Stress (mechanics)
Physical quantity describing internal forces during material deformation.
Stress (mechanics) is a physical quantity in continuum mechanics that describes forces present during deformation of a material. It expresses the internal forces that neighboring particles of a continuous material exert on each other, with dimension of force per area and SI units of pascals (Pa).
- field
- Continuum mechanics
- known_for
- Describing internal forces during deformation, Cauchy stress tensor
- SI_unit
- Pascal (Pa) or N/m²
- common_unit
- Megapascal (MPa) or pounds per square inch (psi)
- symbol
- σ (sigma)
Lore & Background
Humans have known about stress inside materials since ancient times, with understanding largely intuitive and empirical until the 17th century. Architects and builders learned to shape wood beams and stone blocks to withstand stress using capitals, arches, cupolas, trusses, and flying buttresses. Ancient and medieval architects developed some geometrical methods and simple formulas for proper sizes of pillars and beams, but scientific understanding became possible only after tools like Galileo's experimental method, Descartes's coordinates, Newton's laws, and calculus were invented.
Reader's Guide
Augustin-Louis Cauchy gave the first rigorous and general mathematical model of a deformed elastic body by introducing the notions of stress and strain. He observed that the force across an imaginary surface was a linear function of its normal vector and must be a symmetric function. Stress is defined as the force across a small boundary per unit area for all orientations, expressed by the Cauchy traction vector. The stress state must be described by a tensor, which can be represented as a symmetric matrix of 3×3 real numbers. Stress may exist even without deformation, as in prestressed concrete and tempered glass, and can be imposed by changes in temperature, chemical composition, or electromagnetic fields. The relation between stress, strain, and strain rate can be complicated, though a linear approximation may be adequate for sufficiently small quantities. Stress exceeding certain strength limits results in permanent deformation such as plastic flow, fracture, or cavitation.
Did You Know?
- Stress has dimension of force per area, with SI units of newtons per square meter (N/m²) or pascal (Pa).
- Stress may exist even when deformation is negligible or non-existent, as in prestressed concrete and tempered glass.
- The Cauchy stress tensor can be represented as a symmetric matrix of 3×3 real numbers.
- Stress in liquids started with Newton, who provided a differential formula for friction forces (shear stress) in parallel laminar flow.
More in Materials And States Of Matter 1-22
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