Finite Shear Strain Research Articles

Energy conserving time integration scheme for geometrically exact beam

An energy conserving finite-element formulation for the dynamic analysis of geometrically non-linear beam-like structures undergoing large overall motions has been developed. The formulation uses classical displacement-based planar beam finite elements described in an inertial frame. It takes into account finite axial, bending and shear strains. A theoretically consistent approach is used to derive a novel and simple energy conserving scheme, using the unconventional incremental strain update rather than the standard strong form. Numerical examples demonstrate perfect energy and momenta conservation, stability and robustness of the scheme, and good convergence properties in terms of both the Newton–Raphson method and time step size.

Quartz veins deformed by diffusion creep-accommodated grain boundary sliding during a transient, high strain-rate event in the Southern Alps, New Zealand

The crystallographic preferred orientations (CPOs) and microstructures of deformed quartz veins were measured for four samples in the hanging-wall of the Alpine Fault in the Southern Alps, New Zealand. Their deformation and exhumation has occurred since 4 Ma. The quartz veins have been ductilely sheared to finite shear-strains of 5–15 in late Cenozoic shear zones at 450±50 °C, 310±90 MPa and strain-rates between 2×10 −11 and 2×10 −9 s −1. The sheared veins have a polygonal microstructure with few subgrains and an average grain-size of ∼100 μm. The CPO of the veins is random to very weak within the shear zones. We suggest that dislocation creep accommodated initial shear deformation, at high stresses and strain-rates. The deformation must have created a strong CPO and concomitant dynamic recrystallization reduced the grain-size significantly. Dissipation of stresses during initial deformation lead to a stress and strain-rate drop required for a switch to diffusion creep-accommodated grain boundary sliding (GBS). Continued shearing accommodated by GBS destroyed the CPO. Post-deformational grain growth gave rise to a final polygonal microstructure with a similar grain size in veins and in the wall rocks. Analysis of existing experimental data suggest that this sequence of events is possible in the time available. Rates of all processes may have been enhanced by the presence of a water-rich fluid within the shear zones. These observations of naturally deformed rocks provide a model for the processes that may occur during short-lived deformation at transiently-high stresses at mid-crustal depths or deeper.

Structural geology and kinematic history of rocks formed along low-angle normal faults, Death Valley, California

Several late Cenozoic low-angle normal, or detachment, faults on the western flank of the Black Mountains are each characterized by the following, in descending structural order: (1) a hanging wall of upper Tertiary to Quaternary sedimentary and volcanic strata that displays little evidence for fault-related damage other than widely spaced planar or listric normal faults; (2) a sharp, planar, and locally striated principal slip plane forming the lower boundary of the hanging wall; (3) an upper zone—zone I—of very fine grained, fault-generated rocks composed dominantly of gouge; (4) a lower zone—zone II—of coarser-grained fault rocks consisting chiefly of foliated breccia; and (5) a variably damaged footwall, consisting of partly mylonitic Precambrian units or Tertiary plutonic rocks, that has been exhumed from depths of 10–12 km since late Miocene time. The fault rocks, which were mostly derived from the footwalls, preserve evidence for cataclastic and particulate flow. Fault rocks contain authigenic minerals but lack the cyclically deformed, mineral-filled syntectonic veins that are abundant in some other late Cenozoic high-angle and strike-slip faults. Meso- and microscale fabrics in zones I and II indicate that finite shear strains increase progressively upward, toward the principal slip plane. In a conceptual kinematic model of a shear box, displacements of the hanging wall produced a shearing flow in the fault rocks below. Some of the slip on the principal slip plane was also partitioned into localized slip on discrete sliding surfaces in zones I and II. Since 770 ka, during the latest stages of incremental deformation in the brittle shear zones, distributed flow in the fault rocks alternated with slip that was chiefly localized on the principal slip planes. In this respect, the detachment faults differ from inactive segments of the San Andreas system, along which displacements were progressively and irreversibly localized onto a single principal slip surface. The strain gradients and corresponding changes in grain size in the shear zones resemble those in mylonitic shear zones except in their symmetry. Strain gradients in the Black Mountains are notably asymmetric: they are present only below the principal slip planes, not above.

