Fine-scale Deformation Research Articles

Effect of stress unloading rate on fine-scale deformation mechanism of rock under high osmotic pressure

To explore the influence of the working face excavation rate on the rock deformation mechanism and seepage characteristics, deformation and seepage tests of sandstone under different loading and unloading stress paths, such as constant axial pressure unloading confining pressure and loading axial pressure unloading confining pressure, were carried out. Particle Flow Code in 3 Dimensions (PFC3D) and Python were used to realize fluid-solid coupling, and numerical simulation calculations were performed along the test path to analyze the influence of the unloading rate on the fine-scale deformation mechanism and permeability characteristics of sandstone, and the relationship between crack type and permeability was obtained. A sandstone fracture mechanics model is established to analyze the stress concentration degree at the end of the branch crack of the test path. The results show that the rate of confining pressure unloading is inversely proportional to the strain. Additionally, permeability correlates with the principal stress difference in an exponential manner. Interestingly, the sensitivity of permeability to stress shows an inverse trend with the unloading rate of confining pressure. Furthermore, there exists a linear relationship between permeability and the number of cracks. During the unloading process, tensile cracks predominate, and the propagation of shear cracks lags behind that of tensile cracks. The proportion of tensile cracks decreases with the increase of the unloading rate when the axial pressure is unchanged but increases when axial pressure is added, resulting in axial compression deformation and expansion deformation along the unloading direction. These research outcomes offer theoretical insights for the prudent selection of mining rates, and they hold significant implications for mitigating water inrush disasters in deep mining operations.

Multiscale modelling of sandwich structured composites using direct FE2

In finite element analyses, composite laminates are often homogenised and modelled using beam and plate elements for computational efficiency. Aside from difficulties in deriving homogenised properties for nonlinear materials and the loss in fine-scale deformation details, such structural elements are notoriously inaccurate for laminates comprising plies of distinctly different in-plane stiffnesses, notably, sandwich structured composites. A multiscale layerwise beam model is proposed to address these shortcomings. The model is based on the Timoshenko-Ehrenfest beam theory with layerwise kinematics incorporated to capture the key deformation modes of bending and transverse shear, and implemented using Direct FE2 – a versatile computational homogenisation scheme. Beyond homogenisation for the structural elements, Direct FE2 also captures deformation mechanisms at the mesoscale. More importantly, it is readily implemented using available functions in commercial FE codes, allowing for ease of adoption. A foam core sandwich structure is modelled to demonstrate that the proposed approach leads to macroscale responses and resolution to the mesoscale deformations that are almost identical to that of finely meshed solid element models, while taking only 23% of the computation time.

Automated identification of slip system activity fields from digital image correlation data

Crystallographic slip system identification methods are widely employed to characterize the fine scale deformation of metals. While powerful, they usually rely on the occurrence of discrete slip bands with clear slip traces and can struggle when complex mechanisms such as cross-slip, curved slip, diffuse slip and/or intersecting slip occur. This paper proposes a novel slip system identification framework, termed SSLIP (for Slip Systems based Local Identification of Plasticity), in which the measured displacement gradient fields (from Digital Image Correlation) are locally matched to the kinematics of one or multiple combined theoretical slip systems, based on the measured crystal orientations. To identify the amount of slip that conforms to the measured kinematics, an optimization problem is solved for every datapoint individually, resulting in a slip activity field for every considered slip system. The identification framework is demonstrated and validated on an HCP virtual experiment, for discrete and diffuse slip, incorporating 24 slip systems. Experimental case studies on FCC and BCC metals show how full-field identification of discrete slip, diffuse slip and cross-slip becomes feasible, even when considering 48 slip systems for BCC. Moreover, the methodology is extended into a dedicated cross-slip identification method, which directly yields the orientation of the local slip plane trace orientation, purely based on the measured kinematics and on one or two chosen slip directions. For even more challenging cases revealing a persistent uncertainty in the slip identification, a two-step identification approach can be employed, as is demonstrated on a highly challenging HCP virtual experiment.

Difficulty-aware hierarchical convolutional neural networks for deformable registration of brain MR images.

The aim of deformable brain image registration is to align anatomical structures, which can potentially vary with large and complex deformations. Anatomical structures vary in size and shape, requiring the registration algorithm to estimate deformation fields at various degrees of complexity. Here, we present a difficulty-aware model based on an attention mechanism to automatically identify hard-to-register regions, allowing better estimation of large complex deformations. The difficulty-aware model is incorporated into a cascaded neural network consisting of three sub-networks to fully leverage both global and local contextual information for effective registration. The first sub-network is trained at the image level to predict a coarse-scale deformation field, which is then used for initializing the subsequent sub-network. The next two sub-networks progressively optimize at the patch level with different resolutions to predict a fine-scale deformation field. Embedding difficulty-aware learning into the hierarchical neural network allows harder patches to be identified in the deeper sub-networks at higher resolutions for refining the deformation field. Experiments conducted on four public datasets validate that our method achieves promising registration accuracy with better preservation of topology, compared with state-of-the-art registration methods.

