What is recorded here?
Hertz solves the local frictionless contact of smooth isotropic elastic solids, obtaining an elliptical pressure patch and nonlinear load-indentation scaling, with a conditional quasi-static collision application. Even two apparently rigid spheres flatten slightly when pressed together. Hertz treats the small region where smooth elastic bodies meet, replacing their nearby surfaces by quadratic shapes and their interiors by elastic half-spaces. The resulting contact patch is an ellipse, with pressure greatest inside and falling to zero at its edge. For spheres, the contact radius grows as the cube root of the normal load, while indentation grows as the two-thirds power. These relations let engineers connect force, deformation and local pressure without treating the bodies as perfectly rigid. Hertz also applies the contact law to slow elastic impacts when stress waves can cross the relevant bodies much faster than the collision lasts. The calculation does not cover friction, adhesion, plastic deformation or large contact patches. Its discussion of crack initiation is an informed conjecture, not a universal fracture criterion. The original is signed January 1881; the journal publication is conventionally catalogued as 1882, despite the public mirror header using 1881.
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Scientific scope
The contact theory assumes small deformation, elastic materials, smooth local surface geometry and the stated frictionless contact approximation. Adhesion, plasticity, large deformation and arbitrary rough contacts are outside it. Predicted contact shape/pressure depend on material and geometry assumptions; this is not a universal wear law or independently reproduced experiment.
Read the original work
- Heinrich Hertz: UeberdieBeruehrungfesterelastischerKoerper, original156-171
- Komvopoulos2008: roughness/frictionalheating contact extension context
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People and systems
Heinrich Hertz
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English catalogue narrative
Hertz: force and deformation meet over a small elastic contact patch
Hertz solves the local frictionless contact of smooth isotropic elastic solids, obtaining an elliptical pressure patch and nonlinear load-indentation scaling, with a conditional quasi-static collision application.
Even two apparently rigid spheres flatten slightly when pressed together. Hertz treats the small region where smooth elastic bodies meet, replacing their nearby surfaces by quadratic shapes and their interiors by elastic half-spaces. The resulting contact patch is an ellipse, with pressure greatest inside and falling to zero at its edge. For spheres, the contact radius grows as the cube root of the normal load, while indentation grows as the two-thirds power. These relations let engineers connect force, deformation and local pressure without treating the bodies as perfectly rigid. Hertz also applies the contact law to slow elastic impacts when stress waves can cross the relevant bodies much faster than the collision lasts. The calculation does not cover friction, adhesion, plastic deformation or large contact patches. Its discussion of crack initiation is an informed conjecture, not a universal fracture criterion. The original is signed January 1881; the journal publication is conventionally catalogued as 1882, despite the public mirror header using 1881.
Scientific scope
The contact theory assumes small deformation, elastic materials, smooth local surface geometry and the stated frictionless contact approximation. Adhesion, plasticity, large deformation and arbitrary rough contacts are outside it. Predicted contact shape/pressure depend on material and geometry assumptions; this is not a universal wear law or independently reproduced experiment.
People and systems
Heinrich Hertz