Deformation Analysis Method Research Articles

Mixed Method for Isogeometric Analysis of Coupled Flow and Deformation in Poroelastic Media

Pressure oscillations at small time steps have been known to be an issue in poroelasticity simulations. A review of proposed approaches to overcome this problem is presented. Critical time steps are specified to alleviate this in finite element analyses. We present a mixed isogeometric formulation here with a view to assessing the results at very small time steps. Numerical studies are performed on Terzaghi’s problem and consolidation of a layered porous medium with a very low permeability layer for varying polynomial degrees, continuities across knot spans and spatial discretizations. Comparisons are made with equal order simulations.

Effect of fillers on compression loading performance of modified re-entrant honeycomb auxetic sandwich structures

The auxetic sandwich panels for structures have been designed to provide impact protection. The aim of this work is to modify an auxetic (re-entrant) honeycomb cell to reduce the stress concentrations within the cell structure, and further enhancement of this design. The auxetic structure was filled to achieve a greater energy absorbance and enhance safety applications. Analytical and elastic three-dimensional finite element approaches were used to investigate the structural strength performance. The basic model (i.e. modified re-entrant strut cell design) consisted of the honeycomb auxetic polypropylene (PP) structure sandwiched between two steel plates (known as safety panels) which were placed under static compression loading. The cell geometry and size were then modified to reduce the stress concentration zones. The structure cells were filled with silly putty and polyvinyl chloride (PVC) foam. The effect of the filling the cells on the stress concentration and energy absorbance were analysed using elastic stress and deformation analysis methods. During the stress path analysis, it was found that an increase in Young’s modulus of the filling was directly proportional to a decrease in internal stresses. It was concluded that while filling the basic model with soft materials reduced the stress concentration, but it led to a reduction in the energy absorbance capability. Further on, the lower stress produced by the enhanced could be useful to prevent significant penetration of the protective panel. Compared to similar structures of steel, auxetic foam panels have the advantage of having only a fraction of the weight and being corrosion resistant at the same time as keeping impact strength. Graphical abstract [Formula: see text]

A decoupled Arbitrary Lagrangian-Eulerian method for large deformation analysis of saturated sand

In the finite element analysis, large deformation caused by saturated sand liquefaction may lead to numerical problems owing to mesh distortion. Based on the soil–water two-phase mixing theory, the governing equations of the two-phase mixture are derived in the study. Using the operator splitting technique and the decoupled Arbitrary Lagrangian-Eulerian (ALE) frame, a decoupled ALE Finite Element Method is developed to solve the numerical problems caused by the possible mesh distortion in the liquefaction large deformation analysis. The method is applied to one-dimensional consolidation analysis and dynamic liquefaction large deformation analysis of an embankment. The results show that the method can keep the deformed mesh in a healthy state and ensure the accuracy of the numerical solutions in large deformation analysis.

A coupling model of element-based peridynamics and finite element method for elastic-plastic deformation and fracture analysis

An element-based peridynamics (EBPD) and finite element method (FEM) coupling model is proposed to solve the elastic-plastic deformation and failure problems. The FEM and EBPD are used in the boundary region and the interior elastic-plastic crack growth region, respectively. A scheme is proposed to improve the computation efficiency of EBPD by deleting the bad quality elements in the horizon of each PD node. EBPD has the non-local stress and non-local strain concepts to conveniently describe the yield stress and equivalent plastic strain, and does not have instability problems. The elastic-plastic computation framework is used in the coupling model solved by the incremental method to calculate the elastic-plastic deformation and failure process. The coupling model can calculate the elastic-plastic problem with the linear and nonlinear hardening laws. A 2D elastic-plastic crack propagation process is also simulated by the proposed coupling model.

Characterization of surface motion patterns in highly deformable soft tissue organs from dynamic MRI: An application to assess 4D bladder motion

