Continuum mechanics

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.

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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

• Engineering
  • Structural engineering
  • Computational fluid dynamics

See also

• Equation of state
• Finite deformation tensors