Geometric numerical integrators based on the Magnus expansion inbifurcation problems for non-linear elastic solids
Journal Title: Frattura ed Integrità Strutturale - Year 2014, Vol 8, Issue 29
Abstract
We illustrate a procedure based on the Magnus expansion for studying mechanical problems whichlead to non-autonomous systems of linear ODE’s. The effectiveness of the Magnus method is enlighten by theanalysis of a bifurcation problem in the framework of three-dimensional non-linear elasticity. In particular, foran isotropic compressible elastic tube subject to an azimuthal shear primary deformation we study thepossibility of axially periodic twist-like bifurcations. The approximate matricant of the resulting differentialproblem and the first singular value of the bifurcating load corresponding to a non-trivial bifurcation aredetermined by employing a simplified version of the Magnus method, characterized by a truncation of theMagnus series after the second term.
Authors and Affiliations
A. Castellano, P. Foi, S. Marzano, M. D. Piccioni
Keywords
Related Articles
- EP ID EP88631
- DOI 10.3221/IGF-ESIS.29.12
- Views 124
- Downloads 0
High temperature fatigue tests and crack growth in 40CrMoV13.9 notched components
The present paper addresses experimentally the high temperature fatigue of 40CrMoV13.9 steel and the effect of surface roughness on fatigue strength and crack initiation. The 40CrMoV13.9 steel is widely used in d...
Critical plane approach to multiaxial variable amplitude fatigue loading
A new critical plane approach based on the modified Manson-Coffin curve method (MMCCM) is presented in this paper for predicting fatigue lifetime under variable amplitude (VA) multiaxial fatigue loading. The crit...
On a kinked crack model to describe the influence of material microstructure on fatigue crack growth
Threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection. In the present paper, a theoretical model of a p...
Damage initiation in brittle and ductile materials as revealed from a fractoluminescence study
A set of heterogeneous and homogeneous materials differing in their brittle and ductile characteristics (granite, marble, silica ceramics, silicon carbide, organic glass) were subjected to impact damaging by a fa...
Cold spray technology: future of coating deposition processes
Cold spray (CS) belongs to a wide family of thermal spray technology with the difference that it is a solid state process in which spray particles are deposited via supersonic velocity impact at a temperature much...