Mechanics of Materials

• Molecular bonds act like springs.

• Stress measures the force intensity in a material.

• Strain measures deformation intensity.

• Hooke's "law": forces are proportional to deformations.

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  • This is more of an observation than a law, since it is not always true.

• E-modulus defines material stiffness: E-modulus (a.k.a. Modulus of elasticity, Young's modulus) is the ratio of stress divided by strain, and extends Hooke's law in terms of stresses and strains rather than forces and deformations.

• Linear elastic does not apply to all materials or at all timesy to all materials or at all times: The direct proportionaly of stress and strain is called linear elastic behavior and is true only for some materials in limited stress-strain ranges.

• Three key material properties (among others):

  • Strength measures how hard it is to yield or break the material. Strength is measured by the stress level at which there is a significant change in the state of the material, such as yield stress or ultimate stress.

  • Stiffness measures how hard it is to stretch or squeeze the material: Stiffness is measured by E-modulus, the ratio of stress to strain in the linear elastic range, and the slope of the stress-strain curve in that range.

  • Ductility measures how much inelastic strain there is before material failure. Ductiliy is measured by comparing the inelastic strain range to the elastic strain range, typically by calculating the ratio of the maximum strain at failure to the strain at yield.