kontinuitetsmekanikk

Kontinuitetsmekanikk, often called continuum mechanics in English, is the branch of physics that models materials as continuous media, ignoring atomic discreteness. It employs fields such as displacement, velocity, stress, and strain that vary smoothly in space and time. This approach is essential for describing fluids, solids and complex materials in engineering, geophysics, and biomechanics.

The central equation of kontinuitetsmekanikk is the continuity equation, which expresses local conservation of mass for a fluid with density ρ and velocity field v. In differential form it reads ∂ρ/∂t + ∇·(ρv)=0, linking density changes to the divergence of mass flux. For incompressible flow where ρ is constant, the equation reduces to ∇·v=0. Additional balance laws—momentum, angular momentum, and energy—lead to Navier–Stokes equations for fluids and Navier–Cauchy equations for deformable solids.

Applications span a wide range of fields. In aerodynamics, continuum mechanics models airflow over wings, enabling design of efficient aircraft. In civil engineering, it predicts soil and rock deformation under loads, crucial for foundations and earthworks. Biomedical engineers apply it to simulate blood flow and soft tissue mechanics. The theory also underpins numerical methods such as finite element analysis and computational fluid dynamics, which are indispensable tools in research and industry.

Key texts include "Continuum Mechanics" by J.P. Knowles, "Fluid Mechanics" by F. M. White, and the classic journal "Journal of Continuum Mechanics." These resources provide deeper mathematical formulations, derivations, and applications for advanced study.