Complex Deformation Fields Research Articles

Damage evolution of coal with a strong bursting liability and 3D measurement method for elastic deformation energy distribution

When coal with a strong bursting liability is disturbed by a load, catastrophic instability disasters and rockbursts can easily occur. Loaded coal with a strong bursting liability undergoes complex damage evolution and failure behavior due to the intricate interplay among loads, gangue, fractures, and the coal matrix. Intuitively quantifying and characterizing the complex discontinuous structural features, deformation fields, and energy fields within coal is the foundation for the scientific analysis and prevention of disaster mechanisms caused by rockbursts. Therefore, studying the distribution and evolutionary processes of deformation fields and energy fields caused by the evolution of discontinuous structures within coal is highly important for the prevention and control of coal mine rockburst disasters and the protection of coal mine safety during mining operations. In this study, a series of X-ray computed tomography (X-CT) tests were conducted on coal specimens with varying gangue contents under uniaxial compressive loading. The X-CT images clearly illustrated the internal damage evolution of coal with a strong bursting liability, revealing fracture propagation, shear bands, and localized failure under varying loading conditions. Image segmentation was employed to quantitatively analyze the development of damage in coal with a strong bursting liability, revealing the influence patterns of gangue content on the prepeak deformation localization and strength of coal. Additionally, using digital volume correlation, the 3D volumetric displacement and strain of loaded impact-prone coal were determined based on the changes in natural speckle images. The nonuniform distribution of strain was mainly caused by the nonuniform distribution of gangue and pore fractures at the microscopic scale, which explains the localized deformation in coal materials. Importantly, this study provides new full-field strain tensor data and a novel method for measuring the elastic deformation energy of the 3D deformation and cracking processes of loaded coal.

The novel strength criterion and the associated constitutive model based on the finite deformation behavior for the rock under the disturbance stress paths

To develop a novel 3D Hoek–Brown strength criterion and an associated constitutive model based on the finite deformation behavior of rock under the disturbance stress paths, a series of mechanical tests are initially conducted under designed disturbance stress paths (hydrostatic stress stage (HSS), initial loading–unloading stage (ILUS), and disturbance stage (DS)). Additionally, low disturbance (LD), medium disturbance (MD), and high disturbance (HD) modes are taken into consideration. Then, the finite deformation theory is employed to study the nonlinear behavior. This nonlinear behavior can be regarded as a nonlinear relationship between the stress and strain of rock under loading, especially the initial compression stage and plastic stage, as well as a complex deformation field, which is described by the finite deformation theory and featured by the mean rotation angle (Θ). Afterwards, the damage variable (DV) regarding Θ is proposed and used to establish a novel strength criterion (NSC) based on the current Hoek–Brown strength criterion. Finally, by considering the NSC, an associated elasto-plastic constitutive model is developed. The results show that the initial confining pressure (ICP) and disturbance mode have a significant effect on the elastic modulus (E). Meanwhile, the ICP has a higher effect on E than the disturbance mode. Then, the evolution of Θ is closely associated with the nonlinear deformation of rock masses because the σ1−Θ curves can be divided into three stages. Those stages can match well with the initial compression stage, elastic stage, and plastic stage, respectively. Regarding Θ as a parameter of the damage variable (DV), the NSC is established. Additionally, it can be observed that the failure envelopes of the NSC scale down gradually with increasing Θ on the deviatoric plane. Meanwhile, as the value of the coefficient of determination (DC) is higher than that of other strength criteria, the NSC may exhibit better agreement with the experimental data. Furthermore, a constitutive model based on the aforementioned strength criterion and the hardening function that takes Θ and the disturbance of rock masses (D) into account is proposed and validated as a solution to predict the nonlinear behavior of rock specimens under the disturbance stress paths.

Digital image correlation based on convolutional neural networks

As an indispensable non-destructive testing technique, digital image correlation (DIC) has been increasingly applied to various engineering areas concerning deformation characterization. Inspired by artificial intelligence-related technologies, we here develop a new convolutional neural network-based theoretical framework for DIC analyses, hereafter called DIC-Net. A pyramidal structure is designed to ensure robustness and reliability of measurement results. Simultaneously, the second-order shape function is adopted to create training dataset, making the DIC-Net more suitable for solving complex deformation fields. Different from conventional DIC algorithms, the developed DIC-Net does not require specific correlation criterion, nor is it necessary to perform numerical iterative computations, which greatly enhances the efficiency of correlation calculations. The proposed DIC-Net not only provides an alternative approach to achieve accurate, precise and reliable deformation measurements, but also paves the way for developing high-efficiency DIC with real-time processing capabilities.

