Generalized Korn's inequality and conformal Killing vectors

Korn's inequality plays an important role in linear elasticity theory. This inequality bounds the norm of the derivatives of the displacement vector by the norm of the linearized strain tensor. The kernel of the linearized strain tensor are the infinitesimal rigid-body translations and rotations (Killing vectors). We generalize this inequality by replacing the linearized strain tensor by its trace free part. That is, we obtain a stronger inequality in which the kernel of the relevant operator are the conformal Killing vectors. The new inequality has applications in General Relativity.Comment: 8 page

Elasto-Plastic Stress Analysis in Rotating Disks and Pressure Vessels Made of Functionally Graded Materials

Abstract A new elastio-plastic stress solution in axisymmetric problems (rotating disk, cylindrical and spherical vessel) is presented. The rotating disk (cylindrical and spherical vessel) was made of a ceramic/metal functionally graded material, i.e. a particle-reinforced composite. It was assumed that the material's plastic deformation follows an isotropic strain-hardening rule based on the von-Mises yield criterion. The mechanical properties of the graded material were modeled by the modified rule of mixtures. By assuming small strains, Hencky's stress-strain relation was used to obtain the governing differential equations for the plastic region. A numerical method for solving those differential equations was then proposed that enabled the prediction of stress state within the structure. Selected finite element results were also presented to establish supporting evidence for the validation of the proposed approach

Influence of thermally induced chemorheological changes on the torsion of elastomeric circular cylinders

When an elastomeric material is deformed and subjected to temperatures above some characteristic value T cr (near 100 ∘ C for natural rubber), its macromolecular structure undergoes time and temperature-dependent chemical changes. The process continues until the temperature decreases below T cr . Compared to the virgin material, the new material system has modified properties (reduced stiffness) and permanent set on removal of the applied load.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46097/1/161_2006_Article_9.pd

A theory of stress softening of elastomers based on finite chain extensibility

In this paper we develop a theory to describe the Mullins effect in rubber-like solids, based on the notion of limiting chain extensibility associated with the Gent model of rubber elasticity. We relate the theory to the mechanisms of network alteration and to the pseudo-elasticity theory of the Mullins effect. The inherently anisotropic nature of the Mullins effect is also discussed