Background and objectives: Dynamic Magnetic Resonance Imaging (MRI) may capture temporal anatomical changes in soft tissue organs with high-contrast but the obtained sequences usually suffer from limited volume coverage which makes the high-resolution reconstruction of organ shape trajectories a major challenge in temporal studies. Because of the variability of abdominal organ shapes across time and subjects, the objective of the present study is to go towards 3D dense velocity measurements to fully cover the entire surface and to extract meaningful features characterizing the observed organ deformations and enabling clinical action or decision.Methods: We present a pipeline for characterization of bladder surface dynamics during deep respiratory movements. For a compact shape representation, the reconstructed temporal volumes were first used to establish subject-specific dynamical 4D mesh sequences using the large deformation diffeomorphic metric mapping (LDDMM) framework. Then, we performed a statistical characterization of organ dynamics from mechanical parameters such as mesh elongations and distortions. Since we refer to organs as non-flat surfaces, we have also used the mean curvature change as metric to quantify surface evolution. However, the numerical computation of curvature is strongly dependant on the surface parameterization (i.e. the mesh resolution). To cope with this dependency, we employed a non-parametric method for surface deformation analysis. Independent of parameterization and minimizing the length of the geodesic curves, it stretches smoothly the surface curves towards a sphere by minimizing a Dirichlet energy. An Eulerian PDE approach is used to derive a shape descriptor from the curve-shortening flow. Intercorrelations between individuals’ motion patterns are computed using the Laplace-Beltrami Operator (LBO) eigenfunctions for spherical mapping.Results: Application to extracting characterization correlation curves for locally-controlled simulated shape trajectories demonstrates the stability of the proposed shape descriptor. Its usability was shown on MRI acquired for seven healthy participants for which the bladder was highly deformed by maximum of inspiration. As expected, the study showed that deformations occured essentially on the top lateral regions.Conclusion:Promising results were obtained, showing the organ in its 3D complexity during deformation due to strain conditions. Smooth genus-0 manifold reconstruction from sparse dynamic MRI data is employed to perform a statistical shape analysis for the determination of bladder deformation.

Evaluation of the fire performance of unprotected composite beams with fin-plate joints

PurposeThis paper aims to investigate the fire performance of composite beams when considering the hogging moment resistance of the fin-plate beam-to-girder joints including the effect of continuity of reinforcements.Design/methodology/approachExperiments on composite beams with fin-plate joints protected only at the beam ends are conducted. The test parameter is the specification of reinforcement, which affects the rotational restraint of the beam ends. In addition, a simple method for predicting the failure time of the beam using an evaluation model based on the bending moment resistance of the beam considering the hogging moment resistance of the fin-plate joint and the reinforcement is also presented.FindingsThe test results indicate that the failure time of the beam is extended by the hogging moment resistance of the joints. This is particularly noticeable when using a reinforcing bar with a large plastic deformation capability. The predicted failure times based on the evaluation method corresponded well with the test results.Originality/valueRecent studies have proposed large deformation analysis methods using FEM that can be used for fire-resistant design of beams including joints, but these cannot always be applicable in practice due to the cost and its complexity. Our method can consider the hogging moment resistance of the joint and the temperature distribution in the axial direction using a simple method without requirement of FEM.

Key group analysis based on DDA method for rock slope stability analysis

Inhomogeneity and discontinuities play a key role in resistance and behavior of rock masses. Today engineers have a wide range of methods to analyze the stability of rock slopes. Due to its simplicity and speed of evaluation, static analysis methods continue to play a special role in the stability assessment of jointed rock slopes. One of the most well-known static methods used in the stability analysis of rock slopes is the Key Block method (KBM), which is based on the key block finding and analyzing. In this method, if none of the key blocks are unstable, it implies that rock mass is stable. Occasionally, the combination of a number of stable blocks has led to formation a group of blocks that sometimes leads to instability. Therefore, the stability analysis of the jointed rock masses leads to study of groups of blocks that are potentially dangerous for the stability of a rock slope. The Key Group method (KGM), with its progressive approach, finds these critical groups and focuses the stability calculations on these groups. In order to increase the efficiency, accuracy and speed of this method and to develop it in three dimensions, it is decided to combine it with one of the numerical methods. The standard Discontinuous Deformation Analysis method (DDA) is an implicit method based on the finite element method. This is a sophisticated numerical method for modeling the quasi-static and dynamic behavior of rock block systems in discontinuous rock masses. The goal of this paper is to use of the potency of the numerical method of DDA to analyze the candidate key group. For this purpose, the DDA computer program was developed with Mathematica programming language and combined with the KGM software. The resulting package, after selecting the key group by the KGM method, proceeds to analyze it with the DDA method. Two examples solved illustrating the reasonable results and the efficiency of this developed method compared to that of the original KGM and SKGM. The results validated the proper accuracy and good performance of the procedure developed in this research.

Strain Analysis based on Numerical Simulation of Bending Deformation of Tree Branch under Distributed Load

Tree branches are deformed with large deflection under mechanical loads such as wind, rain and snow weight, and also deformed by own weights including fruits. Stress and strain distribution characteristics under loading are important information to evaluate the mechanical strength of tree branch formations. In this study, a numerical analysis method of large bending deformation was proposed and used for evaluating the deformation behavior of branch focusing on the base angle and diameter changes. The branch model was created as a curved cantilever of tapered shape with a constant elastic modulus. As the simulation results, the large bending deformation for downward under the distributed load condition reduced the bending moment applied at the base end of branch model. And the base angle for upward directions made severe bending strain on the tip side. This simulation was available to estimate the large deflection geometries of cantilever and could be used to predict the failure location on the tree branch.

