STRAIN RATE–DEPENDENT BEHAVIOR OF UNCURED RUBBER: EXPERIMENTAL INVESTIGATION AND CONSTITUTIVE MODELING

ABSTRACT The strain rate dependence of uncured rubber is investigated through a series of tensile tests (monotonic, multistep relaxation, cyclic creep tests) at different strain rates. In addition, loading/unloading tests in which the strain rate is varied every cycle are carried out to observe their dependence on the deformation history. A strain rate–dependent viscoelastic–viscoplastic constitutive model is proposed with the nonlinear viscosity and process-dependent recovery properties observed in the test results. Those properties are implemented by introducing evolution equations for additional internal variables. The identified material parameters capture the experiments qualitatively well. The proposed model is also evaluated by finite element simulations of the building process of a tire, followed by the in-molding.

Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity

In this paper, we investigate spectral stability of traveling wave solutions to 1D quantum hydrodynamics system with nonlinear viscosity in the [Formula: see text], that is, density and velocity, variables. We derive a sufficient condition for the stability of the essential spectrum and we estimate the maximum modulus of eigenvalues with non-negative real part. In addition, we present numerical computations of the Evans function in sufficiently large domain of the unstable half-plane and show numerically that its winding number is (approximately) zero, thus giving a numerical evidence of point spectrum stability.

Алгоритм нелинейной вязкости с возмущением для нерасширяющих многозначных отображений

The viscosity iterative algorithms for finding a common element of the set of fixed points for nonlinear operators and the set of solutions of variational inequality problems have been investigated by many authors. The viscosity technique allow us to apply this method to convex optimization, linear programming and monoton inclusions. In this paper, based on viscosity technique with perturbation, we introduce a new nonlinear viscosity algorithm for finding an element of~the set of~fixed points of nonexpansive multi-valued mappings in a Hilbert spaces. Furthermore, strong convergence theorems of~this algorithm were established under suitable assumptions imposed on~parameters. Our results can be viewed as a generalization and improvement of various existing results in the current literature. Moreover, some numerical examples that show the efficiency and implementation of our algorithm are presented.

Spatial estimates for Kelvin–Voigt finite elasticity with nonlinear viscosity: Well behaved solutions in space

We provide some spatial estimates for the nonlinear partial differential equation governing anti-plane motions in a nonlinear viscoelastic theory of Kelvin–Voigt type when the viscosity is a function of the strain rate. The spatial estimates we prove are an alternative of Phragmen–Lindelöf type. These estimates are possible when a precise balance between the elastic and viscoelastic nonlinearities holds.