Deformation/strain and stress

2021 ◽  
pp. 1-19
Author(s):  
Jean-Luc Bouchez ◽  
Adolphe Nicolas
Keyword(s):  
Shear Modulus ◽  
Simple Shear ◽  
Graphical Representation ◽  
Pure Shear ◽  
Flow Lines ◽  
Strain Measurements ◽  
Deformation Strain ◽  
Small Strains ◽  
Simple Shear Deformation ◽  
The Relationship

The necessary vocabulary, fundamentals and definitions for ‘deformation’, ‘strain’ and ‘stress’ are provided. Types of deformation, incremental or progressive, pure shear and simple shear, deformation regimes, flow lines and vorticity number, shortening, extension and strain measurements are explained. The concept of stress acting on a surface, through its normal and shear components is presented, along with their graphical representation using the Mohr diagram. In the elastic domain that characterizes very small strains, the relationship between stress and strain is discussed through the elastic constants among which the shear modulus and Poisson’s coefficient are notable. Finally, the stress–strain relationships for the ductile (plastic) and viscous behaviours, characteristic of large deformations, are discussed. These form the basis of understanding the rheology of the Earth, and hence Tectonics.

scholarly journals Positive or negative Poynting effect? The role of adscititious inequalities in hyperelastic materials

2011 ◽  
Vol 467 (2136) ◽  
pp. 3633-3646 ◽  
Author(s):  
L. Angela Mihai ◽  
Alain Goriely
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Shear Force ◽  
Pure Shear ◽  
Hyperelastic Materials ◽  
Isotropic Materials ◽  
Poynting Effect ◽  
Simple Shear Deformation ◽  
Biopolymer Gels

Motivated by recent experiments on biopolymer gels whereby the reverse of the usual (positive) Poynting effect was observed, we investigate the effect of the so-called ‘adscititious inequalities’ on the behaviour of hyperelastic materials subject to shear. We first demonstrate that for homogeneous isotropic materials subject to pure shear, the resulting deformation consists of a triaxial stretch combined with a simple shear in the direction of the shear force if and only if the Baker–Ericksen inequalities hold. Then for a cube deformed under pure shear, the positive Poynting effect occurs if the ‘sheared faces spread apart’, whereas the negative Poynting effect is obtained if the ‘sheared faces draw together’. Similarly, under simple shear deformation, the positive Poynting effect is obtained if the ‘sheared faces tend to spread apart’, whereas the negative Poynting effect occurs if the ‘sheared faces tend to draw together’. When the Poynting effect occurs under simple shear, it is reasonable to assume that the same sign Poynting effect is obtained also under pure shear. Since the observation of the negative Poynting effect in semiflexible biopolymers implies that the (stronger) empirical inequalities may not hold, we conclude that these inequalities must not be imposed when such materials are described.

scholarly journals Finite strain variation across the Mahabharat Thrust in central Nepal Himalaya

2007 ◽  
Vol 35 ◽  
pp. 11-20
Author(s):  
Deepak Chamlagain ◽  
Daigoro Hayashi
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Pure Shear ◽  
Hanging Wall ◽  
Three Dimensional ◽  
Strain Analysis ◽  
Central Nepal ◽  
Dynamic Recrystallisation ◽  
Simple Shear Deformation ◽  
Augen Gneiss

This paper deals with the three-dimensional strain across the Mahabharat Thrust (MT) in the Malekhu area in central Nepal. The MT served as a glide plane for the Kathmandu Nappe. Its footwall is made up of phyllites, quartzites, and amphibolites, whereas the hanging wall contains garnetiferous schists, biotite schists, and quartzites with a few lenses of augen gneiss. A three-dimensional strain analysis reveals that Nadai’s amount of strain intensity (€s ) ranges from 0.396 to 0.575 in the footwall indicating an increasing trend towards the proximity of the MT. In contrast, the hanging wall shows an increase in (€ s) magnitude away from the MT and its value varies between 0.556 (at the basal part) and 0.795 (upper part). Microtextures and structures revealed dynamic recrystallisation of the footwall and static recrystallisation of the hanging wall rocks. The shape of three dimensional strain ellipsoids, types of microstructures, and mechanisms of grainscale deformation indicated that the footwall was dominantly affected by simple shear deformation at lower temperatures while the hanging wall suffered from pure shear with minor sub-simple shear deformation at relatively higher temperatures.

