Stress (mechanics)
Physical quantity describing internal forces during material deformation.
Stress, in continuum mechanics, is a physical quantity representing the internal forces that develop within a continuous material when it is deformed. These forces arise between neighboring particles of the material. For instance, a stretched elastic band experiences tensile stress, which tends to elongate it, while a compressed sponge undergoes compressive stress, which shortens it. The magnitude of stress depends on both the applied force and the area over which it acts; a larger force or a smaller cross-sectional area results in greater stress. Stress is measured as force per unit area, with SI units of newtons per square meter, also known as pascals. It is commonly denoted by the lowercase Greek letter sigma (σ).
Stress is a macroscopic concept, meaning it averages out the effects of countless intermolecular forces and collisions between molecules. It is defined as the force acting across an imaginary boundary within a material, divided by the area of that boundary, for any orientation of the boundary. This definition allows stress to be analyzed without reference to the material's specific nature. Strain, by contrast, measures the relative deformation of the material. While external forces like gravity or contact pressure can cause strain, any deformation of a solid generates an internal elastic stress that resists the change, similar to a spring's reaction. In fluids, only volume-changing deformations produce persistent elastic stress; gradual deformations instead generate viscous stress. Both elastic and viscous stresses are collectively termed mechanical stress.
Significant stress can exist even without visible deformation, as in prestressed concrete or tempered glass. Stress may also arise from non-mechanical sources, such as temperature changes, chemical alterations, or electromagnetic fields, as seen in piezoelectric materials. When stress exceeds a material's strength limits, it can cause permanent deformation, including plastic flow, fracture, or cavitation. Historically, humans understood stress intuitively for millennia, enabling technologies like composite bows and Gothic cathedrals. A rigorous scientific model emerged only after the 17th and 18th centuries, with Augustin-Louis Cauchy formalizing the concepts of stress and strain. He showed that the force across any surface is a linear, symmetric function of the surface's orientation.
- field
- Continuum mechanics
- known_for
- Describing internal forces during deformation; Cauchy stress tensor; normal and shear stress
- SI_unit
- Pascal (Pa) or newtons per square meter (N/m²)
- symbol
- σ (sigma)
- types
- Tensile stress, compressive stress, shear stress, viscous stress, elastic stress
Lore & Background
Humans have known about stress inside materials since ancient times, with architects and builders learning to shape wood beams and stone blocks to withstand and distribute 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 the 17th and 18th centuries with tools from Galileo Galilei, René Descartes, and Isaac Newton. Augustin-Louis Cauchy gave the first rigorous mathematical model of a deformed elastic body by introducing the notions of stress and strain, observing that force across an imaginary surface was a linear function of its normal vector and must be symmetric.
Reader's Guide
Stress is a fundamental concept in continuum mechanics, quantifying internal forces that arise during deformation of materials. It is defined as force per unit area across a boundary, with normal stress (tension or compression) perpendicular to the surface and shear stress parallel to it. The Cauchy stress tensor, a symmetric 3×3 matrix, describes the stress state at a point, varying with position and time. Stress can exist without external forces, as in prestressed concrete and tempered glass, and can be caused by temperature changes, chemical composition, or electromagnetic fields. The relationship between stress, strain, and strain rate can be complex, but linear approximations are often adequate for small quantities. Stress exceeding material strength limits results in permanent deformation such as plastic flow, fracture, or cavitation. Understanding stress has enabled engineering achievements from ancient composite bows and Gothic cathedrals to modern structures, with units measured in pascals or pounds per square inch.
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.
- Augustin-Louis Cauchy gave the first rigorous mathematical model of a deformed elastic body by introducing stress and strain.
- In liquids and gases, only deformations that change volume generate persistent elastic stress.
More in Classical Mechanics And Dynamics 1-24
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