Recurrent Tissue-Aware Network for Deformable Registration of Infant Brain MR Images.

Deformable registration is fundamental to longitudinal and population-based image analyses. However, it is challenging to precisely align longitudinal infant brain MR images of the same subject, as well as cross-sectional infant brain MR images of different subjects, due to fast brain development during infancy. In this paper, we propose a recurrently usable deep neural network for the registration of infant brain MR images. There are three main highlights of our proposed method. (i) We use brain tissue segmentation maps for registration, instead of intensity images, to tackle the issue of rapid contrast changes of brain tissues during the first year of life. (ii) A single registration network is trained in a one-shot manner, and then recurrently applied in inference for multiple times, such that the complex deformation field can be recovered incrementally. (iii) We also propose both the adaptive smoothing layer and the tissue-aware anti-folding constraint into the registration network to ensure the physiological plausibility of estimated deformations without degrading the registration accuracy. Experimental results, in comparison to the state-of-the-art registration methods, indicate that our proposed method achieves the highest registration accuracy while still preserving the smoothness of the deformation field. The implementation of our proposed registration network is available online https://github.com/Barnonewdm/ACTA-Reg-Net.

Unsupervised deformable image registration network for 3D medical images

Image registration aims to establish an active correspondence between a pair of images. Such correspondence is critical for many significant applications, such as image fusion, tumor growth monitoring, and atlas generation. In this study, we propose an unsupervised deformable image registration network (UDIR-Net) for 3D medical images. The proposed UDIR-Net is designed in an encoder-decoder architecture and directly estimates the complex deformation field between input pairwise images without any supervised information. In particular, we recalibrate the feature slice of each feature map that is propagated between the encoder and the decoder in accordance with the importance of each feature slice and the correlation between feature slices. This method enhances the representational power of feature maps. To achieve efficient and robust training, we design a novel hierarchical loss function that evaluates multiscale similarity loss between registered image pairs. The proposed UDIR-Net is tested on different public magnetic resonance image datasets of the human brain. Experimental results show that UDIR-Net exhibits competitive performance against several state-of-the-art methods.

Deformable Registration of Coronary Arteries with Topological Constraints for Image-Guided Vascular Interventions.

2D/3D registration of preoperative computed tomography angiography with intra-operative X-ray angiography improves image guidance in percutaneous coronary intervention. However, previous registration methods are inaccurate and time-consuming due to simple deformation and iterative optimization, respectively. In this paper, we propose a novel method for non-rigid registration of coronary arteries based on a point set registration network, which predicts the complex deformation field directly without iterative optimization. In order to maintain the structure of coronary arteries, we advance the classical point set registration network with a loss function containing global and local topological constraints. The method was evaluated on ten clinical data, and it achieved a median chamfer distance of 73.60 pixels with a run time of less than 1s on CPU. Experimental results demonstrate that the proposed method is highly accurate and efficient.

Progressively Trained Convolutional Neural Networks for Deformable Image Registration.

Deep learning-based methods for deformable image registration are attractive alternatives to conventional registration methods because of their short registration times. However, these methods often fail to estimate larger displacements in complex deformation fields, for which a multi-resolution strategy is required. In this article, we propose to train neural networks progressively to address this problem. Instead of training a large convolutional neural network on the registration task all at once, we initially train smaller versions of the network on lower resolution versions of the images and deformation fields. During training, we progressively expand the network with additional layers that are trained on higher resolution data. We show that this way of training allows a network to learn larger displacements without sacrificing registration accuracy and that the resulting network is less sensitive to large misregistrations compared to training the full network all at once. We generate a large number of ground truth example data by applying random synthetic transformations to a training set of images, and test the network on the problem of intrapatient lung CT registration. We analyze the learned representations in the progressively growing network to assess how the progressive learning strategy influences training. Finally, we show that a progressive training procedure leads to improved registration accuracy when learning large and complex deformations.