Kinematics of rock flow in a crustal-scale shear zone: implication for the orogenic evolution of the southwestern Hellenides

2000 ◽  
Vol 137 (1) ◽  
pp. 81-96 ◽  
Author(s):  
P. XYPOLIAS ◽  
T. DOUTSOS
Keyword(s):  
Shear Deformation ◽  
Shear Zone ◽  
Simple Shear ◽  
Root Zone ◽  
Pure Shear ◽  
Thrust Belt ◽  
The West ◽  
Simple Shear Deformation ◽  
Tectonic Extrusion ◽  
Scale Shear

Combined shear-sense criteria, finite-strain data and vorticity analyses were used to study the deformation path in a curved crustal-scale shear zone (Phyllite–Quartzite Series) of the southwestern Hellenides. The results are combined with data on the structural evolution of a cover nappe (Pindos thrust belt) to provide new insights into the orogenic evolution of this region.Ductile deformation within the Phyllite–Quartzite Series was associated with a top-to-the-west-southwest shearing and was partitioned into two structural domains: a root zone and a frontal domain. The root zone is characterized by vertical coaxial stretching, high strain and upward movement of the material, while the frontal domain comprises simple-shear deformation at the base and pure shear at the top. This pattern suggests superposition of pure shear on simple-shear deformation, and implies tectonic extrusion of the material from the root zone.The initiation of brittle deformation in the Pindos thrust belt was associated with westward translation above the sub-horizontal Pindos Thrust. Later, as the mountain range elevated, normal faulting at high altitudes and migration of thrusting to the west occurred, while east-directed folding and thrusting in the belt started to the east.According to the proposed model, crustal thickening was taking place throughout the Oligocene and early Miocene, including the subduction of the Apulian beneath the Pelagonian microcontinent and the intracontinental subduction of the Phyllite–Quartzite Series. During the lower Miocene, vertical buoyancy forces led to the successive steepening of the shear zone and the simultaneous duplexing of its basement, facilitating tectonic extrusion of the material from its root zone. Finally, an indentation process caused vertical expulsion of the orogenic wedge and gravity collapse in the brittle crust.

The Tarskavaig Nappe of Skye, northwest Scotland: a re-examination of the fabrics and their kinematic significance

1987 ◽  
Vol 124 (3) ◽  
pp. 231-248 ◽  
Author(s):  
R. D. Law ◽  
G. J. Potts
Keyword(s):  
Simple Shear ◽  
Grain Shape ◽  
Pure Shear ◽  
Strain Compatibility ◽  
Transport Direction ◽  
Thrust Zone ◽  
Strain Paths ◽  
Simple Shear Deformation ◽  
Moine Thrust Zone ◽  
Tectonic Movements

AbstractEarly petrofabric studies of quartz c axis preferred orientation within the Tarskavaig Nappe, located at the southern end of the Moine thrust zone, have been interpreted as indicating that structures within the nappe have been produced by tectonic movements acting at right angles to those responsible for formation of structures within the overlying, but immediately adjacent, Moine Nappe. Such a dramatic contrast in inferred transport direction has not been recognized within the rest of the thrust zone.Re-examination of the microstructures and c axis fabrics within mylonitic metasediments from the western part of the Tarskavaig Nappe has revealed that these tectonites are characterized by maximum principal extension axes which trend sub-parallel to the WNW-trending Moine thrust zone transport direction. Later folding has reorientated and modified these structures within the eastern part of the nappe producing fabrics which have erroneously been taken to indicate a transport direction orientated sub-perpendicular to that of the rest of the Moine thrust zone.WNW-trending maximum principal extension axes and WNW-directed overthrust senses are indicated by microstructures within schists from the adjacent Moine Nappe, suggesting that structures within both the Tarskavaig and Moine nappes may be associated with a common west-northwest transport direction.Essentially coaxial (pure shear) strain paths (indicated by symmetrical c axis fabrics) dominate the internal parts of the Tarskavaig Nappe. Close to the base of the nappe, non-coaxial strain paths, originally associated with WNW-directed overthrusting, are indicated by asymmetrical c axis fabrics and oblique grain shape alignments. Strain compatibility considerations indicate that the lower kinematic domain (which must either be contemporaneous with, or later than, formation of the upper domain) must be characterized by a combination of pure and simple shear deformation.

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