Finite Strain Analysis Research Articles

Elasticity of epidote at high pressure and its implications for the velocity anomaly in subduction zone

Hydrous minerals play a critical role in modifying the physical and chemical properties of the Earth’s interior. Among those, epidote is an important hydrous mineral in greenschist and blueschist phases of the metamorphosed subducting crust at shallow depth (30-60 km). Here, we measured the compressional (P) and shear (S) wave velocities of a polycrystalline epidote sample at pressures up to 7 GPa and room temperature by means of ultrasonic interferometry. The obtained sound velocities and elastic moduli of epidote increase monotonically with pressure. Finite strain analysis on those data set yielded the elastic moduli and their pressure derivatives of epidote at ambient condition as follows: KS0=115.2GPa, G0=66.7GPa, Ks′=4.6, G′=1.1. Using the elastic properties of epidote, we set up a model to better understand the velocity jumps in the subducted oceanic crusts concerning the blueschist-eclogite transition at 60-90 km depths. Our results indicate that the calculated P and S wave velocity jumps are in good agreement with those seismic observations in the typical subduction zones such as northeastern Japan and southwestern Japan. The eclogitization from epidote bearing blueschist may provide an explanation for the wave velocity anomalies occurred in those regions.

Differential pressure sensors based on transfer-free piezoresistive layered PdSe2 thin films

Piezoresistive layered two-dimensional (2D) crystals offer intriguing promise as pressure sensors for microelectromechanical systems (MEMS) due to their remarkable strain-induced conductivity modulation. However, integration of the conventional chemical vapor deposition grown 2D thin films onto a micromachined silicon platform requires a complex transfer process, which degrades their strain-sensing performance. In this study, we present a differential pressure sensor built on a transfer-free piezoresistive PdSe2 polycrystalline film deposited on a SiN x membrane by plasma-enhanced selenization of a metal film at a temperature as low as 200 °C. Based on the resistance change and finite element strain analysis of the film under membrane deflection, we show that a 7.9 nm thick PdSe2 film has a gauge factor (GF) of −43.3, which is ten times larger than that of polycrystalline silicon. The large GF enables the development of a diaphragm pressure sensor with a high sensitivity of 3.9 × 10−4 kPa−1 within the differential pressure range of 0–60 kPa. In addition, the sensor with a Wheatstone bridge circuit achieves a high voltage sensitivity of 1.04 mV·kPa−1, a rapid response time of less than 97 ms, and small output voltage variation of 8.1 mV in the temperature range of 25 °C to 55 °C. This transfer-free and low-temperature grown PdSe2 piezoresistive thin film is promising for MEMS transducer devices.

Consistent C-bar radial-basis Galerkin method for finite strain analysis

For finite-strain problems of quasi-incompressible materials, with hyperelastic and hyperelasto-plastic behavior, we develop a mixed polynomial-enriched radial-basis function (RBF) interpolation. It is characterized by decoupling quadrature and polynomials for the deviatoric and volumetric terms of the right Cauchy–Green tensor. With an enriched interpolation, first and second derivatives of the deformation gradient are continuous. A finite-element mesh is employed for quadrature purposes with the corresponding distribution of Gauss points. In terms of discretization, linear, quadratic and cubic polynomials are combined and function support is established from the number of pre-assigned nodes. Due to the adoption of a Lagrangian kernel, finite strain elasto-plastic constitutive developments are based on the Mandel stress. Combined with the C¯ technique, these developments are found to be convenient from an implementation perspective, as RBF formulations for finite strain plasticity have been limited in terms of generality and amplitude of deformations in the quasi-incompressibility case. Three benchmark tests are successfully solved, and it was found that a combination of reduced integration with a deviatoric cubic basis and volumetric quadratic basis provides superior results in the quasi-incompressible case. Numerical testing shows very good convergence behavior of the results. Besides absence of locking with selective interpolation, outstanding Newton convergence was observed regardless of strain levels.

