Modeling of Materials for Sports Equipment 1 introduction

Modeling of Materials for Sports
Equipment
1.1 INTRODUCTION
The chapters in Part II of this book cover the design and materials used in particular sports with an emphasis on how the interrelationship of design and materials affects performance. In the field of sports equipment—as in all other applications such as aerospace, automotive, and biomedical—it is the combination of materials and design that achieves the requirements specific to that application. The most suitable materials for the application are, therefore, those that most completely and readily achieve the mix of properties (mechanical, physical, chemical, and nontechnical) in the desired shapes and dimensions. In this way“sports materials”do not differ from any other type of “material,” but are materials designed for the operating conditions pertinent to sporting applications. Of the particular sports covered in Part II, the operating conditions are between 25°C and 140°C, involve exposure to moisture, and cover a range of strain rates.
Additionally, sports equipment, such as bats and clubs, interact strongly with the athletes using them. This includes force transfer and vibrations to the athletes, whose soft tissue can suffer damage and injury at strains and strain rates that would be negligible for structures such as aircraft or power generation plant.
Modeling of materials covers a range of scales and outcomes that relate to different engineering disciplines, including:
1. Atomistic or ab initio modeling (Wahn & Neugebauer, 2006) based on interatomic potentials which can be used to design specific localized properties, such as doping of semiconductor devices.
2. Analytical models: these operate at the micron to millimeter scale and
involve thermodynamics and kinetics for structural changes as well as
dislocation motion relating to strength and fracture. They are used in designing material compositions and microstructures to achieve properties over a limited portion of the structure (Ghosh, Van de Walke, Asta, & Olson, 2002; Robson, 2004). This could be viewed as the ideal or target composition and microstructure for the processed component.
3. Process modeling (Grong, 1994): these models often involve numerical methods, such as finite element (FE) and computational fluid dynamics in order to determine thermomechanical and fluid flow conditions throughout complete components such as shaped castings or forgings.
They give structures and properties which are more average, that is,
they do not have the fine-scale resolution of structure possible in (2),
but do give variations across full components and can predict defects
such as porosity in castings (Lee, Chirazi, Atwood, & Wang, 2004).
4. Continuum mechanics: these models (also often numerical) are used to define the properties, for example, strength and stiffness, required at different positions throughout the component.
Design and materials for various applications are assisted through
computational modeling based mostly on an iterative combination of
(2)(4), although the resources of smaller manufacturers may only allow some aspects, for example (4), to be carried out. Models are only as good as the data that they use and, therefore, if a full mix of models and data are not available, it is important to understand which of the many database values usually available are appropriate for use in the models. As the range of properties and materials is very wide, this chapter will concentrate on the more commonly used materials (metallic alloys, polymers, and polymer matrix composites) and properties (modulus and yield stress) encountered in sporting applications.