The influence of matrix rheology and vorticity on fabric development of populations of rigid objects during plane strain deformation

The influence of vorticity and rheology of matrix material on the development of shape-preferred orientation (SPO) of populations of rigid objects was experimentally studied. Experiments in plane strain monoclinic flow were performed to model the fabric development of two populations of rectangular rigid objects with object aspect ratios ( R ob) 2 and 3. The density of the rigid object populations was 14% of the total area. Objects were dispersed in a Newtonian and a non-Newtonian, power law matrix material with a power law exponent n of 1.2. The kinematic vorticity number ( W n) of the plane strain monoclinic flow was 1, 0.8 and 0.6 with finite simple shear strain of 4.6, 3.0 and 0.9, respectively. In experiments with R ob=3, the SPO is strongly influenced by W n and the material properties of the matrix. Deformation of a power law matrix material and low W n resulted in a stronger SPO than deformation of a linear viscous matrix and high W n. Strain localization coupled with particle interaction plays a significant role in the development of a shape-preferred orientation. High strain simple shear zones separate trains of rigid objects that are surrounded by low strain zones with W n lower than the bulk W n. In fabrics involving populations of objects with R ob=2, rheology of the matrix materials does not systematically influence the intensity of the SPO.

Development of antitaxial strain fringes during non-coaxial deformation: an experimental study

Strain fringes were modelled experimentally around wooden objects in a simple-shear box containing Polydimethylsiloxane (PDMS). The fringes were made of paraffin wax that was periodically poured into dilated sites next to the core-object and left to crystallise. In the experiments fringes and core-object rotated at similar decreasing rotation rates relative to extensional incremental stretching axes (ISA) of flow and rotated relative to each other by small amounts. Fringes did not necessarily open parallel to ISA due to interactions between fringes and core-object. Therefore, neither displacement-controlled fibres nor object-centre paths can be expected to record the exact orientation of the extensional ISA, but only give estimates. Existing methods to calculate finite strain were applied to the experimental fringes. These methods generally underestimate the actual finite shear-strain. This study illustrates that different final fringe shapes can develop in the same shear zone depending on core-object shape and its initial orientation with respect to the shear zone boundary. A classification of final fringe shapes is presented based on the initial orientation of elongate core-objects.

Progressive development of mantle structures around elongate porphyroclasts: insights from numerical models

This paper presents a generalized theoretical approach towards two-dimensional numerical modeling of the mantle geometry of inequant porphyroclasts of varying shapes within a Newtonian matrix during progressive, general type of bulk deformation. The analysis takes into account the effects of synkinematic size reduction of the porphyroclast with concomitant mantle development in response to dynamic recrystallization. Numerical simulations reveal that the principal factors governing the geometry of mantle structures are: (1) the initial aspect ratio of the porphyroclast ( a/ b), (2) the rate of clast-size reduction, and (3) the ratio of the rates of pure shear and simple shear ( S r) or the kinematic vorticity ( W k) in the general type of non-coaxial deformation. In general, porphyroclasts develop δ-, φ- and finally, σ-type mantle structures, as the rate of clast-size reduction is progressively increased. The tails of equant porphyroclasts tend to be characterized by wings with increase in bulk shear during progressive deformation. In contrast, inequant objects ( a/ b>1) develop composite tails with multiple wings, even at low finite shear strains. However, with increase in aspect ratio δ geometry tends to dominate the overall mantle structure. Porphyroclasts with a large aspect ratio ( a/ b=3) form tails with overturned δ-wings, as described in Passchier, C.W., Simpson, C., 1986. “Porphyroclast system as kinematic indicators”, Journal of Structural Geology 8, 831–844. In general the type of non-coaxial deformation, with decrease in kinematic vorticity (or increase in S r), porphyroclasts irrespective of their initial shapes, tend to form atypical δ-like tails that do not cross the central reference plane.

Brownian dynamics simulations of the stress and molecular configuration of polymers in exponential and linearly-ramped shear flow

