On continuous dependence in finite elasticity

Continuous Dependence of Solutions in Magneto-elasticity Theory

We prove continuous dependence on the intensity coefficient and continuous dependence on the external data in the theory of magneto-elasticity. We do not require the Lamé coefficients to be positive. We use logarithmic convexity arguments similar to those of Ames and Straughan (1992) in classical thermoelasticity. 1. Introduction. In recent years, much attention has been directed to the knowled...

On the Displacement-Stress Continuous Finite Elements

For the analysis of composite media, three different compatible and mixed finite element formulations are presented which apriori enforce the continuity of stresses as well as displacements at the element interfaces. The formulations are applied for the analysis of hi-material interfaces in two problems often encountered in the field of orthopaedic biomechanics, that is the fixation analysis in...

Continuous Dependence and Differentiation of Solutions of Finite Difference Euqations

Polygonal finite elements for finite elasticity

Nonlinear elastic materials are of great engineering interest, but challenging to model with standard fi nite elements. The challenges arise because nonlinear elastic materials are characterized by nonconvex stored-energy functions as a result of their ability to undergo large reversible deformations, are incompressible or nearly incompressible, and often times possess complex microstructures. ...

On a dependence relation in finite lattices

We study a dependence relation between the join-irreducible elements of a finite lattice that generalizes the classical perspectiuity relation between the atoms of a geometric lattice. This relation is useful in the axiomatic approach of latticial consensus problems, since if it is strongly connected one can get arrowian theorems. First we show that the dependence relation is linked with the ar...