Jatkuvuusmekaniikan

Jatkuvuusmekaniikka, known in English as continuum mechanics, is a branch of mechanics that studies the mathematically described mechanical behavior of continuous media. A continuous medium is a collection of matter that is treated as if it were a continuum, meaning that its properties are defined at every point in space occupied by the matter, and the material is assumed to be infinitely divisible. This abstraction allows for the application of differential and integral calculus to describe the behavior of materials like solids, liquids, and gases, even though they are composed of discrete molecules.

The core principles of continuum mechanics involve defining the state of the material at any point using fields, such as displacement, velocity, stress, and strain. These fields are then related through constitutive equations that describe the material's response to applied forces and deformations. Key concepts include conservation of mass, momentum, and energy, which are expressed as partial differential equations. Continuum mechanics provides the theoretical foundation for many fields, including solid mechanics, fluid mechanics, and thermodynamics, and is essential for analyzing phenomena such as structural deformation, fluid flow, and wave propagation.