Stiffness

3 Key excerpts on "Stiffness"

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  3D Cell-Based Biosensors in Drug Discovery Programs

  Microtissue Engineering for High Throughput Screening

  • William S. Kisaalita(Author)
  • 2010(Publication Date)
  • CRC Press

    (Publisher)

  169 7 Material Physical Property and Force Microenvironmental Factors 7.1 BASICS 7.1.1 Y OUNG ’ S M ODULUS , S TIFFNESS , AND R IGIDITY Imagine a material in equilibrium and under a simple load (subjected to a force, F ) as shown in Figure 7.1a. If an imaginary section is introduced at XX, normal to the plane of F , the total force carried must be equal to F and the distribution of F as internal forces of cohesion is called stress ( σ ). If the force is uniformly distributed over the section, then σ = F A , (7.1) where A is the cross-sectional area of the material. In Figure 7.1a, the forces are tensile, but can be compressive as well. Strain ( ε ) is a measure of deformation produced in the material under F , defined as elongation ( x ) divided by original materials length ( l ): ε = x l . (7.2) Strain is proportional to the stress that causes it (Hooke’s law), which is obeyed within certain limits of stress by some materials (e.g., glass, timber, concrete, etc.) and not obeyed by others (e.g., soft materials like hydrogels). Within the limits for which Hooke’s law is obeyed, the ratio of the stress to the strain produced is called the modulus of elasticity or Young’s modulus ( E ) (Figure 7.1b): E = σ ε , (7.3) E is usually the same in both tension and compression and is a constant for a given material. An average value of E can be established for a given range of stress for materials that do not obey Hooke’s law. Where a number of forces are acting together on a material, the resultant strain will be the sum of the individual strains caused by each force acting separately (principle of superposition). The commonly used word in the literature to describe the physical characteristic of materials is “Stiffness.” 170 3D Cell-Based Biosensors in Drug Discovery Programs Stiffness is the property of a solid body to resist deformation, used interchangeably with “rigidity.” A material with a high E exhibits high Stiffness or rigidity and vice versa.

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  Bones

  Structure and Mechanics

  • John D. Currey(Author)
  • 2013(Publication Date)
  • Princeton University Press

    (Publisher)

  If the bones were floppy, they would not be constrained in the same way and the movements of the muscles would be futile (fig. 2.1). On the other hand, if the bones are stiff, but break, they become useless, and so the strength is of great but secondary importance. The Stiffness of a bone and its strength depend on two factors: the Stiffness and strength of the bone material itself and the build of the whole bone. By build I mean the amount of the bone material and how it is distributed in space. The question of the build or architecture of bones will be discussed in chapter 7. 2.2 Mechanical Properties of Stiff Materials In this chapter I shall be concerned with the basis of the whole book: the mechanical properties of stiff materials in general. Because many readers may not be too clear about the mechanical matters to be dis- cussed, I shall run through various basics now. Later, slightly more re- 2 . 2 M E C H A N I C A L P R O P E R T I E S O F S T I F F M A T E R I A L S 29 condite mechanical concepts will be introduced. Only the minimum necessary for the understanding of this book will be given. Readers wishing to go further should read such things as Fung (1993), Vincent (1990), Wainwright et al. (1982), Cowin (2001a), and a good book on strength of materials. 2.2.1 Stress, Strain, and Their Relationship First, stress and strain. Consider a bar acted on by a force F tending to stretch it (fig. 2.2). If its original length is L, it will undergo some in- crease in length, ∆L. Usually it will also get thinner, and its breadth B will decrease by an amount ∆B. The proportional changes in length, ∆L/L and ∆B/B, are called normal strains. They are often given the Greek letter ε. Note, first, that strains refer to changes in length in par- ticular directions, and, second, that the strains tell us nothing, directly, about the forces causing them. By convention, if a dimension increases in length the strain is positive and if it decreases it is negative.

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  Materials

  Engineering, Science, Processing and Design

  • Michael F. Ashby, Hugh Shercliff, David Cebon(Authors)
  • 2009(Publication Date)
  • Butterworth-Heinemann

    (Publisher)

  mode of loading . The cover picture illustrates the common ones. Ties carry tension—often, they are cables. Columns carry compression—tubes are more efficient as columns than solid rods because they don’t buckle as easily. Beams carry bending moments, like the wing spar of the plane or the horizontal roof beams of the airport. Shafts carry torsion, as in the drive shaft of cars or the propeller shaft of the plane. Pressure vessels contain a pressure, as in the tires of the plane. Often they are shells: curved, thin-walled structures.

  Stiffness is the resistance to change of shape that is elastic , meaning that the material returns to its original shape when the stress is removed. Strength (Chapter 6 ) is its resistance to permanent distortion or total failure. Stress and strain are not material properties; they describe a stimulus and a response. Stiffness (measured by the elastic modulus E , defined in a moment) and strength (measured by the elastic limit σ y or tensile strength σ ts ) are material properties. Stiffness and strength are central to mechanical design, often in combination with the density, ρ . This chapter introduces stress and strain and the elastic moduli that relate them. These properties are neatly summarised in a material property chart —the modulus–density chart—the first of many that we shall explore in this book.

  Density and elastic moduli reflect the mass of the atoms, the way they are packed in a material and the Stiffness of the bonds that hold them together. There is not much you can do to change any of these, so the density and moduli of pure materials cannot be manipulated at all. If you want to control these properties you can either mix materials together, making composites, or disperse space within them, making foams. Property charts are a good way to show how this works.

  4.2 Density, stress, strain and moduli

  Density

  Many applications (e.g. sports equipment, transport systems) require low weight and this depends in part on the density of the materials of which they are made. Density is mass per unit volume. It is measured in kg/m3 or sometimes, for convenience, Mg/m3 (1 Mg/m3 = 1000 kg/m3 ).

  The density of samples with regular shapes can be determined using precision mass balance and accurate measurements of the dimensions (to give the volume), but this is not the best way. Better is the ‘double weighing’ method: the sample is first weighed in air and then when fully immersed in a liquid of known density. When immersed, the sample feels an upward force equal to the weight of liquid it displaces (Archimedes’ principle1 ). The density is then calculated as shown in Figure 4.1

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