In:
Géotechnique, Thomas Telford Ltd., Vol. 51, No. 1 ( 2001-02), p. 15-36
Abstract:
This paper describes some new descriptions of plane strain, based on a frame attached to the soil rather than an external coordinate frame. The new descriptions are not limited to small strain processes. The paper starts with physical interpretations of the deformation gradient and right Cauchy–Green strain tensors. A new set of ‘zensor’ quantities are then derived, based on a conceptual frame that is attached to the soil and deforms with it. This parallels the physical reality of strain-gauge measurements. It is then shown that invariants in plane strain are intimately associated with three specific linear operators on zensors, here called the scale, relativistic and arc operators. This leads to identification of three independent in-plane strain-increment invariants, not just two, and three independent work-conjugate in-plane effective stress invariants. Fixed-frame zensor transformation laws in plane strain are then derived. As well as the familiar concept of change of frame, these also allow change of reference state to be handled. Finally, some advantages of the new approach to continuum mechanics are discussed.
Type of Medium:
Online Resource
ISSN:
0016-8505
,
1751-7656
DOI:
10.1680/geot.2001.51.1.15
Language:
English
Publisher:
Thomas Telford Ltd.
Publication Date:
2001
detail.hit.zdb_id:
240560-X
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