Code verification of non‐linear immersed boundary simulations using the method of manufactured solutions

AbstractNon‐standard finite element technologies, such as immersed boundary approaches, are typically based on novel algorithms and advanced methods, which require reliable testing of the implemented code. For this purpose, the method of manufactured solutions (MoMS) offers a great framework, enabling an easy and straightforward derivation of closed‐form reference solutions. In this contribution, the focus is kept on non‐linear analysis via the finite cell method (FCM), which is typically based on an unfitted geometry discretization and higher‐order shape functions. The code verification via MoMS generally requires the application of boundary conditions to all boundaries of the simulation domain, which need to be enforced in a weak sense on the immersed boundaries. To avoid this, we propose a novel way of deriving manufactured solutions, for which the necessary constraints on the embedded boundaries are directly fulfilled. Thus, weak boundary conditions can be eliminated from the FCM simulation, and the simulation complexity is reduced when testing other relevant features of the immersed code. In particular, we focus on finite strain analysis of 3D structures with a Neo‐Hookean material model, and show that the proposed technique enables a reliable code verification approach for all load steps throughout the deformation process.

A structure-preserving integrator for incompressible finite elastodynamics based on a grad-div stabilized mixed formulation with particular emphasis on stretch-based material models

We present a structure-preserving scheme based on a recently-proposed mixed formulation for incompressible hyperelasticity formulated in principal stretches. Although there exist several different Hamiltonians introduced for quasi-incompressible elastodynamics based on different multifield variational formulations, there is not much study on the fully incompressible materials in the literature. The adopted mixed formulation can be viewed as a finite-strain generalization of Herrmann variational formulation, and it naturally provides a new Hamiltonian for fully incompressible elastodynamics. Invoking the discrete gradient and scaled mid-point formulas, we are able to design fully-discrete schemes that preserve the Hamiltonian and momenta. Our analysis and numerical evidence also reveal that the scaled mid-point formula is non-robust numerically. The generalized Taylor–Hood element based on the spline technology conveniently provides a higher-order, robust, and inf-sup stable spatial discretization option for finite strain analysis. To enhance the element performance in volume conservation, the grad-div stabilization, a technique initially developed in computational fluid dynamics, is introduced here for elastodynamics. It is shown that the stabilization term does not impose additional restrictions for the algorithmic stress to respect the invariants, leading to an energy-decaying and momentum-conserving fully discrete scheme. A set of numerical examples is provided to justify the claimed properties. The grad-div stabilization is found to enhance the discrete mass conservation effectively. Furthermore, in contrast to conventional algorithms based on Cardano’s formula and perturbation techniques, the spectral decomposition algorithm developed by Scherzinger and Dohrmann is robust and accurate to ensure the discrete conservation laws and is thus recommended for stretch-based material modeling.

Sound velocities of natural clinohumite at high pressures and implications for seismic velocities of subducted slabs in the upper mantle

Clinohumite is one of the major transformation products of serpentine at high pressures and an important H2O and F carrier in the upper mantle at subduction zones. Sound velocity measurements on clinohumite under high P-T conditions are crucial for modeling slab structure, arc magmatism, seismicity, and deep H2O cycling process. The compressional (P-) and shear (S-) wave velocities of a natural F-bearing clinohumite [Mg8.17Ti0.19Fe0.01(SiO4)4O0.38(OH)1.17,F0.74] were investigated using ultrasonic interferometry technique up to 14.6 GPa at room temperature in a multi-anvil apparatus. The variations of both the P- and S-wave velocities of clinohumite with pressure are the smallest when compared to the common anhydrous and other dense hydrous magnesium silicate (DHMS) phases in the upper mantle. Finite strain analysis of the acoustic velocities and density data yields the adiabatic bulk (KS) and shear (G) moduli and their pressure derivatives: KS0 = 121.0(5), G0 = 76.5(2), KS’ = 3.9(1), G' = 1.1(1). Furthermore, the density and seismic velocity profiles of subducted harzburgite assemblages with various degrees of hydration were calculated up to 14 GPa along an isotherm at 1073 K. Our results indicate that clinohumite has a larger effect on the density of peridotite than phase A and 23 Å phase under the same degree of hydration of peridotite in the upper mantle. Moreover, the VP and VS velocity contrasts between dry harzburgite and harzburgite with 2 wt% H2O from clinohumite are about ∼1.6% and ∼ 1.0%.