The rheological and optical properties of dilute polymer solutions during the startup and subsequent relaxation in exponential shear flow are studied using Brownian dynamics simulations of freely draining, flexible bead-rod chains. We find that exponential shear flow is capable of effecting large molecular deformation for finite shear rates and strains, and furthermore, the polymer undergoes an initial stress and index of refraction relaxation that is much faster than a single exponential decay upon cessation of flow. When we compare the first normal stress difference ( τ 11– τ 22) to the corresponding components of the index of refraction tensor, n 11– n 22, we find that there is hysteresis when plotted over the course of a full startup and relaxation experiment. This is very similar to the hysteresis originally discovered by Doyle et al. [J. Non-Newtonian Fluid Mech. 76 (1998) 79–110] for uniaxial extensional flow. Moreover, the shear components of the stress and index of refraction tensors ( τ 12 and n 12) also exhibit hysteretic behavior. However, whereas the hysteresis loop for the 11–22 component traverses up the left branch during startup and relaxes on the right branch, that for the 12 component is in the completely opposite direction, i.e. the right branch corresponds to startup and the left branch relaxation. The presence of stress-index of refraction hysteresis clearly has important implications for the stress-optic rule. We calculate the stress-optic coefficient for the startup process, and find that the normal and shear components give the same value, but that it is strongly dependent on Wi. This result is consistent with that found by Doyle et al. during the startup of steady shear flow [Doyle and Shaqfeh, Dynamic simulation of freely-draining, flexible bead-rod chains: startup of extensional and shear flow, J. Non-Newtonian Fluid Mech. 76 (1998) 43–78]. We also simulated shear flows with a linearly ramped shear rate to compare to our results for exponential shear. We find that for comparable final shear rate and time, both exponential and linear ramping shear produce very similar hysteresis effects in both the shear and normal components suggesting that there may be many unsteady shear flow capable of creating large polymer stretch and stress-birefringence hysteresis. Finally, we compare our bead-rod chain simulations to the FENE dumbbell model, and we find that while the latter can qualitatively capture the normal stress hysteresis, it predicts negligible shear stress hysteresis at equivalent shear rates and shear strains.

Simple graphical constructions for the direction of shear

The determination of the direction and sense of the resolved shear stress on a generally-oriented plane is greatly simplified by the use of a graphical technique based on the geometry of the representation quadric of a ‘reduced stress tensor’. This tensor is obtained by subtracting a constant equal to σ 3 from each of the principal stress values. The calculation requires knowledge of the orientations of the principal stress axes and the ratio of the principal stress differences. A construction for finding the direction and sense of finite shear strain on a given plane is derived in an analogous fashion.

Orthorhombic distortion energy for monatomic fcc crystals

The potential energy barrier and the geometry of the volume-conserving orthorhombic distortion for monatomic face-centered cubic (fcc) crystals in the absence of thermal motion have been investigated. It is shown that the orthorhombic transformation path can continuously transform a fcc crystal structure into six neighboring fcc crystal structures. Each of the new fcc lattices is equivalent to the original one but has a different orientation. The only difference of the six new fcc monatomic structures is that all the atoms change one pair of twelve atoms in the first coordination sphere into another pair and the structure has finite shear strains. The height of the potential energy barrier between the two neighboring stable fcc structures is calculated with the Morse and Mie two-body potentials under constant volume expansion or contraction. The barrier height is several times less than the energy corresponding to dilatations (the melting energy) where the lattice cohesion is lost. The total energy difference between body- and face-centered cubic crystal structures is equal to the minimum barrier height for large values of the effective radius of interatomic interaction. For small values of the radius, the minimum barrier height is less than this difference. The growth of the effective radius of the interatomic interaction decreases the height of the energy barrier. The height increases greatly with the volume contraction and decreases with the volume expansion of the fcc structures.

Grenvillian extensional tectonics in northwest Scotland

New structural data indicate that eclogite-bearing gneisses in the Glenelg-Attadale inlier of the Caledonian Moine thrust nappe, northwest Scotland, were involved in a major pre-Caledonian system of extensional top-to-the-east ductile shear zones. These shear zones coalesce upward to constitute a major extensional detachment below metasedimentary rocks of the Moine Supergroup. Both the eclogite-bearing gneisses and the Moinian metasedimentary rocks display evidence of extensional deformation, but the latter contain structures indicative of a lower intensity of bulk finite shear strain and may have experienced only the later of two discrete phases of extension that we recognize in the inlier. Coplanar Caledonian brittle-ductile, top-to-the-west thrusting has resulted in only localized and limited reactivation. Timing of the extensional deformation is bracketed by a published Sm/Nd age of 1.08 Ga for eclogite equilibration and by a minimum age of deposition for the Moine Supergroup of 840 Ma. We propose that the eclogite-bearing lower crust was exhumed as a result of collapse of the Grenville Orogen, and that the evolution of the Moinian basin was controlled by this extensional event.

