Elasticity (physics)

Elasticity is a fundamental property in physics and materials science. It is the ability of a body to resist a distorting influence. When a force is removed, an elastic object returns to its original size and shape. This behavior is distinct from plasticity. In plasticity, an object remains in its deformed state after the force is gone. Understanding elasticity is essential for engineering structures and studying biological systems. It allows us to predict how materials will react under different loads.

The physical mechanism of elasticity depends on the material's structure. In metals, the atomic lattice changes size and shape when forces are applied. This process adds energy to the system. When the forces are removed, the lattice returns to its original, lower energy state. For polymers like rubber, elasticity comes from the stretching of long polymer chains. These chains act like tiny springs that pull back when released. Even some non-Newtonian fluids can show elasticity. These viscoelastic fluids may return to their shape if a small strain is applied rapidly.

Scientists use several types of elastic moduli to measure a material's resistance to deformation. A modulus quantifies the amount of stress needed to achieve a unit of strain. Young's modulus measures resistance to extension or compression. The shear modulus measures resistance to shear, which is a sliding motion. Both Young's and shear moduli apply only to solids. The bulk modulus is different because it applies to solids, liquids, and gases. These values are measured in pascals (Pa). Most engineering materials have very high moduli, often measured in gigapascals (GPa).

In 1675, Robert Hooke formulated a geometric version of these rules. He first shared his discovery as a Latin anagram: "ceiiinosssttuv." In 1678, he published the solution: "Ut tensio, sic vis." This translates to "As the extension, so the force." This principle is known as Hooke's law. It states that the force required to deform an elastic object is directly proportional to the distance of deformation. This linear relationship is often used to model small deformations in many materials.

Materials are often described using a stress–strain curve. Stress is the average restorative internal force per unit area. Strain is the relative deformation of the object. For many materials, this relationship is linear for small deformations. However, most materials are only purely elastic up to a certain point. This threshold is called the elastic limit or yield strength. If the stress exceeds this limit, plastic deformation begins. This means the change becomes irreversible and permanent.

Different models exist to describe large deformations, known as finite elasticity. Cauchy elastic materials are models where stress depends only on the current state of deformation. Hyperelastic materials, or Green elastic materials, are conservative models. These are derived from a strain energy density function. Hyperelasticity is used to model elastomers like gaskets. It is also used to study biological materials like cell membranes and soft tissues. These models help scientists understand complex, large-scale movements.

Several factors can change how a material behaves elastically. In an isotropic solid, porosity plays a major role. A more porous material generally shows lower stiffness. The size and distribution of pores also matter. Cracks and fractures can make a body more brittle. The presence of cracks decreases the Young's modulus and the shear modulus. This happens faster for the Young's modulus as fracture density increases. Understanding these variables helps engineers design safe beams, plates, and shells.