Continuümmodellen

Continuümmodellen is a foundational framework in physics and engineering that describes matter as a continuous distribution rather than as a collection of discrete particles. It assumes properties such as density, velocity, and stress vary smoothly in space and time, and that interactions occur locally. The model is typically applied when the length scales of interest are much larger than the material’s microscopic structure.

The core idea is to express conservation laws for mass, momentum, and energy through field variables that depend on position and time. For fluids, this leads to the Navier–Stokes equations, which describe how velocity fields evolve under forces and viscous effects. For solids, the theory yields elastic or viscoelastic equations that relate stress to strain via constitutive relations, such as Hooke’s law in linear elasticity. Boundary conditions and initial conditions complete the formulation. The framework of continuum mechanics encompasses fluid dynamics, solid mechanics, acoustics, heat conduction, and electromagnetism viewed as a continuum.

History and development trace back to early work by Euler, Cauchy, Navier, and Stokes in the 18th and 19th centuries, with the broader term “continuum mechanics” now used for the field. The continuum model excels when microstructure can be averaged out and the fields are well behaved, but it has limitations at very small scales or far-from-equilibrium situations where kinetic or molecular descriptions are needed.

Applications span engineering, geophysics, biomechanics, and materials science, including computational methods such as finite element, finite difference, and finite volume techniques. Extensions include relativistic continuum mechanics and specialized constitutive theories for complex materials.