Hermitian numerical manifold method for large deflection of irregular Föppl-von Kármán plates

We proposed the Hermitian manifold numerical method (HNMM) fitted for finite strain analysis of thin plates with irregular domains. The large deflection of elastic thin plates is generally characterized by Föppl-von Kármán (FvK) equations, coupled with nonlinear fourth-order partial differential equations. The corresponding primal variational formulation requires the solution function to be globally C1 continuous but piecewise C2 continuous (namely H2 regular). Hermitian numerical manifold method (HNMM) can easily construct an approximation to solutions that satisfy the H2 regular requirements with structured meshes. Furthermore, those classical plate elements in finite element history can be embedded in the framework of HNMM and be more flexible and adaptable to solve plates with irregular domains. Thus, HNMM is formulated based on the Föppl-von Kármán (FvK) model using the dual cover system and a triplet attributes group on the physical patches. The numerical results demonstrate the accuracy of HNMM in large deflection of Föppl-von Kármán plate with complex domain shape.

The analysis of internal stresses on a welded joint in Grade 91 steel under creep test loading: Synchrotron X-ray diffraction measurements and modelling

The analysis and understanding of creep damage of Grade 91 steel welded joints is an important topic in the energy industry. Creep tests on welded joints were carried out at 600∘C, 100MPa and then interrupted at 0%, 10%, 30%, 50%, 80% of the expected life and after failure. Creep damage is characterised by cavity bands located exclusively in the core of the sample in the InterCritical Heat Affected Zone (ICHAZ). These samples were tested using in situ synchrotron X-ray Diffraction (XRD) along the welded joint under creep conditions for the different creep times. The experimental results show a significant evolution of strain and creep damage characteristics on the welded joint, with a local maximum at the Heat Affected Zone (HAZ). Subsequently, a finite element creep strain analysis was performed for comparison with the experimental results.

One–dimensional nonlinear finite strain analysis of self–weight consolidation of soft clay considering creep

Creep as an intrinsic property of clay is non–negligible in predicting ground settlements in land reclamation construction and foundations on reclaimed land and soft soils, but it is unfortunately difficult to characterize in current self–weight consolidation analysis. This paper develops a one–dimensional (1D) finite strain consolidation model to take into account the creep of soft clay, particularly during the early stages of reclamation construction, mainly in a self-weight consolidation process. In this model, the Yin–Graham 1D Elastic Visco-Plastic (EVP) model is first extended for modelling self-weight finite strain consolidation of soft clays to describe the creep of soil skeleton under extremely high water content. The Darcian and non-Darcian flow, nonlinear compressibility and permeability of soft clays with a huge variety of water content are also considered. Governing partial differential equations using the EVP model are derived. These nonlinear partial differential equations are solved using the Crank–Nicholson finite difference method. Three case studies involving a wide range of initial void ratio values are simulated, which show that the present model, with more realistic consideration of creep feature of clays than previous ones, can capture the self-weight consolidation process well when compared with physical model test results.

Structural evolution and Microstructural analysis for al Faydh area, southern Arabian shield, Saudi Arabia

Al Faydh area is a major significant tectonic structure in southwestern part of Arabian shield, and it was estimated using finite strain analysis and microstructural investigation. Our research focuses structural features of the Al Faydh area in order to obtain field identification and better comprehend the tectonic setting for studied region. The Rf/φ and Fry techniques were used the most of quartz and feldspar for felsic minerals and biotite and hornblende for mafic minerals. The axial ratios with the mean average about 1.09–1.83 (using Rf/φ method) and 1.13 to 1.95 (using the Fry method) in the XZ section for the collected samples of metavolcanic, metasedimentary and meta-granite (gneisses). The finite strain direction displays clustering with slight plunging along a W–E trend along the long axes. The Z axes are related the sub-vertical and sub-horizontal foliation. The majority results suggest oblate strain symmetry and there is noticeable rise in strain magnitudes toward the tectonic contacts. The volume change was related the accumulation of finite strain in the different lithologies during a polyphase deformation regime. Applying the finite strain and microstructural analysis data from Al Faydh region concluded that the structural contacts for different lithologies were generated during faults, plutonic intrusion and fracture zones. Also, the deformation in the Al Faydh region are formed under brittle to semi-ductile deformational with simple shearing.

