We introduce a framework for analyzing symmetry of 2D and 3D objects using elastic deformations of their boundaries. The basic idea is to define spaces of elastic shapes and to compute shortest (geodesic) paths between the objects and their reflections using a Riemannian structure. Elastic matching, based on optimal (nonlinear) re-parameterizations of curves, provides a better registration of p...

This paper proposes a new fundamental model of deformable objects for real-time and interactive applications. It is based on the mass-and-spring model, but in which the unit of elastic force definition for computation of dynamics is expanded from a spring to a volume element divided by the boundaries formed by mass-and-spring lattice. Displacements of the vertices of the volume element are defi...

In this paper, a modification on the fixed grid finite element method is presented and used in the solution of 2D linear elastic problems. This method uses non-boundary-fitted meshes for the numerical solution of partial differential equations. Special techniques are required to apply boundary conditions on the intersection of domain boundaries and non-boundary-fitted elements. Hence, a new met...

Materials characterized by spatially homogeneous elastic moduli undergo affine distortions when subjected to external stress at their boundaries, i.e., their displacements from a uniform reference state grow linearly with position , and their strains are spatially constant. Many materials, including all macroscopically isotropic amorphous ones, have elastic moduli that vary randomly with positi...

Neuronavigation systems are usually subject to inaccuracy due to intraoperative changes like brain shift or tumor resection. In order to correct for these deformations a biomechanical model of the brain is proposed. Not only elastic tissues, but also fluids are modeled, since an important volume of the head contains cerebrospinal fluid, which does not behave like soft tissues. Unlike other appr...

The scanning acoustic microscope gives strong contrast from small caries lesions in sections of human enamel. The uniqueness of the acoustic microscope lies in its ability to image elastic properties. In addition to revealing the extent and the shape of lesions, the microscope may also be used to measure the elastic properties point by point across an area of interest. Since enamel is anisotrop...

A simple, but scientifically rigorous, framework is proposed for estimation of effectiveness of elastic materials for the reduction of pressure fluctuations. The framework employs the intrinsic correspondence between a transformation of vorticity perturbations into acoustic waves at the elastic boundary and the conversion of transverse (shear) waves to radiated longitudinal (pressure) waves. Th...

An elastic wave propagating in a metal loses a portion of its energy from scattering caused by acoustic impedance differences existing at the boundaries of anisotropic grains. Theoretical scattering models capture this phenomena by assuming the incoming wave is described by an average elastic moduli tensorC0 i jkl (x) that is perturbed by a grain with elasticityCi jkl (x ′) where the scattering...

Abstract We study a family of gradient obstacle problems on compact Riemannian manifold. prove that the solutions these free boundary are uniformly semiconcave and, as consequence, we obtain some fine convergence results for and their boundaries. More precisely, show elastic $$\lambda $$ λ -elastic sets Hausd...

Characterization of properties of composites has attracted a great deal of attention towards exploring their applications in engineering. The purpose of this work is to study the difference of two computational microstructure models which are widely used for determining effective transverse elastic properties of unidirectional fiber reinforced composites. The first model based on the classic me...