Shock (mechanics)

Lore & Background

Shock measurement is of interest in many fields, including measuring heel shock propagation through a runner's body, determining the fragility of items, and evaluating shock attenuation through athletic flooring. Shocks are usually measured by accelerometers, though other transducers and high-speed imaging are also used. Field shocks are highly variable and often have uneven shapes, while even laboratory-controlled shocks may include short-duration spikes; noise can be reduced by appropriate filtering.

Reader's Guide

Shock testing typically falls into two categories: classical shock testing and pyroshock or ballistic shock testing. Classical shock impulses include half sine, haversine, sawtooth wave, and trapezoid, and can be performed on electrodynamic shakers, free fall drop towers, or pneumatic shock machines. A classical shock impulse is created when the shock machine table changes direction abruptly, causing a rapid velocity change. Proper test methods and verification protocols are important for all phases of testing and evaluation. Mechanical shock can damage items in various ways: brittle items may fracture, malleable items may bend, repeated low-level shocks can cause fatigue failure, and cumulative minor damage may eventually render an item unusable. Shock may also reduce reliability or cause an item to become out of adjustment. When damage is possible, courses of action include reducing the input shock at the source, modifying the item, using shock absorbers or cushions, or planning for failures with redundant systems.

Did You Know?

• A shock pulse can be characterized by its peak acceleration, duration, and shape (half sine, triangular, trapezoidal, etc.).
• The shock response spectrum is a method for further evaluating a mechanical shock.
• Cushioning reduces peak acceleration by extending the duration of the shock.

The Hertzian Foundation

The phenomenon he described, now called Hertzian contact stress, captures the localized stresses that arise when two curved surfaces meet and deform slightly under imposed loads. The magnitude of that deformation is governed by the modulus of elasticity of the materials involved, and the resulting stress can be expressed as a function of the applied normal force, the radii of curvature of both bodies, and their respective elastic moduli. This classical solution underpins the engineering equations used to determine load-bearing capacity and fatigue life in bearings, gears, and virtually any mechanism where two surfaces press against one another. Hertz's work also established the broader distinction between normal stresses acting perpendicular to contacting surfaces and shear frictional stresses acting tangentially, a framework that continues to organize the entire discipline.

The Adhesive Contact Controversy

Nearly a century after Hertz laid the groundwork for frictionless elastic contact, a new question emerged: what happens when surfaces actually stick together? In the 1970s, Kenneth L. Johnson, Kevin Kendall, and Alan D. Roberts derived a solution for adhesive elastic contact, but their theory was met with outright rejection from Boris Derjaguin and his colleagues, who had independently proposed a competing adhesion model. The two frameworks became known as the Johnson–Kendall–Roberts (JKR) model and the Derjaguin–Muller–Toporov (DMT) model, respectively. Rather than settling the debate, the rejection proved to be a catalyst. It spurred the development of parameters introduced by David Tabor and later refined by Daniel Maugis, which quantify which of the two models more accurately describes adhesive contact for a given pair of materials. This back-and-forth illustrated a broader truth about contact mechanics: even seemingly straightforward physical interactions—two clean, dry surfaces pressed together—can generate genuinely competing theoretical descriptions, and resolving which applies demands careful attention to material properties and the scale of the interaction.

Roughness, Micro-Contacts, and the True Contact Area

For much of the early twentieth century, contact mechanics treated mating surfaces as ideally smooth. That assumption was shattered in the mid-twentieth century when Frank Philip Bowden and David Tabor demonstrated that surface roughness fundamentally alters how two bodies interact. Their investigations revealed that the true area of contact between friction partners is considerably smaller than the apparent area suggested by the outer dimensions of the parts. This insight redirected the entire field of tribology and spawned a new branch devoted to rough-surface contact. J. F. Together, these findings transformed how engineers model friction, wear, and load distribution in real-world assemblies.

From Locomotives to Nanotechnology

Contact mechanics sits squarely within mechanical engineering, drawing its mathematical and physical foundations from mechanics of materials and continuum mechanics. The discipline addresses elastic, viscoelastic, and plastic bodies in both static and dynamic contact, providing the quantitative information needed for safe, energy-efficient design of technical systems. Its reach extends across an extraordinary range of applications: locomotive wheel-rail interfaces, coupling devices, braking systems, tires, bearings, combustion engines, mechanical linkages, gasket seals, metalworking and metal forming, ultrasonic welding, and electrical contacts. Beyond these macro-scale concerns, the field also underpins the study of tribology, contact stiffness, electrical contact resistance, and indentation hardness. Current challenges include the stress analysis of contact and coupling members and understanding how lubrication and material design influence friction and wear. Perhaps most strikingly, the principles of contact mechanics now extend into the micro- and nanotechnological realm, where the same fundamental questions about deformation, adhesion, and force distribution must be answered at scales where surface effects dominate over bulk behavior.