Deformation and temperature variation along thrust-sense shear zones in the hinterland-foreland transition zone of collisional settings: A case study from the Barbagia Thrust (Sardinia, Italy)

In the Internal Zone of a continental collisional orogen, first-order contractional shear zones accommodate crustal shortening. Structural investigations at different scales, flow kinematics, and finite strain analyses are fundamental tools to determine how deformation is accommodated and partitioned. Spatial temperature variations can be responsible for the dynamic weakening and strain localization in the crust, therefore understanding the thermal conditions of shearing and deformation is critical. We integrate field observations, meso- and microstructural analyses, kinematic vorticity estimations, and finite strain data with a quantitative thermometric analysis by Raman spectroscopy on carbonaceous material along a ductile shear zone: the Barbagia Thrust (BT) in the hinterland-foreland transition zone of the Sardinian Variscan belt. These analyses, performed in two different parts of the shear zone, yield similar finite strain gradients, albeit with an increasing component of simple shear with increasing temperature, highlighting the feedback between temperature and vorticity. Our results best fits with a tectonic scenario with shear heating, where higher magnitude gradients correspond to higher vorticity and finite strain values, which indicate greater shear and heating values. The heating quantified along the BT (~50°C) is compared favorably to numerical and mechanical models. We demonstrate how the BT represents a major tectonic boundary separating the internal sector belonging to the metamorphic core of the belt from the external one involved in the orogenic wedge system.

Tectonic shortening and strain magnitudes across the Chapada Diamantina Fold and Thrust Belt: New insights into the tectonic evolution of the Paramirim Aulacogen

In this study, strain magnitudes and tectonic shortening across the Chapada Diamantina fold-and-thrust belt are calculated by finite strain analysis, cross-section restoration and kinematic forward models. A total of 9 complete 3D strain analyses on oriented samples were conducted by the Inertia Tensor method and best fit ellipsoids were computed, resulting in strain ratios (X/Z) varying from 1.190 to 2.504. Predominant oblate shaped ellipsoids related to down-dipping stretching directions are associated with regional transport direction from SW to NE, with reverse faults, upright axial-plane fold and sub-horizontal axis. The restoration of the cross-section yielded a shortening of 19.37%, understood as the minimum tectonic shortening. The adopted model assumes the inversion of former extensional faults (steep thrusts), where the structural architecture of the area is mainly controlled by the inherited rift basin architecture, with basement involvement in a combination of thick and thin skin deformation. Similarly, the assessment of kinematic forward models resulted in a minimum shortening of 18.5%. Comparably, finite strain data integration techniques yielded a total of 21.65% of regional tectonic shortening, representing the horizontal component of ductile flattening strain across the section due to penetrative strain. Therefore, we present, by three different and independent approaches, an estimate range of tectonic shortening between 18%–22% at the western Chapada Diamantina region, but the total amount of shortening across the Paramirim aulacogen might have been greater. These results suggest that the western and eastern parts of the São Francisco craton could not be considered as rigidly linked during the Neoproterozoic–Cambrian Brasiliano orogeny, with the Paramirim aulacogen exerting an import role.

Strain pattern and vorticity analysis in the transpressional Kamandan area within the Sanandaj-Sirjan Metamorphic Belt, Iran

New structural data on radiolarite and quartz mylonite rocks from the well-exposed Kamandan area are presented with the aim to shed light on the quantitative finite strain and vorticity analyses and strain partitioning along the Zagros transpression zone. Duplex structures, imbricate fans, thrust sheets and shear zones are well developed in the Kamandan region, located in the Sanandaj-Sirjan Metamorphic Belt, western Iran. Kinematic shear sense indicators associated with Kamandan shear zone show top-to-the-NE sense of ductile shearing deformation. Integrated quantitative finite strain and kinematic vorticity analyses of deformed rocks indicate deformation pattern and geometry. The strain parameter measurements vis. strain ratios and strain ellipsoid shape (k) show that radiolarite and quartz mylonite rocks have deformed in the constrictional to approximately plane-strain conditions. The quartz mylonite rocks highlight general-shear (sub-simple shear) deformation (Wm = 0.68–0.81) associated with the spatial increase in simple-shear component (47%–60%) from NE to SW. Our results of structural, strain, and vorticity analyses confirm a dextral transpression with strain partitioning into the pure-shear and simple-shear components in the Kamandan shear zone. Estimated Wm-values display the θ angle between the transpressional boundary and the maximum instantaneous strain axis (ISA) is the range from 63 to 69°. Accordingly, the oblique convergence angle (α) between the flow apophyses was estimated at about 35–48° that causes a horizontal shortening of ∼32–42% perpendicular to the boundaries of the Kmandan shear zone.

