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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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Journal ArticleDOI
Abstract: The state of the art in the rheology of polymer fluids (polymer solutions and melts) and filled composites is reviewed. This review includes two parts: analysis of the basic principles for the construction of rheological constitutive equations in terms of the continuum mechanics and finding correlations between the rheological characteristics and molecular structure of polymers on the basis of molecular models. Possible approaches to the formulation of constitutive equations are discussed. Special attention is focused on the correct selection of the form of the elastic potential for rubbery deformations induced under the flow of polymer fluids. The use of a power-law potential leads to the best results. To gain unequivocal results and minimize the number of free constants, viscoelastic characteristics of polymer fluids should be described in terms of a continuous relaxation spectrum as a power-law function limited by the maximum relaxation time. To solve the boundary problems by the selected constitutive equation, analysis of the dynamic stability is required, because the combination of viscosity and elasticity controls the limits of flow upon shear and tensile. Deformation can also lead to changes in the phase state of a polymer system. Furthermore, correct formulation of the boundary conditions is necessary because, in many cases, polymer fluids and, in particular, filled materials tend to efficient slip along walls. The existing molecular models adequately describe the characteristics of monodisperse polymers; however, on passing to polydisperse polymers, the additional use of semiempirical approaches is required. The modern level of experimental studies allows test measurements over a wide range of deformation rates, frequencies, and temperatures. However, in this field, the mainstream tendency in experimental studies is concerned with hybrid methods, which combine direct rheological measurements with optical observations of local structure and its evolution in the material. In this case, various physical principles of measurements are applied. In recent years, much interest has been focused on studying polymer compositions containing nanosized fillers, which are able to produce their structures in melt.

53 citations

Journal ArticleDOI
TL;DR: In this paper, the authors show that without the mathematical concept of partial diAerentiation (as in the biharmonic equation of elasticity theory that brings strain compatability, Hooke's law, and stress equilibrium together) these spatial and temporal variations cannot be accounted for explicitly.

53 citations

Journal ArticleDOI
TL;DR: The phase field method coupled with the Navier-Stokes equations is a rather new approach for scale-resolving numerical simulation of interfacial two-phase flows as mentioned in this paper, and the intention is to implement it as finite-volume method in the OpenFOAM® and make it freely available.
Abstract: The phase-field method coupled with the Navier-Stokes equations is a rather new approach for scale-resolving numerical simulation of interfacial two-phase flows. The intention is to implement it as finite-volume method in the open source library for computational continuum mechanics OpenFOAM® and make it freely available. An overview on the governing equations is given and the numerical method is shortly discussed. The focus is on application and validation of the code for some fundamental wetting phenomena, namely the capillary rise in a narrow channel and the spreading of a droplet on a flat surface, which is chemically homogeneous or regularly patterned. The numerical results on static meshes agree well with analytical solutions and experimental/numerical results from literature. Also, first 3D finite-volume simulations with adaptive mesh refinement near the interface are presented as a key element to achieve CPU-time efficient simulations.

53 citations

Journal ArticleDOI
TL;DR: In this paper, the elastic buckling and vibration characteristics of isotropic and orthotropic nanoplates using finite strip method were analyzed using Eringen's nonlocal continuum elasticity.

53 citations


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