Continuum mechanics

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

A single theory for some quasi-static, supersonic, atomic, and tectonic scale applications of dislocations

Abstract: We describe a model based on continuum mechanics that reduces the study of a significant class of problems of discrete dislocation dynamics to questions of the modern theory of continuum plasticity As applications, we explore the questions of the existence of a Peierls stress in a continuum theory, dislocation annihilation, dislocation dissociation, finite-speed-of-propagation effects of elastic waves vis-a-vis dynamic dislocation fields, supersonic dislocation motion, and short-slip duration in rupture dynamics

Thermoelasticity in the framework of the fractional continuum mechanics

Abstract: Fractional continuum mechanics is the generalization of classical mechanics utilizing fractional calculus. Contrary to classical theory, the obtained description is non-local, which is inherently the consequence of the fractional derivative definition based on the interval. So, all fields obtained in the framework of this new formulation, such as temperature, thermal stresses, total stresses, displacements, etc., at the specific point of interest, depend on the information from its surroundings. The dimensions of these surroundings and the ways of influencing the results are governed by the fractional differential operator applied. In this article, the application of the fractional continuum mechanics to thermoelasticity is presented. A classical solution is obtained as a special case.

An inverse for the Jaumann derivative and some applications to the rheology of viscoelastic fluids

Abstract: By using a generalization of the matrizant of matrix calculus, it is shown how one can construct formally an inverse, or integral, for the well-knownJaumann derivative of continuum mechanics. Some applications to fluid rheology are then considered. First, it is shown that this integral provides, via theBoltzmann super-position principle, a generalization of Oldroyd's quasi-linear fluid model, which is related to the molecular model ofBueche. Explicit expressions for the stresses arising in a general laminar shear flow are then derived for this model. Secondly, it is indicated how the operation can be used with rheological equations which are nonlinear in the deformation-rate, but quasi-linear in stress, to solve explicitly for the stress in terms of kinematic quantities. As an example, a rheological equation for suspensions of viscoelastic spheres in aNewtonian fluid is treated.

Microstructural Stress Tensor of Granular Assemblies With Volume Forces

Abstract: This paper focuses on the discrete expression of stress tensors of assemblies containing discrete particles with volumetric loads acting on them in addition to boundary forces. Instead of the concept of continuum point, a domain containing a finite number of grains is considered. This domain is replaced by a suitably chosen equivalent continuum whose average stress is expressed-assuming that the grains are in equilibrium-in terms of contact forces and properly defined branch vectors. Symmetry of the stress tensor is also analyzed.