Tertiary deformation and metamorphism SE of Tibet: The folded Tiger‐leap décollement of NW Yunnan, China

The Yulong‐Haba Xue Shan range, in the northwestern part of Yunnan (China), is a large N‐S antiform that folds the Paleozoic series of the Yangzi platform. The upper Yangzi River (Jinsha Jiang) has cut a 3500 m‐deep valley (Hu Tiao gorge) across this antiform, thus exposing folded, bedding‐parallel, ductile shear zones (décollements), with transport toward the SSW (in the present geographical coordinates). The large finite shear strain implies tens of kilometers of transport, pointing to the regional significance of these décollements. Rb/Sr radiometric dating of phlogopites that crystallized in marbles within the foliation planes yields the age of the metamorphic and deformation event (35.9 ± 0.3 (2σ) Ma). The age derives from an internal Rb‐Sr isochron, made on different size fractions of the same mineral, which provides a novel demonstration of the feasibility of such plots. Transport on the décollement and related shortening occurred prior to, or at the onset of, extrusion of Indochina along the Ailao Shan‐Red River shear zone, ≈80 km west of the Yulong Shan. The 39Ar/40Ar age spectra of K‐feldspar from the core of the Yulong Shan suggest uplift by antiformal folding around 17 Ma, as Indochina's extrusion came to an end. We infer that other large‐scale Cenozoic décollements such as that exhumed in the Yulong Shan underlie some of the vast, folded areas that surround the eastern Himalayan syntaxis. Transport on such décollements, first toward the south and then toward the east, and folding above them, might have occurred during two principal shortening phases, whose ages bracket Indochina's escape toward the SE.

Mechanism of shear-induced metallization

It is well-known that volumetric compression converts insulators into metals (the Herzfeld-Mott transition). Not so well-known is the fact that finite shear strains have a similar effect. For example, uniaxial compression of Si and Ge causes them to become metallic. A simple band-structure model for this is presented in this paper. Shear induced metallization has several important consequences, including: mechanically induced phase transformations, other mechanochemistry; the hardnesses of semiconductors and carbides; and ultra-fast reactions at detonation fronts.

Flow mixing, object-matrix coherence, mantle growth and the development of porphyroclast tails

The kinematic ‘stability fields’ of common porphyroclast types have been defined using a computer program that simulates low Reynolds number Newtonian shearing flow in the vicinity of a rigid spherical object. The principal variables governing the geometry of porphyroclast tails at a given finite shear strain are: (1) porphyroclast-matrix coherence, and (2) mantle recrystallization history, both of which affect the extent to which mantle material becomes mixed with the matrix as deformation progresses.

A kinematically exact space finite strain beam model — finite element formulation by generalized virtual work principle

