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# Continuum mechanics

Continuum mechanics
Conservation of mass
Conservation of momentum
Navier-Stokes equations
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Continuum mechanics is a branch of physics (specifically mechanics) that deals with the analysis of the kinematic and mechanical behavior of materials modeled as a continuum, e.g., solids and fluids (i.e., liquids and gases). A continuum is a body that can be continually sub-divided into infinitesimal small elements with properties being those of the bulk material.

The continuum concept ignores the fact that matter is made of atoms, is not continuous, and that it commonly has some sort of heterogeneous microstructure. It assumes that the substance of the body is distributed uniformly throughout, and completely fills the space it occupies, allowing the approximation of physical quantities, such as energy and momentum, at the infinitesimal limit. Differential equations can thus be employed in solving problems in continuum mechanics. Some of these differential equations are specific to the materials being investigated and are called constitutive equations, while others capture fundamental physical laws, such as conservation of mass or conservation of momentum and energy.

Continuum mechanics deals with physical quantities, of solids and fluids, which are independent of any particular coordinate system in which they are observed. These physical quantities are then represented by tensors, which are mathematical objects that are independent of coordinate system. These tensors can be expressed in coordinate systems for computational convenience.

In fluids, the Knudsen number is used to assess to what extent the approximation of continuity can be made.

## Applications

 Continuum mechanics Solid mechanics is the study of the physics of continuous solids with a defined rest shape. Elasticity (physics) describes materials that return to their rest shape after removal of an applied force. Plasticity describes materials that permanently deform (change their rest shape) after a large enough applied force. Rheology: Given that some materials are viscoelastic (exhibiting a combination of elastic and viscous properties), the boundary between solid mechanics and fluid mechanics is blurry. Fluid mechanics (including Fluid statics and Fluid dynamics) deals with the physics of fluids. An important property of fluids is viscosity, which is the force generated by a fluid in response to a velocity gradient. Non-Newtonian fluids Newtonian fluids