A novel inhomogeneous deformation field model for cylindrical specimens for unconfined compression testing

Abstract Compression methods when testing polymer materials from quasi-static to dynamic loading rates require the use of cylindrical specimens due symmetry. For soft materials, which have more complex non-linear response such as hyperelastic or viscoelastic compared to traditional engineering materials, additional challenges arise when obtaining their material parameters. Previous studies have been found scarce in investigating and developing mathematical models to predict this complex deformation field whenever friction is considered during unconfined compression testing. We present an analytical approach to model this “barreling effect” that is derived from inhomogeneous deformation field that accumulates mass in the center region of the specimen. This reduces the contact surface area that directly affects the computation of material constants e.g. stress. Our novel method successfully describes this effect quantitatively, providing an analytical solution that models the deformation field for a wide range of finite strains and variety materials. This approach has been experimentally proved to dramatically increase the accuracy by up to 17% compared to existing methodologies that are based only on the homogeneous deformation approach, which to date, is the most common model to characterize the general material's mechanical response.

Nonuniform transformation behaviour of NiTi in a discrete geometrical gradient design

Shape memory alloys exhibit unique thermomechanical properties, e.g., the shape memory effect and the pseudoelasticity. By proper geometrical gradient design, these alloys can be made to exhibit different and more intricate thermomechanical behaviour to enable innovative applications. This paper reports the design of geometrically gradient NiTi and characterisation of its complex and nonuniform transformation and deformation fields. The study investigated two designs, with one using multiple pseudoelastic NiTi strips of different lengths in parallel arrangement to create a discrete geometrical gradient in the direction perpendicular to the loading axis and the other a tapered plate to give a continuous length gradient in the lateral direction for comparison with the former. The geometrically gradient structures exhibited partial stress gradient during stress-induced transformation. A maximum stress window of 520 MPa was achieved, giving an expanded stress interval for shape memory actuation control. Finite element modelling was applied to characterise the deformation behaviour of such structures under tensile loading and to reveal the complex propagation of the stress-induced transformation in such structures.

3D full-field quantification of cell-induced large deformations in fibrillar biomaterials by combining non-rigid image registration with label-free second harmonic generation.

To advance our current understanding of cell-matrix mechanics and its importance for biomaterials development, advanced three-dimensional (3D) measurement techniques are necessary. Cell-induced deformations of the surrounding matrix are commonly derived from the displacement of embedded fiducial markers, as part of traction force microscopy (TFM) procedures. However, these fluorescent markers may alter the mechanical properties of the matrix or can be taken up by the embedded cells, and therefore influence cellular behavior and fate. In addition, the currently developed methods for calculating cell-induced deformations are generally limited to relatively small deformations, with displacement magnitudes and strains typically of the order of a few microns and less than 10% respectively. Yet, large, complex deformation fields can be expected from cells exerting tractions in fibrillar biomaterials, like collagen. To circumvent these hurdles, we present a technique for the 3D full-field quantification of large cell-generated deformations in collagen, without the need of fiducial markers. We applied non-rigid, Free Form Deformation (FFD)-based image registration to compute full-field displacements induced by MRC-5 human lung fibroblasts in a collagen type I hydrogel by solely relying on second harmonic generation (SHG) from the collagen fibrils. By executing comparative experiments, we show that comparable displacement fields can be derived from both fibrils and fluorescent beads. SHG-based fibril imaging can circumvent all described disadvantages of using fiducial markers. This approach allows measuring 3D full-field deformations under large displacement (of the order of 10μm) and strain regimes (up to 40%). As such, it holds great promise for the study of large cell-induced deformations as an inherent component of cell-biomaterial interactions and cell-mediated biomaterial remodeling.

Elastic deformations driven by non-uniform lubrication flows

The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics and reconfigurable microfluidic devices. In this work, we examine non-uniform lubrication flow as a mechanism to create complex deformation fields in an elastic plate. We consider a Kirchhoff–Love elasticity model for the plate and Hele-Shaw flow in a narrow gap between the plate and a parallel rigid surface. Based on linearization of the Reynolds equation, we obtain a governing equation which relates elastic deformations to gradients in non-homogeneous physical properties of the fluid (e.g. body forces, viscosity and slip velocity). We then focus on a specific case of non-uniform Helmholtz–Smoluchowski electro-osmotic slip velocity, and provide a method for determining the zeta-potential distribution necessary to generate arbitrary static and quasi-static deformations of the elastic plate. Extending the problem to time-dependent solutions, we analyse transient effects on asymptotically static solutions, and finally provide a closed form solution for a Green’s function for time periodic actuations.

