Mechanical Properties of Materials

It is important to know how stress and strain are related in an object. The present chapter concerns this issue. For example, with the knowledge of stresses, we can determine strains (and deformations). Deflections or deformations in a body are caused by loading in the body. The force–deflection relationship depends on the physics of the process. Correspondingly, the stress–strain relation is a mechanical property of the material. It is governed by the material properties of the body, or “physics” of the material, and is called a constitutive relation . It has to be applied to solve the complete problem of mechanics of materials. “Compatibility” is assumed in the problem. “Equilibrium,” which is governed by Statics, must be satisfied as well. The main contents of the chapter are the following: Constitutive relation, Tensile test which experimentally determines the stress–strain behavior, Hooke’s law, which gives the linear stress–strain relationship. Associated material parameters include Young’s modulus, shear modulus, and Poisson’s ratio, Material behavior: linear, nonlinear, elastic, plastic, work hardening, creep, fatigue, and fracture, Material properties: homogeneity, isotropy, elasticity, rigidity, strength, elongation, resilience, toughness, and hardness, Material types: ductile, brittle, soft, hard, strong, tough, and Strain energy; moduli of resilience and toughness.