page_title: Strength of materials
section_title: Stress–strain relations
hierarchical_section_title: Strength of materials / Definition / Stress–strain relations
context_page_description: Strength of materials, also called mechanics of materials, deals with the behavior of solid objects subject to stresses and strains. The complete theory began with the consideration of the behavior of one and two dimensional members of structures, whose states of stress can be approximated as two dimensional, and was then generalized to three dimensions to develop a more complete theory of the elastic and plastic behavior of materials. An important founding pioneer in mechanics of materials was Stephen Timoshenko.
  The study of strength of materials often refers to various methods of calculating the stresses and strains in structural members, such as beams, columns, and shafts. The methods employed to predict the response of a structure under loading and its susceptibility to various failure modes takes into account the properties of the materials such as its yield strength, ultimate strength, Young's modulus, and Poisson's ratio; in addition the mechanical element's macroscopic properties, such as its length, width, thickness, boundary constraints and abrupt changes in geometry such as holes are considered.
context_section_description: Elasticity is the ability of a material to return to its previous shape after stress is released. In many materials, the relation between applied stress is directly proportional to the resulting strain (up to a certain limit), and a graph representing those two quantities is a straight line.
  The slope of this line is known as Young's modulus, or the "modulus of elasticity." The modulus of elasticity can be used to determine the stress–strain relationship in the linear-elastic portion of the stress–strain curve. The linear-elastic region is either below the yield point, or if a yield point is not easily identified on the stress–strain plot it is defined to be between 0 and 0.2% strain, and is defined as the region of strain in which no yielding (permanent deformation) occurs.
  Plasticity or plastic deformation is the opposite of elastic deformation and is defined as unrecoverable strain. Plastic deformation is retained after the release of the applied stress. Most materials in the linear-elastic category are usually capable of plastic deformation. Brittle materials, like ceramics, do not experience any plastic deformation and will fracture under relatively low strain, while ductile materials such as metallics, lead, or polymers will plastically deform much more before a fracture initiation.
  Consider the difference between a carrot and chewed bubble gum. The carrot will stretch very little before breaking. The chewed bubble gum, on the other hand, will plastically deform enormously before finally breaking.
caption: Basic static response of a specimen under tension