Galerkin-based finite strain analysis with enriched radial basis interpolation

We present an enriched radial basis function (RBF) interpolation, which is combined with a symmetric Galerkin method to solve finite strain problems. Specifically, Wendland compact support radial basis functions (RBF) are enriched with a quadratic polynomial, whose parameters are condensed-out during the shape-function construction phase. A total Lagrangian technique is adopted and for finite strain plasticity the formalism with the Mandel stress is adopted. These recent developments are especially convenient from the implementation perspective, as RBF formulations for finite strain plasticity have been limited by interpolation updating. We also note that, although tetrahedra are adopted for quadrature in the undeformed configuration, mesh deformation is of no consequence for the results. Four benchmark tests are successfully solved, with extensive convergence studies and showing clear advantages with respect to finite-element in terms of robustness and with respect to classical Element-Free Galerkin (EFG) formulations in terms of efficiency.

Moving least-squares in finite strain analysis with tetrahedra support

A finite strain finite element (FE)-based approach to element-free Galerkin (EFG) discretization is introduced, based on a number of simplifications and specialized techniques in the context of a Lagrangian kernel. In terms of discretization, a quadratic polynomial basis is used, support is determined from the number of pre-assigned nodes for each quadrature point and quadrature points coincide with the centroids of tetrahedra. Diffuse derivatives are adopted, which allow for the use of convenient non-differentiable weight functions which approximate the Dirac-Delta distribution. Due to the use of a Lagrangian kernel, recent finite strain elasto-plastic constitutive developments based on the Mandel stress are adopted in a direct form. These recent developments are especially convenient from the implementation perspective, as EFG formulations for finite strain plasticity have been limited by the previous requirement of updating the kernel. We also note that, although tetrahedra are only adopted for integration in the undeformed configuration, mesh deformation is of no consequence for the results. Four 3D benchmark tests are successfully solved.

Kinematic vorticity, finite strain, and deformation thermometry analyses of the exhumed mylonites in the Samen ductile shear zone (Sanandaj-Sirjan Metamorphic Belt, Iran)

Quantitative microstructural investigations involving finite strain and vorticity analyses of quartz-rich mylonites provide significant information regarding the kinematic characteristics of the Samen shear zone (SSZ) within the Sanandaj–Sirjan Metamorphic Belt, Zagros Mountain of Iran. A dominant top-to-the-SE sense shear in the study area is recognized by several kinematic indicators. The results of the finite strain analyses indicate approximately plane strain deformation conditions (Rxz = 2.46–3.53). The mylonitic granitoid rocks record general-shear deformation (Wm = 0.37–0.94) associated with a spatial increase in simple-shear component (23%–78%) from W to E. In the study area, kinematic analyses indicate spatial variations of finite strain, deformation temperature, and the kinematic vorticity numbers resulted in partitioned progressive deformation. These spatial variations reveal an increase of all values towards the Samen thrust sheet. Ductile SSZ developed under greenschist-amphibolite facies metamorphic conditions (464–619 °C), as indicated by the presence of quartz, feldspar, biotite, muscovite, hornblende mineral assemblages, opening angles (OAs) of quartz c-axis fabrics and recrystallization regimes. The dynamic and kinematic characteristics of the study area were generally controlled by ongoing oblique convergence of the Afro-Arabian plate and the Iranian plateau with estimation of a horizontal shortening of ∼20–38% measured perpendicular to the boundaries of the SSZ.

Superconducting and structural properties of the type-I superconductor PdTe2 under high pressure

The transition metal dichalcogenide $\mathrm{Pd}{\mathrm{Te}}_{2}$ has attractive features based on its classification as a type-II Dirac semimetal and the occurrence of type-I superconductivity, providing a platform for discussion of a topological superconductor. Our recent work revealed that type-I superconductivity persists up to pressures of $\ensuremath{\sim}2.5$ GPa and the superconducting transition temperature ${T}_{\mathrm{c}}$ reaches a maximum at around 1 GPa, which is inconsistent with the theoretical prediction. To understand its nonmonotonic variation and investigate superconductivity at higher pressures, we performed structural analysis by x-ray diffraction at room temperature below 8 GPa and electrical resistivity measurements at low temperatures from 1 to 8 GPa. With regard to the superconductivity beyond 1 GPa, the monotonic decrease in ${T}_{\mathrm{c}}$ is reproduced without any noticeable anomalies; ${T}_{\mathrm{c}}$ changes from 1.8 K at 1 GPa to 0.82 K at 5.5 GPa with $d{T}_{\mathrm{c}}/dP\ensuremath{\sim}\ensuremath{-}0.22$ K/GPa. The crystal structure with space group $P\overline{3}m1$ is stable in the pressure range we examined. On the other hand, the normalized pressure-strain analysis (finite strain analysis) indicates that the compressibility changes around 1 GPa, suggesting that a Lifshitz transition occurs. We here discuss the effect of pressure on the superconducting and structural properties based on the comparison of these experimental results.

