Continuum Mechanics

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Continuum mechanics

Explanation of terms

In continuum mechanics, models are established to describe the mechanical and thermal behaviour of materials and are used to describe and model the mechanical behaviour of components. The material is regarded as a continuum, i.e. as a continuous accumulation of material points [1]. This means that the microscopic structure of the material, its amorphous or crystalline structure, is not taken into account in the models, or that the size scale under consideration is large compared to the atomic distance. The material is regarded as ‘smeared’, which means that all sizes become continuous and do not correlate with structural or morphological sizes [2]. The concept of continuum mechanics does not only refer to the deformation of solid bodies, but can also be extended to liquids and gases.

Classification as a scientific discipline

Continuum mechanics is a part of classical technical mechanics, which in turn is based on fundamental physical laws whose mathematical formulation is the subject of theoretical physics.

Subfields of classical continuum mechanics include, for example, theory of elasticity, theory of plasticity, and creep mechanics.

Tasks of continuum mechanics

The task of continuum mechanics is to determine the stress and strain state as well as the displacement at all points of a body under specified boundary conditions. These boundary value problems are solved using methods from elasticity and plasticity theory. A frequently used mathematical method is the finite element method.

In engineering practice, a further task is to use the determined stresses and deformations to obtain information about the stress state in the material [1].

See also

• Fracture mechanics
• Materials testing
• Deformation rate
• Testing of microcomponents
• Elasticity

References

[1]	Betten, J.: Kontinuumsmechanik – Elastisches und inelastisches Verhalten isotroper und anisotroper Stoffe. Springer, Berlin Heidelberg (2001), (ISBN 978-3-540-42043-9)
[2]	Röster, J.; Harders, M., Böker, M.: Mechanisches Verhalten der Werkstoffe. Teubner Publishing, Stuttgart Leipzig Wiesbaden (2003), (ISBN 3-519-00438-0)

Weblink

• Wikipedia – The Free Encyclopedia: Continuum mechanics https://en.wikipedia.org/wiki/Continuum_mechanics