A new method for the deformation of curves is presented. It is based upon a decomposition of the linear elasticity problem into basic physical laws. Unlike other methods which solve the partial differential equation arising from the physical laws by numerical techniques, we encode the basic laws using computational algebraic topology. Conservative laws use exact global values while constitutive...

The constant γ in the strengthened Cauchy-Bunyakowskii-Schwarz inequality is a basic tool for the construction of two-level and multilevel preconditioning matrices. Therefore many authors consider estimates or computations of this quantity. In this paper the bilinear form arising from 3D linear elasticity problems is considered on a polyhedron. The cosine of the abstract angle between multileve...

Multigrid has been a popular solver method for nite element and nite di erence problems with regular grids for over 20 years. The application of multigrid to unstructured problems is, however, not well understood and has been an active area of research in recent years. The two most promising categories of unstructured multigrid methods are 1) \geometric" methods that use standard nite element c...

This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity (Jiang and Liu 2003) and rate-sensitive plastic flow (Jop et al. 2006) are combined into one universal granular continuum law, capable of predicting flowing regions and stagnant zones simultaneously in any arbitrary 3D f...

This article proposes a hyperelastic 3D deformable template for the segmentation of soft structures. It relies on a template, which is a topological, geometrical and material model of the structure to segment. The template is modeled as an elastic body which is deformed by forces derived from the image. The proposed model is based on the nonlinear three-dimensional elasticity problem with a bou...

We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet’s center is of order h| logh|, where h ! 1 is the thickness of the sheet, we establish matching upper and lower bounds of order h2| logh| for the minimum elastic energy per unit thickness, wit...

In this paper, we present a new computational pipeline for designing and fabricating 4D garments as knitwear that considers comfort during body movement. This is achieved by careful control of elasticity distribution to reduce uncomfortable pressure unwanted sliding caused motion. We exploit the ability knit patterns in different elastic levels single-jersey jacquard (SJJ) with two yarns. desig...

The behavior of elastic waves in a three-dimensional isotropic incompressible material is studied. Unlike compressible elastodynamics, where there are nonlinear interactions of shear and pressure waves, with incompressible elastodynamics the only waves present are shear waves. In an isotropic system, shear waves are linearly degenerate, and therefore global solutions to the perturbative incompr...

For the bulk and monolayer IV group carbides in scope of Keating and/or Harrison models analytical expressions are obtained for second order elastic constants c ij , sound velocities v, third ijk pressure dependencies Grneisen constant, thermal expansion coefficient temperature dependence moduli. It is shown that row SiC-GeC-SnC values all considered characteristics decrease while increases. Al...