Continuum mechanics Conservation of massConservation of momentumNavier–Stokes equations This box: view • talk • edit

Elasticity is a branch of physics which studies the properties of elastic materials. Continuum mechanics is a branch of Mechanics that deals with the analysis of the Kinematics and mechanical behavior of materials modeled as a continuum e The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product The Navier–Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of viscous Fluid substances such A material is said to be elastic if it deforms under stress (e. In Materials science, deformation is a change in the shape or size of an object due to an applied force. Stress is a measure of the average amount of Force exerted per unit Area. g. , external forces), but then returns to its original shape when the stress is removed. In Physics, a force is whatever can cause an object with Mass to Accelerate. The amount of deformation is called the strain.

## Modeling elasticity

The elastic regime is characterized by a linear relationship between stress and strain, denoted linear elasticity. Linear elasticity is the mathematical study of how solid objects deform and become internally stressed due to prescribed loading conditions Good examples are a rubber band and a bouncing ball. This idea was first stated[1] by Robert Hooke in 1675 as a Latin anagram[2] "ceiiinosssttuv", whose solution he published in 1678 as "Ut tensio, sic vis" which means "As the extension, so the force. Robert Hooke, FRS (18 July 1635 – 3 March 1703 was an English Natural philosopher and Polymath who played an important role in the "

This linear relationship is called Hooke's law. In Mechanics, and Physics, Hooke's law of elasticity is an approximation that states that the amount by which a material body is deformed (the The classic model of linear elasticity is the perfect spring. A spring is a flexible elastic object used to store mechanical Energy. Although the general proportionality constant between stress and strain in three dimensions is a 4th order tensor, when considering simple situations of higher symmetry such as a rod in one dimensional loading, the relationship may often be reduced to applications of Hooke's law. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Symmetry generally conveys two primary meanings The first is an imprecise sense of harmonious or aesthetically-pleasing proportionality and balance such that it reflects beauty or

Because most materials are elastic only under relatively small deformations, several assumptions are used to linearize the theory. Most importantly, higher order terms are generally discarded based on the small deformation assumption. In certain special cases, such as when considering a rubbery material, these assumptions may not be permissible. However, in general, elasticity refers to the linearized theory of the continuum stresses and strains.

## Transitions to inelasticity

Above a certain stress known as the elastic limit or the yield strength of an elastic material, the relationship between stress and strain becomes nonlinear. The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material The yield strength or yield point of a Material is defined in Engineering and Materials science as the stress at which a material Beyond this limit, the solid may deform irreversibly, exhibiting plasticity. A solid' object is in the States of matter characterized by resistance to Deformation and changes of Volume. A stress-strain curve is one tool for visualizing this transition. During testing of a material sample the stress–strain curve is a graphical representation of the relationship between stress, derived from measuring the load applied on the

Furthermore, not only solids exhibit elasticity. Some non-Newtonian fluids, such as viscoelastic fluids, will also exhibit elasticity in certain conditions. A non-Newtonian fluid is a Fluid whose flow properties are not described by a single constant value of Viscosity. Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. In response to a small, rapidly applied and removed strain, these fluids may deform and then return to their original shape. Under larger strains, or strains applied for longer periods of time, these fluids may start to flow, exhibiting viscosity. Viscosity is a measure of the resistance of a Fluid which is being deformed by either Shear stress or Extensional stress.