Competition between different strains of a micro-parasite which provide complete cross-protection and cross-immunity against each other selects for maximal basic replacement ratio if, in the absence of the disease, the host population is exclusively limited in its growth by a nonlinear population birth rate. For mass action incidence, the principle of R0 maximization can be extended to exponent...

This paper presents algorithms for optimal development (flattening) of a smooth continuous curved surface embedded in three-dimensional space into a planar shape. The development process is modeled by in-plane strain (stretching) from the curved surface to its planar development. The distribution of the appropriate minimum strain field is obtained by solving a constrained nonlinear programming ...

This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat’s eye stream line topology within a vortex. When the external strain field is smoothly switched off, the cat’s eyes may persist, or they may disappear as the vortex relaxes back to axisymmetry. A numerical study obtains criteria for th...

A finite strain nonlinear viscoelastic constitutive model is used to study the uniaxial tension behaviour of a chemical polyampholyte (PA) gel.

It is shown that the strain field of an edge dislocation in a smectic crystal must be described in the framework of nonlinear theory, even far away from the core region. We present an exact solution of this nonlinear problem. The result of the linear theory is recovered in the limit of large bending rigidity.

The unique lattice structure and properties of graphene have drawn tremendous interests recently. By combining continuum and atomistic approaches, this paper investigates the mechanical properties of single-atomic-layer graphene sheets. A theoretical framework of nonlinear continuum mechanics is developed for graphene under both in-plane and bending deformation. Atomistic simulations are carrie...

Mechanical behavior of articular cartilage was characterized in unconfined compression to delineate regimes of linear and nonlinear behavior, to investigate the ability of a fibril-reinforced biphasic model to describe measurements, and to test the prediction of biphasic and poroelastic models that tissue dimensions alter tissue stiffness through a specific scaling law for time and frequency. D...

The periodontal ligament (PDL) is a soft biological tissue which shows a strongly nonlinear and time dependent mechanical behavior. Recent experiments on rabbit PDL revealed that the rate of stress relaxation is strain dependent. This nonlinear behavior of PDL cannot be described well by the separable quasi linear viscoelasticity theory which is usually used in tissue biomechanics. Therefore, P...

An efficient formulation for dynamic analysis of planar Timoshenko’s beam with finite rotations is presented. Both an inertial frame and a rotating frame are introduced to simplify computational manipulation. The kinetic energy of the system is obtained by using the inertial frame so that it takes a quadratic uncoupled form. The rotating frame together with the small strain assumption is employ...