1990 | OriginalPaper | Buchkapitel
Mechanical Relaxation in Polymers
verfasst von : Ulrich Eisele
Erschienen in: Introduction to Polymer Physics
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
The state of an ideal elastic body under stress and strain due to the influence of a load can be described by corresponding tensors. The components of the strain tensor en and 7ik determine the relative change in the dimensions and angles of a small, cubic volume element. Such an element is imagined to be extracted from within the body under load. In a similar manner, the components of the stress tensor σii and τik can be used to determine the forces operating on the surfaces of the imaginary cube. The usual matrix formulation for tensors leads to the following expressions: $$\varepsilon=\begin{pmatrix} \varepsilon_{11}& \gamma_{12}& \gamma_{13}\\ \gamma_{21}& \varepsilon_{22}& \gamma_{23}\\ \gamma_{31}& \gamma_{32}& \varepsilon_{33}\\ \end{pmatrix} \,\,\, \sigma=\begin{pmatrix} \sigma_{11}& \tau_{12}& \tau_{13}\\ \tau_{21}& \sigma_{22}& \tau_{23}\\ \tau_{31}& \tau_{32}& \sigma_{33}\\ \end{pmatrix}$$