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, a new topology optimization scheme for nonlinear electrostatic systems actuated by Coulomb's forces is presented, which is based on a monolithic formulation based on continuum mechanics theory which simultaneously calculates the electric potential and structural displacements.
51 citations
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TL;DR: In this article, the applicability of nonlocal mechanics to multiscale materials and single-scale materials is discussed, and the existing complications of solving nonlocal field problems, and various methods and approaches to overcome these complications are collected and discussed from the physical and material points of view.
51 citations
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TL;DR: In this article, a method of constructing exact solutions of the equations of molecular dynamics in non-equilibrium settings is described, where the form of the solutions correspond to some viscometric flows, and to certain analogs of viscocetric flows for fibers and membranes with one or more dimensions of atomic scale.
Abstract: We describe a method of constructing exact solutions of the equations of molecular dynamics in non-equilibrium settings. These solutions correspond to some viscometric flows, and to certain analogs of viscometric flows for fibers and membranes that have one or more dimensions of atomic scale. This work generalizes the method of objective molecular dynamics (OMD) ( Dumitrica and James, 2007 ). It allows us to calculate viscometric properties from a molecular-level simulation in the absence of a constitutive equation, and to relate viscometric properties directly to molecular properties. The form of the solutions is partly independent of the form of the force laws between atoms, and therefore these solutions have implications for coarse-grained theories. We show that there is an exact reduction of the Boltzmann equation corresponding to one family of OMD solutions. This reduction includes most known exact solutions of the equations of the moments for special kinds of molecules and gives the form of the molecular density function corresponding to such flows. This and other consequences leads us to propose an addition to the principle of material frame indifference, a cornerstone of nonlinear continuum mechanics. The method is applied to the failure of carbon nanotubes at an imposed strain rate, using the Tersoff potential for carbon. A large set of simulations with various strain rates, initial conditions and two choices of fundamental domain (unit cell) give the following unexpected results: Stone–Wales defects play no role in the failure (though Stone–Wales partials are sometimes seen just prior to failure), a variety of failure mechanisms is observed, and most simulations give a strain at failure of 15–20%, except those done with initial temperature above about 1200 K and at the lower strain rates. The latter have a strain at failure of 1–2%.
51 citations
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TL;DR: In this paper, a modified molecular structure mechanics (MSM) model was proposed for determining the mechanical properties of carbon nanotubes, particularly in the radial direction, where the interactions between two carbon atoms were modeled with the second generation force field using continuum pseudo-rectangular beam elements while the non-bonded van der Waals (vdW) interactions among atoms were simulated with the Lennard-Jones potential using spring elements.
51 citations
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TL;DR: In this paper, a nonlocal continuum with local strain approach was used to predict the response of reinforced concrete structures to pull-out tests, which was shown to be in very good agreement with test data, including size effect data.
Abstract: This paper deals with the application of continuum damage mechanics to the description of the response of reinforced concrete members. Two simplifying assumptions are made: (1) The constitutive law of concrete is the isotropic damage law; and (2) there are no displacement discontinuities at the interface between steel and concrete (this last statement is probably true only if ribbed reinforcing bars are considered). Numerical implementations face the same pathological difficulties related to strain softening and damage localization in shear bands near the steel bars. This problem and its consequence, mesh‐dependency, were solved by using the “nonlocal continuum with local strain” approach. Predictions of pull‐out tests are in very good agreement with test data, including size effect data. The study shows that it is possible to extend the nonlocal damage approach easily to the prediction of the response of reinforced concrete structures.
51 citations