The present paper presents a novel finite element formulation for static analysis of linear elastic spatial frame structures extending the formulation given by Simo and Vu-Quoc [A geometrically-exact rod model incorporating shear and torsion-warping deformation, Int. J. Solids Structures 27 (3) (1991) 371–393], along the lines of the work on the planar beam theory presented by Saje [A variational principle for finite planar deformation of straight slender elastic beams, Internat. J. Solids and Structures 26 (1990) 887–900]. We apply exact non-linear kinematic relationships of the space finite-strain beam theory, assuming the Bernoulli hypothesis and neglecting the warping deformations of the cross-section. Finite displacements and rotations as well as finite extensional, shear, torsional and bending strains are accounted for in the formulation. A deformed configuration of the beam is described by the displacement vector of the deformed centroid axis and an orthonormal moving frame, rigidly attached to the cross-section of the beam. The position of the moving frame relative to a fixed reference frame is specified by an orthogonal matrix, parametrized by the rotational vector which rotates the moving frame from an arbitrary position into the deformed configuration in one step. Also, the incremental rotational vector is introduced, which rotates the moving frame from the configuration obtained at the previous iteration step into the current configuration of the beam. Its components relative to the fixed global coordinate system are taken to be the rotational degrees of freedom at nodal points. Because in 3-D space both the axial and the follower moments are non-conservative, not the variational principle but the principle of virtual work has been introduced as a basis for the finite element discretization. Here we have proposed the generalized form of the principle of virtual work by including exact kinematic equations by means of a procedure, similar to that of Lagrangian multipliers. This makes possible the elimination of the displacement vector field from the principle, so that the three components of the incremental rotational vector field remain the only functions to be approximated in the finite element implementation of the principle. Other researchers, on the other hand, employ the three components of the incremental rotational vector field and the three components of the incremental displacement vector field. As a result, more accurate and efficient family of beam finite elements for the non-linear analysis of space frames has been obtained. A one-field formulation results in the fact that in the present finite elements the locking never occurs. Any combination of deformation states is described equally precisely. This is in contrast with the elements developed in literature, where, in order to avoid the locking, a reduced numerical integration has to be applied, which unfortunately, diminishes the accuracy of the solution. Polynomials have been chosen for the approximation of the components of the rotational vector. In this case the order of the numerical integration can rationally be estimated and the computer program can be coded in such a way that the degree of polynomials need not be limited to a particular value. The Newton method is used for the iterative solution of the non-linear equilibrium equations. In an non-equilibrium configuration, the tangent stiffness matrix, obtained by the linearization of governing equations using the directional derivative, is non-symmetric even for conservative loadings. Only upon achieving an equilibrium state, the tangent stiffness matrix becomes symmetric. Thus, obtained tangent stiffness matrix can be symmetrized without affecting the rate of convergence of the Newton method. For non-conservative loadings, however, the tangent stiffness matrix is always non-symmetric. The numerical examples demonstrate capability of the present formulation to determine accurately the non-linear behaviour of space frames. In numerical examples the out-of-plane buckling loads are determined and the whole pre-and post-critical load-displacement paths of a cantilever and a right-angle frame are traced. These, in the analysis of space beams standard verification example problems, show excellent accuracy of the solution even when employing only one element to describe the displacements of the size of the structure itself, the rotations of 2π, and extensional strains much beyond the realistic values of linear elastic material.

Bounds on strain in large Tertiary shear zones of SE Asia from boudinage restoration

We have used surface-balanced restoration of stretched, boudinaged layers to estimate minimum amounts of finite strain in the mylonitic gneisses of the Oligo-Miocene Red River-Ailao Shan shear zone (Yunnan, China) and of the Wang Chao shear zone (Thailand). The layer-parallel extension values thus obtained range between 250 and 870%. We discuss how to use such extension values to place bounds on amounts of finite shear strain in these large crustal shear zones. Assuming simple shear, these values imply minimum total and late shear strains of, respectively, 33 ± 6 and 7 ± 3 at several sites along the Red River-Ailao Shan shear zone. For the Wang Chao shear zone a minimum shear strain of 7 ± 4 is deduced. Assuming homogeneous shear would imply that minimum strike-slip displacements along these two left-lateral shear zones, which have been interpreted to result from the India-Asia collision, have been of the order of 330 ± 60 km (Red River-Ailao Shan) and 35 ± 20 km (Wang Chao).

Laboratory modelling of strain variation across rheological boundaries

Laboratory models using viscous and viscoplastic silicones to simulate strain variation across competence contrasts are presented. This provides a test for earlier theoretical modelling of strain refraction in layers with Newtonian viscosity contrast, and a method of examining refraction rules for non-Newtonian materials. The main purpose is to test the theoretical rule that the finite shear strain ratio across a boundary is equivalent to the inverse viscosity ratio. Results for simple-shear experiments confirm this within the errors of viscometry and strain measurement. We investigate whether this rule applies to non-Newtonian materials, which necessarily involves a discussion on the nature of viscosity contrast for non-linear materials such as power-law fluids, and its bearing on competence contrasts in rocks. These models also provide data on strain gradients generated by viscosity boundaries, which was not included in the earlier theoretical analyses. In the simple-shear experiments, the normalized shear strain profiles indicate an approximately linear shear stress gradient from the viscosity boundaries. Using an idealized linear shear strain gradient in a Newtonian matrix approaching a contrasting layer, we can derive expressions to predict the viscosity ratio. This may be a viable method of determining approximate viscosity ratios for more general deformations.

