Stress (mechanics)

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.