Mechanical behavior dynamic/static

Static and dynamic forces play key roles in the complex biochemical and biophysical processes that imderlie cell function. The mechanical behavior of individual cells is of interest for many different biologic processes. Single-ceU mechanics, including growth, cell division, active motion, and contractile mechanisms, can be quite dynamic and provide insight into mechanisms of stress and damage of structures. Cell mechanics can be involved in processes that lie at the root of many diseases and may provide opportunities as focal points for therapeutic interventions. 

The mechanical behavior of DEs depends on the type of stimulation. For static stimuli the final deformation will be reached depending on the compliance of the elastomer. In case of dynamic stimulation, transient effects leading to more complex models have to be considered. 

Chapter 1 provides a summary outlook on this complex topic with suggested three key references that address the static and dynamic mechanical behavior and associated degradation of composites from fluid exposure. Since the topic requires mastery of polymer science and engineering, engineering mechanics, chemical and polymer characterization, and thermodynamics of multi-phase materials, the author s perspective is more slanted on solid mechanics aspect of these materials. Jack had consistent financial support for three decades to study this topic from the Solid Mechanics Program managed by Dr. Yapa Rajapakse at the United States Office of Naval Research (ONR). Thus, the author is uniquely qualified to address this complex topic. 

Generally, two different types of measurement are applied to determine the linear viscoelastic behavior, namely static (or equilibrium) and dynamic mechanical measurements. Static tests involve the imposition of a step change in stress and the observation of any subsequent development in time of the strain, whereas dynamic tests involve the application of a harmonically varying strain. In ordinary thermoplastic polymer systems, test conditions such as strain or frequency must be in the linear range otherwise, the results will be dependent on the experimental details rather than on the material under test. 

Davies G R, Smith T and Ward I M (1980) Dynamic mechanical behavior of oriented poly(tetramethylene terephthalate) as a function of static extension. Polymer 21 221-225. 

This chapter introduces tools from statistical mechanics that are useful for analyzing the behavior of static and slowly driven granular media. (For fast dynamics, refer to the previous chapter on Kinetic Theory by Jenkins.) These tools encompass techniques used to predict emergent properties from microscopic laws, which are the analogs of calculations in equilibrium statistical mechanics based on the concept of statistical ensembles and stochastic dynamics. Included, for example, are the Edwards approach to static granular media, and coarse-grained models of... 

In fluid mechanics the principles of conservation of mass, conservation of momentum, the first and second laws of thermodynamics, and empirically developed correlations are used to predict the behavior of gases and liquids at rest or in motion. The field is generally divided into fluid statics and fluid dynamics and further subdivided on the basis of compressibility. Liquids can usually be considered as incompressible, while gases are usually assumed to be compressible. 

As these problems were encountered in the past, it became evident that we did not have at hand the physical or mathematical description of the behavior of materials necessary to produce realistic solutions. Thus, during the past half century, there has been considerable effort expended toward the generation of both experimental data on the static and dynamic mechanical response of materials (steel, plastic, etc.) as well as the formulation of realistic constitutive theories (Appendix A PLASTICS DESIGN TOOLBOX). 

The behavior of materials (plastics, steels, etc.) under dynamic loads is important in certain mechanical analyses of design problems. Unfortunately, sometimes the engineering design is based on the static loading properties of the material rather than dynamic properties. Quite often this means over-design at best and incorrect design resulting... 

The Hamiltonian models are broadly variable. Even for an isolated molecule, it is necessary to make models for the Hamiltonian - the Hamiltonian is the operator whose solutions give both the static energy and the dynamical behavior of quantum mechanical systems. In the simplest form of quantum mechanics, the Hamiltonian is the sum of kinetic and potential energies, and, in the Cartesian coordinates that are used, the Hamiltonian form is written as... 

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