5,751 research outputs found
Global Solutions for Incompressible Viscoelastic Fluids
We prove the existence of both local and global smooth solutions to the
Cauchy problem in the whole space and the periodic problem in the n-dimensional
torus for the incompressible viscoelastic system of Oldroyd-B type in the case
of near equilibrium initial data. The results hold in both two and three
dimensional spaces. The results and methods presented in this paper are also
valid for a wide range of elastic complex fluids, such as magnetohydrodynamics,
liquid crystals and mixture problems.Comment: We prove the existence of global smooth solutions to the Cauchy
problem for the incompressible viscoelastic system of Oldroyd-B type in the
case of near equilibrium initial dat
On 2D Viscoelasticity with Small Strain
An exact two-dimensional rotation-strain model describing the motion of
Hookean incompressible viscoelastic materials is constructed by the polar
decomposition of the deformation tensor. The global existence of classical
solutions is proved under the smallness assumptions only on the size of initial
strain tensor. The proof of global existence utilizes the weak dissipative
mechanism of motion, which is revealed by passing the partial dissipation to
the whole system.Comment: Different contributions of strain and rotation of the deformation are
studied for viscoelastic fluids of Oldroyd-B type in 2
On the Mathematical and Geometrical Structure of the Determining Equations for Shear Waves in Nonlinear Isotropic Incompressible Elastodynamics
Using the theory of hyperbolic systems we put in perspective the
mathematical and geometrical structure of the celebrated circularly polarized
waves solutions for isotropic hyperelastic materials determined by Carroll in
Acta Mechanica 3 (1967) 167--181. We show that a natural generalization of this
class of solutions yields an infinite family of \emph{linear} solutions for the
equations of isotropic elastodynamics. Moreover, we determine a huge class of
hyperbolic partial differential equations having the same property of the shear
wave system. Restricting the attention to the usual first order asymptotic
approximation of the equations determining transverse waves we provide the
complete integration of this system using generalized symmetries.Comment: 19 page
On probabilistic aspects in the dynamic degradation of ductile materials
Dynamic loadings produce high stress waves leading to the spallation of
ductile materials such as aluminum, copper, magnesium or tantalum. The main
mechanism used herein to explain the change of the number of cavities with the
stress rate is nucleation inhibition, as induced by the growth of already
nucleated cavities. The dependence of the spall strength and critical time with
the loading rate is investigated in the framework of a probabilistic model. The
present approach, which explains previous experimental findings on the
strain-rate dependence of the spall strength, is applied to analyze
experimental data on tantalum.Comment: 28 pages, 13 figures, 3 table
- …