A trivariate T-spline based framework for modeling heterogeneous solids

We present a robust framework to conduct material modeling suitable for continuously varying materials with a local material composition control. The geometry and attribute representations are defined using two trivariate T-splines based on the same parametric domain. The optimization process decreases the mismatch of geometry and attribute between the input tetrahedral mesh and the trivariate T-splines, which consists of two alternately executed procedures: progressive fitting and octree-based adaptive refinement. Control points are dynamically updated without constructing large matrices as used in finite element method. To improve computational efficiency of the optimization, adaptive refinement is carried out only in those regions that undergo fine-scale deformation and an octree-based subdivision is directly used to insert control points in the parametric domain. The proposed framework was implemented on medical and synthetic examples to show the robustness of the material modeling framework. The comparison between trivariate T-splines with adaptive refinement and trivariate NURBS with uniform refinement demonstrates the computational efficiency.

Influence of strain on the formation of cold-rolling and grain growth textures of an equiatomic HfZrTiTaNb refractory high entropy alloy

The effect of cold-rolling strain on the evolution of deformation and grain growth textures in an equiatomic HfZrTiTaNb refractory high entropy alloy (RHEA) was investigated. For this purpose, the development of microstructure and texture was compared in 50% and 90% cold-rolled materials. The development of deformation microstructure was accompanied by the formation of extensive deformation heterogeneities. The 90% cold-rolled material showed ultrafine lamellar regions as well as regions severely fragmented by the fine scale deformation heterogeneities. The 50% cold-rolled material showed dominant ND-fiber (ND//<111>), while the 90% cold-rolled material showed presence of both RD (RD//<110>) and ND-fiber components. Profuse deformation heterogeneities presumably weakened the deformation texture considerably. The annealing texture of the 50% and 90% cold-rolled material showed stronger {111}<110> component. Comparison of the annealing texture of the 50% and 90% cold-rolled materials with other BCC HEA phases indicated much weaker texture. The annealing texture of the RHEA was not significantly strengthened by increasing cold-rolling strain, presumably due to the high density of deformation heterogeneities in the cold-rolled microstructure. Thus, deformation heterogeneities significantly influenced the formation of cold-rolling and annealing textures of the equiatomic HfZrTiTaNb RHEA.

Multi-view Performance Capture of Surface Details

This paper presents a novel approach to recover true fine surface detail of deforming meshes reconstructed from multi-view video. Template-based methods for performance capture usually produce a coarse-to-medium scale detail 4D surface reconstruction which does not contain the real high-frequency geometric detail present in the original video footage. Fine scale deformation is often incorporated in a second pass by using stereo constraints, features, or shading-based refinement. In this paper, we propose an alternative solution to this second stage by formulating dense dynamic surface reconstruction as a global optimization problem of the densely deforming surface. Our main contribution is an implicit representation of a deformable mesh that uses a set of Gaussian functions on the surface to represent the initial coarse mesh, and a set of Gaussians for the images to represent the original captured multi-view images. We effectively find the fine scale deformations for all mesh vertices, which maximize photo-temporal-consistency, by densely optimizing our model-to-image consistency energy on all vertex positions. Our formulation yields a smooth closed form energy with implicit occlusion handling and analytic derivatives. Furthermore, it does not require error-prone correspondence finding or discrete sampling of surface displacement values. We demonstrate our approach on a variety of datasets of human subjects wearing loose clothing and performing different motions. We qualitatively and quantitatively demonstrate that our technique successfully reproduces finer detail than the input baseline geometry.

A framework for residual-based stabilization of incompressible finite elasticity: Stabilized formulations and [formula omitted] methods for linear triangles and tetrahedra

A new Variational Multiscale framework for finite strain incompressible elasticity is presented. Significant contributions in this work are: (i) a systematic derivation of multiscale formulations that include the classical F¯ method as a particular subclass, (ii) an error estimation procedure for nonlinear elasticity that emanates naturally from within the present multiscale framework, and (iii) robust performance of linear triangular and tetrahedral elements for modeling nearly incompressible materials in the finite strain range. When viewed from the Variational Multiscale perspective, the classical F¯ method is shown to include only a volumetric or diagonal fine-scale deformation gradient while the proposed formulation includes the full spectrum of inter-scale coupling effects. Also, the error estimation procedure readily carries over from developments conducted for small strain linear problems. The formulation is presented first in the context of displacement-based methods and then extended to more general mixed methods accommodating arbitrary combinations of displacement–pressure interpolations. An extensive set of benchmark problems is investigated to show the performance of the method for a variety of hyperelastic materials exhibiting incompressible response.

