Question

The origins of stiffness

Explain the relationship between the cohesive energy of bonding and the observed stiffness of individual bonds.

How does the stiffness of individual bonds in a solid affect the overall stiffness and elastic modulus of the material?

What is the atomic level mechanism of elastic deformation? In other words, what is occurring within a solid when it is elastically deformed?

Answer 1

Cohesive energy is the energy gained by arranging the atoms in a crystalline state, as compared with the gas state. Insulators and semiconductors have large cohesive energies; these solids are bound together strongly and have good mechanical strength. Metals with electrons in sp-bonds have very small cohesive energies. This type of metallic bond is weak; the crystals are barely held together. Single crystals of simple metals such as sodium are mechanically weak. At room temperature the crystals have the mechanical consistency of warm butter. Special care must be used in handling these crystals, because they are easily distorted. Metals such as magnesium or aluminum must be alloyed or polycrystalline to have any mechanical strength. Although the simple metals are found in a variety of structures, most are in one of the three closest-packed structures: fcc, bcc, and hcp.

The contribution to incremental stiffness from intrinsic muscle properties was measured during electrical stimulation of the deep peroneal nerve at 7-50 Hz. The higher stiffness observed for 1 degree stretches could be due to "short rangestiffness" of the cross bridges.

Young’s modulus is a measure of stiffness in simple extension or compression. There are ways of deforming a material that have different effects on the interatomic forces and therefore different effects on the material. Such a mode of deformation, frequently met, is shear. (Another mode of deformation—volume change, from which is derived the bulk modulus—is ignored here.) As with Young’s modulus, the shear modulus is defined as the ratio of stress to strain

Young's modulus is a measure of stiffness.Young's modulus is a mechanical property that measures the stiffness of a solid material. It defines the relationship between stress (force per unit area) and strain (proportional deformation) in a material in the linear elasticity regime of a uniaxial deformation.

Elastic deformation is a change in shape of a material at low stress that is recoverable after the stress is removed. This type of deformation involves stretching of the bonds, but the atoms do not slip past each other. This results in slip that occurs along parallel planes within the grain.

As deformation occurs, internal inter-molecular forces arise that oppose the applied force. If the applied force is not too great, these forces may be sufficient to completely resist the applied force and allow the object to assume a new equilibrium state and to return to its original state when the load is removed. A larger applied force may lead to a permanent deformation of the object or even to its structural failure.

In the cylinder we can be seen that the compressive loading has caused deformation in the cylinder so that the original shape has changed (deformed) into one with bulging sides. The sides bulge because the material, although strong enough to not crack or otherwise fail, is not strong enough to support the load without change. As a result, the material is forced out laterally. Internal forces (in this case at right angles to the deformation) resist the applied load.