Deformation Rate
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Deformation rate
Terminology
The term deformation rate, which is also used as a synonym for deformation velocity, is used in very different ways in the literature and is used in rheology [1], fluid mechanics (rate of change of shape) [2], solid mechanics [3], materials and polymer testing [4, 5], thermodynamics and fluid mechanics [6]. The general physical definition of deformation rate as the velocity at which a material deforms under the action of a force is certainly too narrow. In the study of geological structures, a distinction is made between externally and temporally imposed deformation rates, which, for example, create new geological formations as a result of pressure or shearing, and temporally unforced deformation rates, such as crystallisation (see also: crystallinity) distinguished [7]. Integral deformation and the associated deformation rate are considered separately from local deformation properties. Regardless of this, an integral or local deformation gradient arises, which characterises the displacement, bending or stretching of material lines in the solid and thus also includes what is known as solid displacement [8].
The deformation gradient in continuum mechanics
In continuum mechanics, the spatial deformation gradient describes the local deformation rate or deformation velocity of virtual structural elements of solid, liquid or gaseous media, i.e. the local changes in the existing velocity field. The x, y and z components of the spatial velocity gradient contain all relevant information about the reference system-invariant specific velocities, such as local strain rate, shear or angular velocity, and are used in the mathematical modelling of physical models and, for example, the deformation gradient of solids in continuum or fluid mechanics.
In continuum mechanics, the deformation gradient describes the local deformation at a specified point that can be stretched, compressed, sheared, rotated, or displaced. From this, the temporal and local changes can be derived, which manifest themselves in stretching, twisting, and distortion, as well as changes in area or volume [8]. In fundamental considerations on the deformation rate by Henky [9], the essential systematic basic laws of technical mechanics and fluid mechanics were introduced, which are still valid today and define the essential loading cases. It became clear that the time differential quotient is generally not identical to the deformation rate, with problems arising in the formulation of relevant laws, particularly in the case of finite deformations of solids.
WIKI explanations of terms relating to velocity
The Wiki-lexicon "Polymer Testing & Diagnostics" from Polymer Service GmbH Merseburg (PSM) also explains the following terms in more detail under the heading ‘Speed’:
See also
- Deformation velocity
- Test speed
- Deformation rate (see: strain rate basics)
- strain rate basics
- Strain rate applications
- Crosshead speed
References
| [1] | Mezger, T. G.: The Rheology Handbook. Vincentz Network Publishing, Berlin (2011), 3rd Edition, (ISBN 978-3-866-30864-0) |
| [2] | Sigloch, H.: Technische Fluidmechanik. Springer, Berlin (2014), 9th Edition, (ISBN 978-3-642-54292-3) |
| [3] | Altenbach, J., Altenbach, H.: Einführung in die Kontinuumsmechanik. Teubner Publishing House, Stuttgart (1994), (ISBN 978-3-519-03096-6) |
| [4] | Blumenauer, H.: Werkstoffprüfung. Wiley-VCH, Weinheim, (2003), 6th extensively revised and expanded edition, (ISBN 978-3-527-30908-5) |
| [5] | Grellmann, W., Seidler, S. (Eds.): Polymer Testing. Carl Hanser, Munich (2022) 3rd Edition (ISBN 978-1-56990-806-8; E-Book: ISBN 978-1-56990-807-5; see AMK-Library under A 22) |
| [6] | Zierep, J., Bühler, K.: Grundzüge der Strömungslehre − Grundlagen, Statik und Dynamik der Fluide. Springer, Berlin (2013), 9th Edition, (ISBN 978-3-658-01605-0) |
| [7] | Sandner, B.: Einführung in die Gefügekunde der geologischen Körper. Teil 1: Allgemeine Gefügekunde und Arbeiten im Bereich Handstück bis Profil. Springer, Wien (1948), (ISBN 978-3-662-36705-6) |
| [8] | Altenbach, H.: Kontinuumsmechanik. Springer Berlin Heidelberg (2018), (ISBN 978-3-662-257504-8); https://doi.org/10.1007/978-3-662-57504-8 |
| [9] | Bauer, O. u. a.: Mitteilungen der deutschen Materialprüfanstalten. Sonderheft XIX, Springer Verlag, Berlin (1932), (ISBN 978-3-642-92044-8) |
Weblink
- Wikipedia – The Free Encyclopedia: [D:\Veröffentlichungen\Encyclopedia of Polymer Testing\Deformation Rate\Deformation gradient Deformation gradient]; https://en.wikipedia.org/wiki/Finite_strain_theory (last accessed on Januar 4, 2026)