Ocena pomeranja inženjerskih struktura u programskom paketu PANDA

The paper describes the assessment of the significance of the displacement of the points of the deformation structure (object) by the geodetic method of deformation analysis using the PANDA software package. According to the pre-assumed displacement and the measurement plan, the data of length measurements in two different time epochs were simulated. and the intensity and direction of deformation were assessed using the PANDA program. Within the deformation assessment, different assessment strategies were analyzed, through a one - and two - step procedure. In both cases, the expected agreement of the displacement estimate with the pre-assumed value was reached.

DDA Simulation Study on Mechanical Failure of Heterogenous Rock

Heterogeneity is an important characteristic that affects the mechanical behavior of rock. In the present work, a statistical rock mesoheterogeneity model based on the Weibull distribution function is introduced into the discontinuous deformation analysis (DDA) method to simulate the mechanical failure of heterogeneous rock, in which the general heterogeneity degree is controlled by a heterogeneity index and the mechanical property of each subblock element is randomly assigned. Brazilian disc and uniaxial compressive rectangular specimens are simulated as examples. Results show that it is more reasonable to consider the heterogeneity of elasticity properties (the elastic modulus and Poisson’s ratio) and strength properties (the tensile strength, cohesion, and friction angle) simultaneously in the heterogeneity model. It is also shown that with a larger heterogeneity index, which means a lower degree of heterogeneity, the reproducibility of the macroscopic response curves of a specimen gets better, while the exact cracking always differs but with less scattered cracks, and the global fracturing failure pattern and mode are weakly influenced by the heterogeneity. Moreover, with the increase in the heterogeneity index, the macroscopic equivalent modulus and strength get larger and approach those of a homogeneous specimen. This work indicates the importance of heterogeneity for rock mechanical behaviors including the macroscopic equivalent response and the fracturing failure. By the subblock DDA method to simulate fracturing realistically, the fracturing failure process of heterogeneous rock can be successfully reproduced, which builds good foundation for the simulation study of heterogeneous rock fracturing in practical problems, e.g., coal and rock fracturing in fluidization mining in the future.

Toppling failure analysis of rock slopes based on a three-dimensional discontinuous deformation analysis method

The present study focused on the study of the toppling failure of rock slopes using a three-dimensional discontinuous deformation analysis (3D DDA) method. The failure conditions and their related impact factors of toppling rock slopes were derived by building the corresponding mathematical models based on the limit equilibrium method (LEM), and the deficiency of the existed LEM for analysing the toppling system was pointed out. Several numerical examples, such as a single rock block of different dimensions, classical toppling rock slope model, and multiple rock blocks of different distributions, were adopted to investigate the toppling failure mechanisms under different conditions. The results showed that the 3D DDA is a very powerful numerical tool to study the failure mechanisms of toppling rock slopes and simulate the failure process of various toppling rock slopes with different distributions of structural planes inside rock mass. The controversial safety factor of the slope stability was avoided in the 3D DDA numerical simulation. Through the 3D DDA results, some more real phenomena of slope failure could also be observed and explained. For example, the slope block toppling tended to be toppling-sliding rather than pure toppling. In addition, the general laws of toppling slope failure were presented.

A method for generating a block system of coarse granular materials that strictly meet gradation requirements

The discontinuous deformation analysis (DDA) method provides unique advantages in simulating the mechanical properties of coarse granular materials. However, the DDA method cannot automatically generate numerical samples of coarse granular materials that can strictly meet the gradation requirements. Therefore, to solve this problem, a new generation method is proposed for generating a block system of coarse granular materials. First, a particle is randomly selected from the basic morphology database and randomly scaled and rotated to match the particle size requirements of the current gradation, based on the relevant requirements for laboratory tests of coarse granular materials. The accumulated particle area will enter the next gradation when it meets the area proportion requirements of the gradation, and this step is repeated gradually from the large particle size group to the small particle size group. Second, the random drop area, which has the same diameter as the coarse granular sample but a height several times that of the sample, is defined. The particles are randomly placed in this area in order of large to small particle size groups, and the requirements of nonoverlapping and noncrossing between particles or between particles and boundaries must be met. When the efficiency of random dropping is very low or even fails, it is important to keep increasing the sample height multiplier. Third, a DDA-based compaction operation is performed to obtain a stable block system with close particle contact. Fourth, a coarse granular material sample that fully meets the gradation requirements is obtained by gradually adjusting the height of the prepared sample. Finally, an example is used to demonstrate the feasibility of the proposed algorithm.

