Recently, Rajagopal [1] has considered an unsteady shearing flow of the incompressible second-order fluid with the constitutive equation for the extra stress S given by S = juAj 4axA2 + «2^i(1) In (1), ju, aj, a2 are constants, with jn > 0; \1 and A2 are the first two Rivlin-Ericksen tensors [2]. Rajagopal [1] showed that the time-dependent plane flow x = u(y,t), y = 0, in {x, y, t) e (-oo, oo)...

We determine a constitutive equation for developed three-dimensional granular flows based on series of discrete element method simulations. In order to capture non-local phenomena, normal stress differences, and secondary flows, we extend previously proposed temperature-sensitive rheological model by considering Rivlin-Ericksen tensors up second order. Three parameters are calibrated with the i...

Dedicated to T. Rivlin on the occasion of his 70th birthday Lower and upper bounds are given for the trace of the inverse tr(A ?1) and the determinant det(A) of a symmetric positive deenite matrix A. They are derived by applying Gaussian quadrature and related theory. The bounds for det(A) appears to be new. For the bounds of tr(A ?1), the Kantorovich inequality is available for providing such ...

The steady flow arising due to the rotation of a non-Newtonian fluid at a larger distance from a stationary disk is extended to the case where the disk surface admits partial slip. The constitutive equation of the non-Newtonian fluid is modeled by that for a Reiner-Rivlin fluid. The momentum equation gives rise to a highly nonlinear boundary value problem. Numerical solution of the governing no...

This study investigates the effects of different solid models on predictions of brain shift for three craniotomies. We created a generic 3D brain model based on healthy human brain and modeled the brain parenchyma as single continuum and constrained by a practically rigid skull. We have used elastic model, hyperelastic 1st, 2nd, and 3rd Ogden models, and hyperelastic Mooney-Rivlin with 2and 5-p...

Assuming that the disc material can be modeled either as Mooney–Rivlin or as Hookean and the steel ring enclosing the disc as Hookean, the energy release rates as a function of the crack length are evaluated and compared. Two loadings are considered––one in which the surface of the star shape hole in the disc is loaded by a uniform pressure and the other in which the temperature of the composit...

Flutes are elongated sediment ridges formed at the base of glaciers and ice sheets. In this paper, we show that flutes can be the product of a corkscrew-like spiral flow in basal ice that removes sediment from troughs between flutes and deposits it at their crests, as first suggested by Shaw and Freschauf. In order to generate the type of basal ice flow required for this mechanism, the viscous ...

We analytically analyze finite plane strain twisting deformations of a hollow cylinder made of an isotropic and inhomogeneousMooney-Rivlinmaterial withmaterial moduli varying in the radial direction. The cylinder is deformed by applying either tangential tractions on the inner surface and tangential displacements on the outer surface or vice versa. The radial variation of the moduli is found th...

for every n ≥ 2, where Fn denotes the set of all polynomials of degree at most n with coefficients from {−1, 0, 1}. Littlewood considered minimization problems of this variety on the unit disk. His most famous, now solved, conjecture was that the L1 norm of an element f ∈ Fn on the unit circle grows at least as fast as c logN , where N is the number of non-zero coefficients in f and c > 0 is an...