Topic
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 paper, the small-scale effect of wave propagation dispersion relation on carbon nanotubes (CNTs) wave numbers and diameters was investigated with two nonlocal continuum mechanics models: elastic Euler-Bernoulli and Timoshenko beam models.
Abstract: Wave propagation in carbon nanotubes (CNTs) is studied with two nonlocal continuum mechanics models: elastic Euler-Bernoulli and Timoshenko beam models [Philos. Mag. 41, 744 (1921)]. The small-scale effect on CNTs wave propagation dispersion relation is explicitly revealed for different CNTs wave numbers and diameters by theoretical analyses and numerical simulations. The asymptotic phase velocities and frequency are also derived from nonlocal continuum mechanics. The scale coefficient in nonlocal continuum mechanics is roughly estimated for CNTs from the obtained asymptotic frequency. In addition, the applicability and comparison of the two nonlocal elastic beam models to CNTs wave propagation are explored through numerical simulations. The research findings are proved effective in predicting small-scale effect on CNTs wave propagation with a qualitative validation study based on the published experimental reports in this field.
609 citations
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TL;DR: In this article, it is shown that failure occurs by progressive distributed damage during which the material exhibits strain-softening, i.e., a gradual decline of stress at increasing strain.
Abstract: In heterogeneous materials such as concretes or rocks, failure occurs by progressive distributed damage during which the material exhibits strain‐softening, i.e., a gradual decline of stress at increasing strain. It is shown that strain‐softening which is stable within finite‐size regions and leads to a nonzero energy dissipation by failure can be achieved by a new type of nonlocal continuum called the imbricate continuum. Its theory is based on the hypothesis that the stress depends on the change of distance between two points lying a finite distance apart. This continuum is a limit of a discrete system of imbricated (regularly overlapping) elements which have a fixed length, l, and a cross‐section area that tends to zero as the discretization is refined. The principal difference from the existing nonlocal continuum theory is that the equation of motion involves not only the averaging of strains but also the averaging of stress gradients. This assures that the finite element stiffness matrices are symmet...
599 citations
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TL;DR: In this paper, the effect of adding nonlocal or gradient terms to the constitutive modeling may enhance the ability of the models to describe such situations, and the relation between these enhancements are examined in a continuum damage setting.
590 citations
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TL;DR: In this paper, a promising approach is connected with the use of continuum mechanics, which has been successfully applied to the analysis of compaction of porous bodies, based upon the theories of plastic and nonlinear-viscous deformation of porous body.
Abstract: Theoretical concepts of sintering were originally based upon ideas of the discrete nature of particulate media. However, the actual sintering kinetics of particulate bodies are determined not only by the properties of the particles themselves and the nature of their local interaction with each other, but also by macroscopic factors. Among them are externally applied forces, kinematic constraints (e.g. adhesion of the sample's end face and furnace surface), and inhomogeneity of properties in the volume under investigation (e.g. inhomogeneity of initial density distribution created during preliminary forming operations). Insufficient treatment of the questions enumerated above was one of the basic reasons hindering the use of sintering theory. A promising approach is connected with the use of continuum mechanics, which has been successfully applied to the analysis of compaction of porous bodies. This approach is based upon the theories of plastic and nonlinear-viscous deformation of porous bodies. Similar ideas have recently been embodied in a continuum theory of sintering. The main results of the application of this theory for the solution of certain technological problems of sintering are introduced including their thermo–mechanical aspects.
581 citations
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01 Oct 1963
TL;DR: In this article, a linear theory is formulated of a threedimensional, elastic continuum which has some of the properties of a crystal lattice as a result of the inclusion, in the theory, of the idea of the unit cell.
Abstract: : A linear theory is formulated of a three-dimensional, elastic continuum which has some of the properties of a crystal lattice as a result of the inclusion, in the theory, of the idea of the unit cell. The equations yield wave-dispersion relations with acoustic and optical branches of the same character as those found at long wave-lengths in crystal lattice theories and observed in neutron scattering experiments. Although specific solutions are not exhibited in detail, it is apparent from the form of the equations that there will be interesting surface effects under conditions of both motion and equilibrium. (Author)
571 citations