Continuum mechanics

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

Generalized constitutive equation for polymeric liquid crystals: Part 2. non-homogeneous systems

Abstract: The Hamiltonian formulation of equations in continuum mechanics through Poisson brackets was used in Ref. 1 to develop a constitutive equation for the stress and the order parameter tensor for a polymeric liquid crystal. These equations were shown to reduce to the homogeneous Doi equations as well as to the Leslie-Ericksen-Parodi (LEP) constitutive equations under small deformations [1]. In this paper, these equations are fitted against the non-homogeneous Doi equations through the simulation of the spinodal decomposition of the isotropic state when it is suddenly brought into a parameter region in which it is thermodynamically unstable. Linear stability analysis reveals the wavelength of the most unstable fluctuation as well as its initial growth rate. Results predicted from this theory compare well with the predictions of Doi for the spinodal decomposition using an extended molecular rigid-rod theory in terms of the distribution function. This completes the development of a generalized constitutive equation for polymeric liquid crystals initiated in Part 1.

A Corpuscular Approach to Continuum Mechanics: Basic Considerations

Abstract: The macroscopic behaviour of a material derives ultimately from its microstructure, which at the molecular level and below is of a fundamentally discrete nature. As much is often known of the microstructure, molecular interactions, and thermal motions associated with specific materials, it is of interest to ascertain whether, and to what extent, such information can usefully be incorporated into continuum models. The first step in this direction is to treat discrete fundamental entities (for example, molecules, ions, or atoms) as particles (point masses) and relate continuum theories to corpuscular considerations. This is, of course, an important feature of the kinetic theory of gases, lattice dynamics, and statistical mechanics. The first two theories take account of particle interactions and thermal motions as these pertain to general motions of moderately rarefied gases and vibrations in ordered solids, respectively, but such considerations play no explicit part in standard formulations of statistical mechanics. Many discussions which bear upon the relations between discrete descriptions of materials and continuum mechanics have been given (motivated in the main by considerations of microstructure), such as the contributions of Ericksen (1960, 1961), Dahler & Scriven (1963), Eringen & Suhubi (1964), Green & Rivlin (1964), Krumhansl (1965), Eringen, Kroner, Krumhansl, Kunin, Mindlin, and Rivlin in Kroner (1968), Rivlin (1968, 1976), Alblas (1976), and Capriz & Podio-Guidugli (1976, 1977). This work is intended to complement the aforementioned by emphasising the roles played in general by corpuscular interactions and thermal motions in the formulation of continuum theories.

Continuum mechanics modelling and augmented Lagrangian formulation of large deformation frictional contact problems

Abstract: Reference LMAF-CONF-2000-002View record in Web of Science Record created on 2005-09-14, modified on 2017-09-24

Granular vortices: Identification, characterization and conditions for the localization of deformation

Abstract: We relate the micromechanics of vortex evolution to that of force chain buckling and, on this basis, formulate the conditions for strain localization in a continuum model of dense granular media. Using the traditional bifurcation analysis of shear bands, we show that kinematic vortex fields are in fact solutions to the boundary value problem satisfying null boundary conditions. To establish an empirical basis for our study, we first develop a method to identify the location of the core and boundary of each vortex from a given displacement field in two dimensions. We then employ this method to characterize the residual deformation field (i.e., the deviation of particle motions from the continuum deformation) in a physical experiment and a discrete element simulation of dense granular samples submitted to biaxial compression. Vortices in the failure regime are essentially confined to the shear band. Primary vortices, the clear majority, rotate in the same direction as the shear band; secondary vortices, the so-called wakes, rotate in the opposite direction. Primary vortices align in spatial succession along the central axis of the band; wakes form next to the band boundaries, in between and beside two adjacent primary vortices. Force chain buckling, the governing mechanism for shear bands, is responsible for vortex formation in the failure regime. Vortex dynamics are consistent with stick-slip dynamics. From quiescent conditions of jamming or stick, vortical motions arise from force chain buckling and associated relative particle rotations and sliding; these in turn precipitate intermittent periods of unjamming or slip, evident in the attendant drops in stress ratio and bursts in both kinetic energy and local nonaffine deformation. A kinematic vortex field inside shear bands is proposed that is consistent with the equations of continuum mechanics and the underlying instability of force chain buckling: such a field is periodic with a repeating unit cell comprising a primary vortex at the center of the band, with two trailing wakes close next to the band boundaries.