outlined at the conclusion of the paper. Finally, our proposed modifications of both Cauchy's linear momentum equation and Newton's rheological constitutive law for fluid-phase continua are noted to be mirrored by counterparts in the literature for solid-phase continua dating back to the classical interdiffusion experiments of Kirkendall and their subsequent interpretation by Darken in terms of diffuse volume transport.

99 citations

Journal ArticleDOI
TL;DR: It is shown that starting from a model based on an explicit discrete particle distribution one can separate the magnetic field inside the MSE into two contributions: one which depends on the shape of the sample with finite size and the other, which depend on the local spatial particle distribution.
Abstract: A new theoretical formalism is developed for the study of the mechanical behaviour of magneto-sensitive elastomers (MSEs) under a uniform external magnetic field This formalism allows us to combine macroscopic continuum-mechanics and microscopic approaches for complex analysis of MSEs with different shapes and with different particle distributions It is shown that starting from a model based on an explicit discrete particle distribution one can separate the magnetic field inside the MSE into two contributions: one which depends on the shape of the sample with finite size and the other, which depends on the local spatial particle distribution The magneto-induced deformation and the change of elastic modulus are found to be either positive or negative, their dependences on the magnetic field being determined by a non-trivial interplay between these two contributions Mechanical properties are studied for two opposite types of coupling between the particle distribution and the magneto-induced deformation: absence of elastic coupling and presence of strong affine coupling Predictions of a new formalism are in a qualitative agreement with existing experimental data

98 citations

Journal ArticleDOI
TL;DR: In this article, a theory for the dynamics of an interface in a two-phase elastic solid with kinetics driven by mass transport and stress is developed, which is based on balance laws for mass and force in conjunction with a version of the second law appropriate to a mechanical system out of equilibrium.
Abstract: We develop a theory for the dynamics of an interface in a two-phase elastic solid with kinetics driven by mass transport and stress. We consider a two-phase system consisting of bulk regions separated by a sharp interface endowed with energy and capable of supporting force. Our discussion is based on balance laws for mass and force in conjunction with a version of the second law-appropriate to a mechanical system out of equilibrium-which we use to develop a suitable constitutive theory for the interface. It is assumed that mass transport is characterized by the bulk diffusion of a single independent species; we neglect mass diffusion within the interface; limit our discussion to a continuous chemical potential and to a coherent interface; neglect the elasticity of the interface; and consider only infinitesimal deformations, neglecting inertia. We show that the field equations and free-boundary conditions can be developed in a simple manner in terms of the diffusion potential and its time derivatives, as opposed to the usual formulation in terms of concentration. Natural consequences of the thermodynamic framework are Lyapunov functions for the resulting evolution problems. This leads to a hierarchy of variational principles that should describe the equilibrium shapes of misfitting particles as well as possible microstructures that might form; these principles are applicable both in the absence and presence of an applied stress.

98 citations

Journal ArticleDOI
TL;DR: In this paper, a single-walled nanotube structure embedded in an elastic matrix is simulated by the nonlocal Euler-Bernoulli, Timoshenko, and higher order beams.

98 citations


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