between two objects scraping/sliding past each other), or rolling (frictional force which prevents slipping but causes a torque to exert on a round object). Stress and strain The stress-strain constitutive relation for linear materials is commonly known as Hooke's law. In its simplest form, the law defines the spring constant (or elasticity constant) k in a scalar equation, stating the tensile/compressive force is proportional to the extended (or contracted) displacement x: meaning the material responds linearly. Equivalently, in terms of the stress σ, Young's modulus E, and strain ε (dimensionless): In general, forces which deform solids can be normal to a surface of the material (normal forces), or tangential (shear forces), this can be described mathematically using the stress tensor: where C is the elasticity tensor and S is the compliance tensor. Solid-state deformations Several classes of deformations in elastic materials are the following: Plastic The applied force induces non-recoverable deformations in the material when the stress (or elastic strain) reaches a critical magnitude, called the yield point. Elastic The material recovers its initial shape after deformation. Viscoelastic If the time-dependent resistive contributions are large, and cannot be neglected. Rubbers and plastics have this property, and certainly do not satisfy Hooke's law. In fact, elastic hysteresis occurs. Anelastic If the material is close to elastic, but the applied force induces additional time-dependent resistive forces (i.e. depend on rate of change of extension/compression, in addition to the extension/compression). Metals and ceramics have this characteristic, but it is usually negligible, although not so much when heating due to friction occurs (such as vibrations or shear stresses in machines). Hyperelastic The applied force induces displacements in the material following a strain energy density function. Collisions The relative speed of separation vseparation of an object A after a collision with another object B is related to the relative speed of approach vapproach by the coefficient of restitution, defined by Newton's experimental impact law: which depends on the materials A and B are made from, since the collision involves interactions at the surfaces of A and B. Usually , in which for completely elastic collisions, and for completely inelastic collisions. It is possible for to occur – for superelastic (or explosive) collisions. Deformation of fluids The drag equation gives the drag force D on an object of cross-section area A moving through a fluid of density ρ at velocity v (relative to the fluid) where