Vector-field-based deformations for three-dimensional texture synthesis

A major drawback of conventional approaches to three-dimensional (3D) texture synthesis is the lack of fine-scale deformations in the synthesised results. This study presents a novel vector-field-based deformation approach to synthesising 3D textures with fine-scale deformations. The pre-process of this approach constructs feature vectors and similarity sets of voxels from an input 3D exemplar to accelerate neighbourhood matching. The synthesis process first introduces 3D vector fields for deforming synthesised results. A 3D pyramid synthesis technique integrated with 3D vector fields is then used to synthesise 3D textures. The proposed approach uses only eight neighbourhoods of each voxel for neighbourhood matching. Experimental results show that the proposed approach efficiently synthesises 3D textures with fine-scale deformations.

Coarse-to-Fine Segmentation and Tracking Using Sobolev Active Contours

Recently proposed Sobolev active contours introduced a new paradigm for minimizing energies defined on curves by changing the traditional cost of perturbing a curve and thereby redefining their gradients. Sobolev active contours evolve more globally and are less attracted to certain intermediate local minima than traditional active contours, and it is based on a well-structured Riemannian metric. In this paper, we analyze Sobolev active contours using scale-space analysis in order to understand their evolution across different scales. This analysis shows an extremely important and useful behavior of Sobolev contours, namely, that they move successively from coarse to increasingly finer scale motions in a continuous manner. This property illustrates that one justification for using the Sobolev technique is for applications where coarse-scale deformations are preferred over fine scale deformations. Along with other properties to be discussed, the coarse-to-fine observation reveals that Sobolev active contours are, in particular, ideally suited for tracking algorithms that use active contours. We will also justify our assertion that the Sobolev metric should be used over the traditional metric for active contours in tracking problems by experimentally showing how a variety of active contour based tracking methods can be significantly improved merely by evolving the active contour according to the Sobolev method.

Microstructure and microtexture of highly cold-rolled commercially pure titanium

The microstructure and texture evolution of a commercially pure titanium sheet during cold-rolling is investigated in detail by X-ray diffraction and by orientation imaging in the FEG-SEM and in the TEM. The experimental data are compared with simulation results obtained by a viscoplastic self-consistent model. The aim of this work is to provide with a detailed description of the fine scale deformation structures obtained after 80% cold-rolling and to identify the mechanisms by which these structures form. Such a detailed investigation is nowadays possible thanks to high spatial resolution orientation imaging techniques. This work highlights the important role of mechanical twinning as one of the grain fragmentation mechanisms. The microstructure obtained after 80% thickness reduction can be separated into two distinct parts: 85 vol.% of the material is fine-subdivided with highly misoriented sub-micron features and the others 15 vol.% consist in lamellar structures formed in grains initially oriented in a particular region of orientation space, which have not undergone twinning. The influence of these structures on recrystallization mechanisms are also discussed.

A hierarchical multi-physics model for design of high toughness steels

In support of the computational design of high toughness steels as hierarchically structured materials, a multiscale, multiphysics methodology is developed for a `ductile fracture simulator.' At the nanometer scale, the method unites continuum mechanics with quantum physics, using first-principles calculations to predict the force-distance laws for interfacial separation with both normal and plastic sliding components. The predicted adhesion behavior is applied to the description of interfacial decohesion for both micron-scale primary inclusions governing primary void formation and submicron-scale secondary particles governing microvoid-based shear localization that accelerates primary void coalescence. Fine scale deformation is described by a `Particle Dynamics' method that extends the framework of molecular dynamics to multi-atom aggregates. This is combined with other meshfree and finite-element methods in two-level cell modeling to provide a hierarchical constitutive model for crack advance, combining conventional plasticity, microstructural damage, strain gradient effects and transformation plasticity from dispersed metastable austenite. Detailed results of a parallel experimental study of a commercial steel are used to calibrate the model at multiple scales. An initial application provides a Toughness-Strength-Adhesion diagram defining the relation among alloy strength, inclusion adhesion energy and fracture toughness as an aid to microstructural design. The analysis of this paper introduces an approach of creative steel design that can be stated as the exploration of the effective connections among the five key-components: elements selection, process design, micro/nanostructure optimization, desirable properties and industrial performance by virtue of innovations and inventions.