Strain uncertainties from two digital volume correlation approaches in prophylactically augmented vertebrae: Local analysis on bone and cement-bone microstructures

Combination of micro-focus computed tomography (micro-CT) in conjunction with in situ mechanical testing and digital volume correlation (DVC) can be used to access the internal deformation of materials and structures. DVC has been exploited over the past decade to measure complex deformation fields within biological tissues and bone-biomaterial systems. However, before adopting it in a clinically-relevant context (i.e. bone augmentation in vertebroplasty), the research community should focus on understanding the reliability of such method in different orthopaedic applications involving the use of biomaterials. The aim of this study was to evaluate systematic and random errors affecting the strain computed with two different DVC approaches (a global one, “ShIRT-FE”, and a local one, “DaVis-DC”) in different microstructures within augmented vertebrae, such as trabecular bone, cortical bone and cement-bone interdigitation. The results showed that systematic error was insensitive to the size of the computation sub-volume used for the DVC correlation. Conversely, the random error (which was generally the largest component of error) was lower for a 48-voxel (1872micrometer) sub-volume (64–221 microstrain for ShIRT-FE, 88–274 microstrain for DaVis-DC), than for a 16-voxel (624micrometer) sub-volume (359–1203 microstrain for ShIRT-FE, 960–1771 microstrain for DaVis-DC) for the trabecular and cement regions. Overall, the local random error did not appear to be influenced by either bone microarchitecture or presence of biomaterial. For the 48-voxel sub-volume the global approach was less sensitive to the gradients in grey-values at the cortical surface (random error below 200 microstrain), while the local approach showed errors up to 770 microstrain. Mean absolute error (MAER) and standard deviation of error (SDER) were also calculated and substantially improved when compared to recent literature for the cement-bone interface. The multipass approach for DaVis-DC further reduced the random error for the largest volume of interest. The random error did not follow any recognizable pattern with the six strain components and only ShiRT-FE seemed to produce lower random errors in the normal strains. In conclusion this study has provided, for the first time, a preliminary indication of the reliability and limitations for the application of DVC in estimating the micromechanics of bone and cement-bone interface in augmented vertebrae.

Velocity and deformation fields in the North Aegean domain, Greece, and implications for fault kinematics, derived from GPS data 1993–2009

GPS rates based on data of an extended continuous and campaign-type GPS network in the North Aegean domain are presented. The data processed for the time period 1993–2009 is used to analyze the complex kinematic and deformation fields in the North Aegean Sea and adjacent regions. The presence of slowly deforming areas is investigated. Southern Bulgaria, eastern Macedonia and Thrace move uniformly southward relative to Eurasia (1.5–3.5mm/yr). Western Macedonia, Epirus, Thessaly and Central Greece rotate rather coherently clockwise. The region comprising the islands of Limnos, Agios Efstratios and Alonnisos moves like a counterclockwise rotating slowly deforming block.The new GPS rates allow a quantification of the spatial change of strike-slip motion and locking depth along the North Aegean trough. Dextral strike-slip motion diminishes from east toward west amounting to 21.2mm/yr along the Saros basin and 12.5mm/yr south of the Chalkidiki peninsula. Less than 5mm/yr (50nstrain/yr shear strain rate) is transferred from the Sporades islands/Pelion toward Northern Evia. The locking depth is shallow for the Ganos fault and the western Saros basin (5.6–8.9km). It is deeper between the Sporades islands and Pelion (~17.7km) corresponding to a more diffuse shear zone.An elementary finite element model is applied to derive slip rates of the three main ENE–WSW to NE–SW trending dextral strike-slip faults in the North Aegean. Large-scale N–S to NNE–SSW extension in the North Aegean domain is analyzed by employing finite element and GPS based strain rate analyses. Pronounced extension (>100 nstrain) is associated with known tectonic structures (e.g., Mygdonian graben, northern Gulf of Evia). In offshore areas such as the Sporades basin the correspondence between GPS derived extension rates and active fault structures is not entirely evident. However, important constraints are provided for seismotectonic interpretations.

