Search results for "continuum mechanic"
showing 7 items of 27 documents
A thermodynamical model of inhomogeneous superfluid turbulence
2007
In this paper we perform a thermodynamical derivation of a nonlinear hydrodynamical model of inhomogeneous superfluid turbulence. The theory chooses as fundamental fields the density, the velocity, the energy density, the heat flux and the averaged vortex line length per unit volume. The restrictions on the constitutive quantities are derived from the entropy principle, using the Liu method of Lagrange multipliers. The mathematical and physical consequences deduced by the theory are analyzed both in the linear and in the nonlinear regime. Field equations are written and the wave propagation is studied with the aim to describe the mutual interactions between the second sound and the vortex t…
Guaranteed Error Bounds I
2014
In Chap. 3, we discussed the main ideas of fully reliable error control methods and the corresponding numerical algorithms with the paradigm of simple elliptic type problems. This chapter is intended to show a deep connection between a posteriori estimates of the functional type and physical relations generating the problem. Also, the goal of this chapter is to consider a wider set of problems arising in various applications and explain things in terms of computational mechanics. For this purpose, we begin with a simple class of mechanical problems (straight beams) and after that consider curvilinear beams and more complicated models of continuum mechanics (linear elasticity, viscous fluids…
Expected principal stress directions under multiaxial random loading. Part I: theoretical aspects of the weight function method
1999
As has been observed experimentally by many authors, the position of the fatigue fracture plane appears to strongly depend on the directions of the principal stresses or strains. In Part I of the present work the expected principal stress directions under multiaxial random loading are theoretically obtained by averaging the instantaneous values of the three Euler angles through some suitable weight functions which are assumed to take into account the main factors influencing fatigue behaviour. Then, in Part II, it is examined how such theoretical principal directions determined by applying the proposed procedure are correlated to the position of the experimental fracture plane for some fati…
New Indicators of Approximation Errors for Problems in Continuum Mechanics
2010
In this paper we present a new error indicator for approximate solutions of elliptic problems. We discuss error indication with the paradigm of the diffusion problem, however the techniques are easily adaptable to more complicated elliptic problems, for example to linear elasticity, viscous flow models and electromagnetic models. The proposed indicator does not contain mesh dependent constants and it admits parallelization. nonPeerReviewed
Biomechanical analysis of Ascending Thoracic Aortic Aneurysm (ATAA)
2021
According to the reports of the World Health Organisation (WHO), cardiovascular diseases are the number one cause of death worldwide. Specifically, arterial disease and degeneration are the major reasons for cardiovascular death and disability. Because these diseases are dependent on the changes of the mechanical properties of the arterial wall, it is very important to know as much as possible about the structural composition of arteries. The human aorta is the biggest artery in the body and consists of three main parts, ascending aorta, aortic arch and descending aorta. The walls of the arteries consist of three layers, the intima, media and adventitia, where each of the layers has differe…