Aggregated Logistics Dynamics Basics

Author: Gu Guofang / et al.
Editor-in-Chief: Cao Jikang
Publisher:
Publish Date: 2002-08-02
Features: This book discusses various rheological behaviors of polymer materials and systematically elaborates on the concepts, theories, and experimental methods of polymer rheology. It can serve as a textbook or teaching reference for undergraduate and graduate students in material science programs in engineering colleges.
Excerpt:
> Why is it necessary to conduct specialized research on the deformation of polymers? This is because classical theories of deformation are not applicable to polymer materials.
1. Classical mechanical models
(1) Classical model of solids
In classical mechanics, two models are generally considered: rigid bodies (Rigid solids) and linear elastic solids (Linear elastic solids) or Hookean solids. Rigid bodies do not change shape. In basic mechanical treatment, only the translation and rotation of objects are considered without considering changes in their shape; such objects are referred to as rigid bodies. The shape of elastic solids depends on the applied force. Clearly, such objects have a definite shape, and when force is applied, their shape changes, but they return to their original shape once the force is removed. For metals, other crystalline solids, and glassy solids, we find that if the deformation is small, the change in length during axial tensile testing is proportional to the applied force. This mechanical model is called linear elasticity and is applicable to many solids. Whether steel is a rigid body or an elastic solid depends on the experimental method. If the force is small and the measurement method is not very precise, steel can be considered a rigid body. If the force is large and the measurement method is more precise, we can measure the deformation of steel, in which case steel can be regarded as an elastic solid. In other experiments (such as damping of vibrations or applying very large forces that cause permanent deformation or fracture of steel), neither of these models applies, and more complex models must be used. Therefore, if we say "steel is an elastic solid," this is imprecise. It should be said, "steel behaves as an elastic solid in these experiments."
(2) Classical model of fluids
In classical mechanics, two models of fluids are often discussed: perfect fluids (Perfect fluids) and linear viscous fluids (Linear viscous fluids) or Newtonian fluids. In a perfect fluid, the force exerted by the fluid on any surface is always perpendicular to that surface. Moreover, the force exerted by one part of the fluid on an adjacent part is always perpendicular to the imaginary interface between these two parts of the fluid. This force is called hydrostatic pressure (Hydrostatic pressure). This model is applied in hydraulics, aerodynamics, and fluid mechanics. For linear viscous fluids, if the fluid is stationary, hydrostatic pressure is also isotropic (Isotropic). If any other force is applied, the fluid deforms, and this deformation is called flow.
A simple experiment is the flow of fluid through a small-bore tube. We find that the flow velocity is proportional to the applied force. For fluids like air and water, the parts farther from the tube wall can be considered perfect fluids, while the parts closer to the tube wall can be considered viscous fluids. In certain experiments (such as those involving ultrasound), a more complex model is required. In fact, a perfect fluid can be considered a special case of a viscous fluid, specifically a viscous fluid with a very small velocity gradient.