Theoretical elasticity

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David J. Steigmann

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Theoretical elasticity / [by] A. E. Green and W. Zerna. - Version details - Trove

Michael Lang. Macromolecules , 52 16 , DOI: Sergey Panyukov.


Loops in Polymer Networks. Macromolecules , 52 11 , Andrei A.

Theory of Elasticity

Macromolecules , 52 9 , Relative contributions of chain density and topology to the elasticity of two-dimensional polymer networks. Soft Matter , 15 28 , Consider a pair of points at locations and which are deformed to locations and. The absolute squared distance between the deformed points can be written as.

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The relation is,. Hook's law of elasticity is an approximation which states that the amount by which a material body is deformed the strain is linearly related to the force causing the deformation the stress.

Finite Elasticity Theory

The most general relationship between stress and strain can be mathematically written as. Of practical interest is the strain arising from a certain stress condition. The strain components can be obtained by inverting Hook's law and utilizing the compliance coefficients,. The Miller indices, denoted as , and , are a symbolic vector representation for the orientation of atomic planes and directions in a crystal lattice. Defining three lattice vectors forming the lattice axes, any crystal plane would intersect the axes at three distinct points.

The Miller indices are obtained by taking the reciprocal of the intercepted values. By convention, negative indices are written with a bar over the indices.

David J. Steigmann

In Fig.