Finite shear strain behavior of a crosslinking polydimethylsiloxane near its gel point

A power law distribution of relaxation times, large normal stress differences, and physical rupture of molecular network strands dominate the shear behavior of polymers at the gel point (critical gels). This is shown in a series of well-defined experiments with increasing magnitude of shear on a model-network polymer system consisting of a linear, telechelic, vinyl-terminated poly-dimethylsiloxane (PDMS) and a four-functional siloxane crosslinker. Stable samples were prepared by stopping the crosslinking reaction at different extents of reaction in the vicinity of the gel point (GP). The Gel Equation has been shown to be valid up to strains of about 2 when using a finite strain tensor. Larger strains have been found to disrupt the network structure of the crosslinking polymer, and introduce a mechanical delay to the gel point. A sample that was crosslinked beyond the gel point (p>p c ) can be reduced from the solid state to a critical gel, or even to a viscoelastic liquid, depending on the magnitude of shear strain. As a consequence, the relaxation exponent of a critical gel created under the influence of shear is less than that of a quiescently crosslinked critical gel.

A Double-Tilt Small Angle Neutron Scattering Experiment on Deformed Poly Mer Systems

AbstractA double rotation goniometer has been mounted in the neutron beam in order to characterize the molecular deformation in polymers subjected to various strain conditions.The results provide a direct verification of the fiber symmetry in solid state coextruded polymethylmethacrylate (PMMA) and polypropylene (PP) homopolymers.In the case of the shear banding phenomenon, we have been able to test the validity of the simple shear assumption: it also provides a direct estimate of the finite shear strain involved in the process. As a last illustration ofthe method, we also consider the biaxial deformation of PP and PMMA squeezed under various temperature and strain-rate conditions.

Transmural myocardial deformation in the canine left ventricle. Normal in vivo three-dimensional finite strains.

To examine transmural finite deformation in the wall of the canine left ventricle, closely spaced columns of lead beads were implanted at a single site on the left ventricular free wall. The three-dimensional coordinates of these myocardial markers were obtained with high-speed biplane cineradiography. Any four noncoplanar markers forming small tetrahedral volumes (less than or equal to 0.1 cc) were used to calculate finite normal and shear strains with respect to a cardiac coordinate system at end diastole. Due to the symmetry of the finite strain tensor, the algebraic eigenvalue problem could be solved to compute principal strains and the directions of the principal axes of deformation with respect to the reference coordinates. An examination of the principal strains in a number of tetrahedra in five animals indicates that deformation increases with depth beneath the epicardium. For example, the transmural variation of principal shortening strain averages -0.014 +/- 0.009 per 10% increment in thickness from epicardium to endocardium. Furthermore, shortening and thickening strains at midwall and deeper are too large (0.10 to 0.40) to be described accurately by infinitesimal theory. These strains are often accompanied by substantial in-plane and transverse shears which are not predicted by typical membrane or shell theories, indicating that these theories must be applied with caution when computing indices of regional ventricular performance. The directions of the principal axes of shortening vary substantially less than the fiber direction varies across the wall (20 degrees - 40 degrees compared with 100 degrees - 140 degrees for fiber direction), supporting the concept that there are substantial interactions between neighboring fibers in the left ventricular wall.

The Fabric of Polycrystalline Ice Deformed in Simple Shear: Experiments in Torsion, Natural Deformation and Geometrical Interpretation

Three cylinders of artificial ice have been deformed in torsion at about –10℃ up to finite shear strains γ of 0.6, 0.95 and 2. The initial random lattice orientation rapidly evolves into a bimodal distribution of the basal slip planes as already observed by Kamb (1972) and Duval (1981) for low‐strains experiments near the melting point. For the γ = 0.6 and 0.95 experiments, one family of grains (> 50%) corresponds to basal planes tending to parallel the imposed shear plane; the basal planes of the other family make a broader maximum at about 60° from the shear plane. The direction of minimum concentration between the two populations approximately corresponds to the flattening plane or to the elongation direction of the strain ellipsoid. With increasing strain (γ = 2) the second submaximum vanishes and only the principal maximum parallel to the shear plane remains. This evolution is conformable with the data of Hudleston (1977) in a natural shear zone in glacial ice; it also compares remarkably well with Etchecopar′s (1977) geometrical computer model of simple shear in the same range of γ values. Single slip on the basal plane with no preferential slip direction in that plane can explain the analogy between fabrics in ice deformed in plane strain and fabrics obtained from the two‐dimensional computer model.The bimodal distribution reflects predominant slip on the basal plane; the progressively increasing heterogeneous strain enhances internal distorsion, rigid body rotation and recrystallization of grains unfavorably oriented for further slip, leading to the unimodal distribution. The adequacy of fabric analyses to infer the strain regime and the sense of shear in plastically deformed rocks is strengthened.