Mathematical Modeling in Mechanics of Granular Materials by Oxana Sadovskaya, Vladimir Sadovskii, Holm Altenbach

Posted by

By Oxana Sadovskaya, Vladimir Sadovskii, Holm Altenbach

This monograph comprises unique leads to the sector of mathematical and numerical modeling of mechanical habit of granular fabrics and fabrics with diverse strengths. It proposes new types assisting to outline zones of the tension localization. The booklet exhibits find out how to examine methods of the propagation of elastic and elastic-plastic waves in loosened fabrics, and constructs versions of combined variety, describing the circulation of granular fabrics within the presence of quasi-static deformation zones. In a final half, the ebook experiences a numerical attention of the versions on multiprocessor computers.
The publication is meant for clinical researchers, academics of universities, post-graduates and senior scholars, who concentrate on the sector of the deformable fabrics mechanics, mathematical modeling and adjoining fields of utilized and calculus mathematics.

Show description

Read Online or Download Mathematical Modeling in Mechanics of Granular Materials PDF

Similar fluid dynamics books

Augmented Lagrangian and operator-splitting methods in nonlinear mechanics

A necessity for a deeper realizing of the convergence houses of augmented Lagrangian algorithms and in their dating to operator-splitting tools reminiscent of alternating-methods course and the improvement of extra effective algorithms brought on the authors to put in writing this booklet. the amount is orientated to purposes in continuum mechanics.

The Navier-Stokes equations

The Navier-Stokes equations have been firmly proven within the nineteenth Century because the approach of nonlinear partial differential equations which describe the movement of most typically taking place fluids in air and water, and because that point particular options were sought by means of scientists. jointly those strategies let a transparent perception into the habit of fluids, delivering a car for novel mathematical equipment and an invaluable money for computations in fluid dynamics, a box within which theoretical learn is now ruled via computational equipment.

Thermal Spray Fundamentals: From Powder to Part

This ebook presents readers with the basics precious for realizing thermal spray know-how. assurance contains in-depth discussions of varied thermal spray techniques, feedstock fabrics, particle-jet interactions, and linked but very severe issues: diagnostics, present and rising functions, floor technology, and pre and post-treatment.

Theoretical and Applied Aerodynamics: and Related Numerical Methods

This booklet covers classical and glossy aerodynamics, theories and comparable numerical tools, for senior and first-year graduate engineering scholars, including:-The classical power (incompressible) circulation theories for low pace aerodynamics of skinny airfoils and low and high element ratio wings. - The linearized theories for compressible subsonic and supersonic aerodynamics.

Additional info for Mathematical Modeling in Mechanics of Granular Materials

Example text

If each function fl (u), where l = 1, . . , n, is convex then the set F = u ∈ Rm fl (u) ≤ 0, l = 1, . . , n is convex as well. To prove it, we consider two elements u and u˜ ∈ F. e. uλ ∈ F. Hence, and fl (u) F is convex. It turns out that any convex set can be described with the help of some convex function. The Minkowski function yields one way of such a description. Assume that F is a convex closed set in the space Rm (u) for which the point 0 (the origin of coordinates) is an interior point (with at least one interior point of the set, this requirement can be always satisfied due to translation of a coordinate system).

Let f (u) be convex. 2) holds. Using the Taylor expansion of its left-hand side in the neighborhood of the point u with the estimate of a remainder term in the Peano form, we obtain the inequality 1 ∂ 2 f (u) (u˜ − u) (u˜ − u) + o |u˜ − u|2 ≥ 0, 2 ∂ u2 which leads to the condition of non-negative definiteness of ∂ 2 f /∂ u2 at the point u ∈ F since u˜ is arbitrary. A proof of the converse statement is based on the Taylor ˜ with a remainder term in the Lagrange form: expansion of the function f (u) ˜ = f (u) + (u˜ − u) f (u) ∂ 2 f (uλ ) ∂ f (u) 1 + (u˜ − u) (u˜ − u), ∂u 2 ∂ u2 where λ ∈ (0, 1).

Later on a medium adapts itself to the periodic load and never achieves a compaction mode (Fig. 17). In the case of an increasing amplitude, the interval of a closed state of a contact is periodically repeated (Figs. 19). With increasing frequency (see Figs. 21), the curve 2 approaches to the curve 1. These curves can coincide exactly only in the case of a rheological scheme involving a single elastic element, hence, the influence of viscosity, plasticity, and heterostrength in comparison with elastic properties of a material becomes insignificant with increasing a loading frequency.

Download PDF sample

Rated 4.56 of 5 – based on 31 votes