Study of structural, deformation temperature, and strain analysis of the quartzarenites of south-central Kaladgi basin, exposed at and around Mullur ghat and Kallur village of Belgaum district, Karnataka, India

Kaladgi rocks are magnificently exposed in Belgaum district of Karnataka state, with adjacent to Maharashtra, the Kaladgi Basin, evolved as a consequence of crustal extension which are resting on the basement of the Archaean Gneisses and are also overlaid by Deccan Traps. The outcrops in the present study area have very well-exposed quartzarenites of south-central part of Kaladgi Basin. New meso- and microscale structural analyses indicate that Kaladgi rocks suffered at least two episodes of deformation preserved in ductile and ductile-brittle structures. Finite strain analyses of the XZ and YZ sections on the collected samples from the Kaladgi basin show pure flattening strain pattern on Hsu and Flinn diagram. This simple flattening strain is attributed due to the sedimentation or lithological loading in the basin. This study area traversed by 3 transverse faults, namely F1, F2, and F3 through K-1, K-5, and M-4 locations, respectively. Finite strain analyses show high strain value in XZ section along the faults as F1 show 1.32 to 1.44, F2 has 2.3 to 1.45, and F3 reflect 1.57 Rs values. Deformation temperature based on the microstructures has high value along the faults as 400 to 500°C; however, rest of the area show low temperature deformation <300°C. This study brings new insights on deformation structures in field and under a microscope.

Asymmetric development of the Himalaya: quantitative evidence from strain analysis in Kimin-Ziro-Tamen area, Arunachal Lesser Himalaya, India

The eastern segment of the Himalaya makes a quarter of the mountain belt. While its plate tectonic setting is well understood, the intensity of deformation along the thrusts is not well constrained. This knowledge gap has restricted a quantitative comparison of deformation and crustal shortening in the Eastern Lesser Himalaya with the Central and Western Lesser Himalaya. In this study field evidence, together with microstructural investigations, and two-dimensional (2D) finite strain analysis are used to decipher the deformation pattern in the Kimin-Ziro-Tamen area of the Eastern Lesser Himalaya. Present investigations reveal that micro-to-outcrop-scale structures such as plastically deformed quartz grains, crenulation cleavages, S-C fabric, pull-apart grains, pinch-n-swell structures, boudins and faults confirm that the rocks have been subjected to ductile and brittle-ductile phases of deformation with a regional top-to-south shear sense. The 2D finite strain estimated here is comparable to that in other parts of Eastern Lesser Himalaya, such as the Sikkim and Bhutan Himalaya. However, the strain estimated here is higher than in the Central and Western Lesser Himalaya, such as in the Central Nepal Himalaya, Almora Crystalline Zone, the Garhwal Lesser Himalaya and the Hazara-Kashmir Syntaxis in Pakistan. This provides quantitative proofs of greater deformation and crustal shortening in the Eastern Lesser Himalaya than the Central and Western Himalaya, and of the asymmetric development of Himalaya.

Quantitative kinematic analyses of the Darizhun shear zone within the hinterland of the Zagros orogenic belt, Iran

The basal decollement Darizhan shear zone in the hinterland of the Zagros orogenic belt exposes the amphibolite-mylonite in NW Iran. In this study, I discuss the deformation partitioning in terms of oblique convergence between the Afro-Arabian continent and the Iranian microcontinent. Rf/ $$\phi $$ -based finite strain analysis, Rxz varies ranging from 2.25 to 3.04 for the XZ-plane of the strain ellipsoid. The flow vorticity (Wm) along the Darizhun shear zone is estimated employing PHD, PAR, RGN and PD techniques. The Wm estimates vary between 0.6 and 0.85 and demonstrate general shear deformation (pure-shear: 35–58% and simple-shear: 42–65%). The Wm values indicate a gradual increase in the simple-shear component towards the Darizhan thrust sheet. Considering both the results of strain and vorticity analyses, we propose a horizontal shortening of (~ 21–36%) normal to the walls of the shear zone.