Rifting and strike-slip shear in central Tibet and the geometry, age and kinematics of upper crustal extension in Tibet

Abstract The youngest deformation structures on the Tibet Plateau are about NNE-trending grabens. We first combine remote-sensing structural and geomorphological studies with structural field observations and literature seismological data to study the Muga Purou rift that stretches at c . 86°E across central Tibet and highlight a complex deformation field. ENE-striking faults are dominated by sinistral strike–slip motion; NNE-striking faults have normal kinematics and outline a right-stepping en-echelon array of grabens, also suggesting sinistral strike–slip; along NW-striking fault sets, the arrangement of grabens may indicate a dextral strike–slip component. Thus, in central Tibet, rifts comprise mostly grabens connected to strike–slip fault zones or are arranged en-echelon to accommodate sinistral wrenching; overall strain geometry is constrictional, in which NNE–SSW and subvertical shortening is balanced by WNW–ESE extension. The overwhelmingly shallow earthquakes only locally outline active faults; clusters seem to trace linkage or propagation zones of know structures. The earthquake pattern, the neotectonic mapping, and the local fault–slip analyses emphasize a distributed, heterogeneous pattern of deformation within a developing regional structure and indicate that strain concentration is weak in the uppermost crust of central Tibet. Thus, the geometry of neotectonic deformation is different from that in southern Tibet. Next, we use structural and palaeomagnetic data along the Zagaya section of southern central Tibet to outline significant block rotation and sinistral strike–slip SE of the Muga Purou rift. Our analysis supports earlier interpretations of reactivation of the Bangong–Nujiang suture as a neotectonic strike–slip belt. Then, we review the existing and provide new geochronology on the onset of neotectonic deformation in Tibet and suggest that the currently active neotectonic deformation started c . 5 Ma ago. It was preceded by c . north–south shortening and c . east–west lengthening within a regime that comprises strike–slip and low-angle normal faults; these were active at c . 18–7 Ma. The c . east-striking, sinistral Damxung shear zone and the c . NE-trending Nyainqentanghla sinistral-normal detachment allow speculations about the nature of this deformation: the ductile, low-angle detachments may be part of or connect to a mid-crustal décollement layer in which the strike–slip zones root; they may be unrelated to crustal extension. Finally, we propose a kinematic model that traces neotectonic particle flow across Tibet and speculate on the origin of structural differences in southern and central Tibet. Particles accelerate and move eastwards from western Tibet. Flow lines first diverge as the plateau is widening. At c . 92°E, the flow lines start to converge and particles accelerate; this area is characterized by the appearance of the major though-going strike–slip faults of eastern-central Tibet. The flow lines turn southeastward and converge most between the Assam–Namche Barwa and Gongha syntaxes; here the particles reach their highest velocity. The flow lines diverge south of the cord between the syntaxes. This neotectonic kinematic pattern correlates well with the decade-long velocity field derived from GPS-geodesy. The difference between the structural geometries of the rifts in central and southern Tibet may be an effect of the basal shear associated with the subduction of the Indian plate. The boundary between the nearly pure extensional province of the southern Tibet and the strike–slip and normal faulting one of central Tibet runs obliquely across the Lhasa block. Published P-wave tomographic imaging showed that the distance over which Indian lithosphere has thrust under Tibet decreases from west to east; this suggests that the distinct spatial variation in the mantle structure along the collision zone is responsible for the surface distribution of rift structures in Tibet. Supplementary material: Containing supporting data is available at http://www.geolsoc.org.uk/SUP18446 .

Multi-affine registration using local polynomial expansion

In this paper, we present a non-linear (multi-affine) registration algorithm based on a local polynomial expansion model. We generalize previous work using a quadratic polynomial expansion model. Local affine models are estimated using this generalized model analytically and iteratively, and combined to a deformable registration algorithm. Experiments show that the affine parameter calculations derived from this quadratic model are more accurate than using a linear model. Experiments further indicate that the multi-affine deformable registration method can handle complex non-linear deformation fields necessary for deformable registration, and a faster convergent rate is verified from our comparison experiment.

