Kumbakonam R. Rajagopal

TL;DR: In this paper, normal stress and stress relaxation of sand asphalt mixtures are measured using a torsional rheometer, and the results show the necessity for developing non-linear constitutive models for asphalt mixture.

TL;DR: In this paper, a mixture theory model is employed for coupled chemo-mechanical problems involving chemically reacting fluids flowing through deformable elastic solids, where the constitutive relations for the constituents in the mixture model are based on maximization of the rate of entropy production.

Abstract: We examine the dynamics of materials characterized by the presence of a deformation threshold beyond which no deformation is possible. The class of bodies that we are interested in studying are described by an implicit constitutive relationship between the Cauchy stress and the deformation gradient. A specific one-dimensional dynamical problem is studied, showing that the mathematical model takes the form of a hyperbolic free boundary problem in which the free boundary conditions can be of two different types, selected according to whether the stress is continuous at the interface (separating the deformable region from the fully strained region), or whether it is discontinuous. Both situations have been analyzed. Sample numerical computations are carried out using data that are relevant to biological materials. A comparison with the problem obtained from a limiting procedure for a constitutive model with a piecewise linear elastic response is performed, showing a very interesting feature, namely that the limit does not lead to the solution of the model with a threshold. This is however not surprising as the latter exhibits dissipative behavior.

TL;DR: In this paper, a boundary integral method suitable for the study of forced convection problems involving laminar fully developed flows in channels of arbitrary cross-sections is discussed, and results based on this method are compared with those available for circular, elliptical, rectangular, and triangular cross sections.

TL;DR: In this article, the authors derived a consistent asymptotic beam theory without the ad hoc assumptions usually made in the development of beam theories by expanding the displacement, the in-plane strain tensor and stress tensor in a Taylor series, leading to a system of nonlinear equations that is solved.