page_title: Stress (mechanics)
section_title: History
hierarchical_section_title: Stress (mechanics) / History
caption_attribution_description: English: A version of File:Roman_era_stone_arch_bridge,_Ticino,_Switzerland.JPG, from the Wikimedia Commons, cropped in height for the Wikipedia article
context_page_description: In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other, while strain is the measure of the deformation of the material. For example, when a solid vertical bar is supporting an overhead weight, each particle in the bar pushes on the particles immediately below it. When a liquid is in a closed container under pressure, each particle gets pushed against by all the surrounding particles. The container walls and the pressure-inducing surface push against them in reaction. These macroscopic forces are actually the net result of a very large number of intermolecular forces and collisions between the particles in those molecules. Stress is frequently represented by a lowercase Greek letter sigma.
  Strain inside a material may arise by various mechanisms, such as stress as applied by external forces to the bulk material or to its surface. Any strain of a solid material generates an internal elastic stress, analogous to the reaction force of a spring, that tends to restore the material to its original non-deformed state.
context_section_description: Since ancient times humans have been consciously aware of stress inside materials. Until the 17th century, the understanding of stress was largely intuitive and empirical; and yet, it resulted in some surprisingly sophisticated technology, like the composite bow and glass blowing.
  Over several millennia, architects and builders in particular, learned how to put together carefully shaped wood beams and stone blocks to withstand, transmit, and distribute stress in the most effective manner, with ingenious devices such as the capitals, arches, cupolas, trusses and the flying buttresses of Gothic cathedrals.
  Ancient and medieval architects did develop some geometrical methods and simple formulas to compute the proper sizes of pillars and beams, but the scientific understanding of stress became possible only after the necessary tools were invented in the 17th and 18th centuries: Galileo Galilei's rigorous experimental method, René Descartes's coordinates and analytic geometry, and Newton's laws of motion and equilibrium and calculus of infinitesimals.  With those tools, Augustin-Louis Cauchy was able to give the first rigorous and general mathematical model for stress in a homogeneous medium.  Cauchy observed that the force across an imaginary surface was a linear function of its normal vector; and, moreover, that it must be a symmetric function (with zero total momentum).
  The understanding of stress in liquids started with Newton, who provided a differential formula for friction forces (shear stress) in parallel laminar flow.
caption: Roman-era bridge in Switzerland
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