Parameter identification for anisotropic plasticity model using digital image correlation

The basic principle of the described procedure for plastic material identification is the generation of a complex and heterogeneous deformation field, which is measured by digital image correlation (DIC) and compared to Finite Element (FE) simulations. In this paper two tests for the identification of the hardening behaviour and the yield locus of DC06 steel are compared: a uni-axial test on a perforated rectangular specimen and a bi-axial tensile test on a cruciform specimen. The work hardening of the material is assumed to be isotropic and the yield locus is modelled by the anisotropic Hill48 criterion. The identification results for the different material parameters, based on both the uni- and the bi-axial test, are discussed and show a significant agreement.

Parameter identification for anisotropic plasticity model using digital image correlation: Comparison between uni-axial and bi-axial tensile testing.

The basic principle of the described procedure for plastic material identification is the generation of a complex and heterogeneous deformation field, which is measured by digital image correlation (DIC) and compared to Finite Element (FE) simulations. In this paper two tests for the identification of the hardening behaviour and the yield locus of DC06 steel are compared: a uni-axial test on a perforated rectangular specimen and a bi axial tensile test on a cruciform specimen. The work hardening of the material is assumed to be isotropic and the yield locus is modelled by the anisotropic Hill48 criterion. The identification results for the different material parameters, based on both the uni- and the bi-axial test, are discussed and show a significant agreement.

Micro- and Nanoscale Deformation Measurement of Surface and Internal Planes via Digital Image Correlation

The digital image correlation (DIC) tech- nique is successfully applied across multiple length scales through the generation of a suitable speckle pattern at each size scale. For microscale measure- ments, a random speckle pattern of paint is created with a fine point airbrush. Nanoscale displacement resolution is achieved with a speckle pattern formed by solution deposition of fluorescent silica nanoparticles. When excited, the particles fluoresce and form a speckle pattern that can be imaged with an optical microscope. Displacements are measured on the surface and on an interior plane of transparent polymer samples with the different speckle patterns. Rigid body translation calibrations and uniaxial ten- sion experiments establish a surface displacement resolution of 1 mm over a 5� 6 mm scale field of view for the airbrushed samples and 17 nm over a 100� 100 mm scale field of view for samples with the fluorescent nanoparticle speckle. To demonstrate the capabilities of the method, we characterize the internal deforma- tion fields generated around silica microspheres em- bedded in an elastomer under tensile loading. The DIC technique enables measurement of complex deformation fields with nanoscale precision over relatively large areas, making it of particular relevance to materials that possess multiple length scales.

Fluorescent Image Correlation for Nanoscale Deformation Measurements

A fluorescence-based digital image correlation technique allows real-time measurement of nanoscale deformations using fluorescent nanoparticles. To demonstrate the capabilities of the method, the complex deformation fields generated around silica microspheres embedded in an elastomer under tensile loading are characterized. Displacement resolutions of 20 nm are obtained over a 100×100 μm field of view (see image).

Contemporary crustal deformation around the southeast borderland of the Tibetan Plateau

We derive a detailed horizontal velocity field for the southeast borderland of the Tibetan Plateau using GPS data collected from the Crustal Motion Observation Network of China between 1998 and 2004. Our results reveal a complex deformation field that indicates that the crust is fragmented into tectonic blocks of various sizes, separated by strike‐slip and transtensional faults. Most notably, the regional deformation includes 10–11 mm/yr left slip across the Xianshuihe fault, ∼7 mm/yr left slip across the Anninghe‐Zemuhe‐Xiaojiang fault zone, ∼2 mm/yr right slip across a shear zone trending northwest near the southern segment of the Lancang River fault, and ∼3 mm/yr left slip across the Lijiang fault. Deformation along the southern segment of the Red River fault appears not significant at present time. The region south and west of the Xianshuihe‐Xiaojiang fault system, whose eastward motion is resisted by the stable south China block to the east, turns from eastward to southward motion with respect to south China, resulting in clockwise rotation of its internal subblocks. Active deformation is detected across two previously unknown deformation zones: one is located ∼150 km northwest of and in parallel with the Longmenshan fault with 4–6 mm/yr right‐slip and another is continued south‐southwestward from the Xiaojiang fault abutting the Red River fault with ∼7 mm/yr left slip. While both of these zones are seismically active, the exact locations of faults responsible for such deformation are yet to be mapped by field geology. Comparing our GPS results with predictions of various models proposed for Tibetan Plateau deformation, we find that the relatively small sizes of the inferred microblocks and their rotation pattern lend support to a model with a mechanically weak lower crust experiencing distributed deformation underlying a stronger, highly fragmented upper crust.