Study on failure mechanism of tunnel-type anchorage using discontinuous deformation analysis method

Tunnel-type anchorage are increasingly used in the construction of long-span suspension bridges. Numerical methods are a major means to study their bearing characteristics and failure modes. The current mainstream research method is still based on continuum mechanics, which cannot simulate the whole failure evolution process of tunnel-type anchorage-surrounding rock system. Therefore, discontinuous deformation analysis method based on discontinuous medium mechanics was used to carry out related research, comprehensively considering the influence of different rock mass quality and faults. The results show that: 1) In the case of soft rock and hard rock, the bearing capacity of the tunnel-type anchorage increases with the increase of the clamping angle, and the change in hard rock is more obvious. 2) Under the condition of soft rock, the envelope area of resistance body increases linearly with the increase of clamping angle. Because of gravity, the envelope area of the resistance body on the lower side of the tunnel-type anchorage is larger than that on the upper side. Under the four clamping angles of 2°, 4°, 6° and 8°, the envelope curves on the upper and lower sides of the tunnel-type anchorage are parallel to each other on their own sides. 3) Compared with the soft rock, the envelope areas of hard rock under the above four clamping angles are significantly increased, and the growth multiple is between 0.44 and 0.87. But in this case, the envelope area has no obvious change with the increase of clamping angle. 4) In soft rock, the envelope shape of the resistance body is a curve that is convex toward the outside of the anchorage; when it is hard rock, it tends to be a curve that is concave toward the inside of the anchorage. 5) Under the condition of hard rock, the integral deformation of surrounding rock on both sides of the tunnel-type anchorage is more obvious, which means that the load transfer range is wider and the clamping effect is more obvious. 6) The ultimate bearing capacity increases with the increase of the clamping angle, and shows a linear change trend. 7) Faults significantly weaken the bearing capacity of tunnel-type anchorage, but the impact of faults at different angles is slightly different. Finally, the whole process of deformation and failure of surrounding rock is intuitively displayed, and the load transfer mechanism can be peeped from it.

CPU-accelerated explicit three-dimensional discontinuous deformation analysis with cloud computing

Prompt feedback based on a numerical simulation, such as discontinuous deformation analysis, plays an important role in digitalized geotechnical engineering. Cloud computing also prevails owing its flexible configuration and computational power. This study proposes an explicit three-dimensional discontinuous deformation analysis method using explicit contact forces that can circumvent the difficulty of not converging the open–close iteration and the inefficiency of classic implicit discontinuous deformation analysis. The serial code is ready to be parallelized by relocating the postjudgment of the contact status and using LDL decomposition to solve fixed-size linear equations. We propose herein the block-wise parallelization concept, which significantly simplifies the work of parallel computation. No modification under the block level is needed. In addition, one can realize parallel computing by adding just three lines of the new code with the help of OpenMP. A simple virtual cloud machine is used to run the program to validate the improved efficiency of the newly developed algorithms. A 3.5 speedup ratio is achieved with four CPU cores and eight processors.

Stability of caisson-type breakwater subjected to strong hydrodynamic impacts using discontinuous deformation analysis method

A numerical study using the Discontinuous Deformation Analysis (DDA) method is proposed to analyze the effect of the caisson sliding subjected to a hydrodynamic loading in the stability of the rear side of the caisson-type breakwater. The study takes into account the slope inclination of the breakwater as well as the contact between the armour units constituting the shoreward of the breakwater, where the contact stresses are imposed through a penalty method. A dimensionless displacement parameter, [Formula: see text], is defined to investigate the instability of armor units. The results of the simulation show that the shape of the armour units plays an important role in the stability of the breakwater, where the tetrapods and the acropods give better stability than the cubic shapes, with a clear superiority of the tetrapods. They also show that the reduction in the slope clearly contributes to the stability of caisson up to a slope of 1: 2, but below this ratio of 1: 2 this stability is no longer obvious. Furthermore, a new relation of the displacement of the armour units according to the slope is established.

Non-invasive deformation metrology using subspace analysis in digital holographic interferometry

For non-invasive precision measurement of deformation using digital holographic interferometry (DHI), reliable estimation of interference phase from complex fringe signal is required. This article introduces a method for estimation of interference phase in DHI. The proposed method is based on computing roots of a frequency estimation function obtained from noise subspace of the fringe signal. The main advantage of the proposed method is robustness against severe noise. In addition, the method also offers the capability of direct phase derivative estimation. The performance of the proposed method is validated using numerical simulations. Our simulation results show that even for signal to noise ratio as low as −5 dB, the proposed method offers root mean square errors of less than 1 radian for phase retrieval. The practical utility of the method for non-invasive deformation analysis is demonstrated using experimental results in DHI.

Techniques for Progressive Failure Simulation of Hard Brittle Surrounding Rockmass: Taking the URL Test Tunnel as an Example

Accurate simulation of the failure process of hard brittle surrounding rockmass is very important for the analysis and control of the structural stability in deep underground engineering. In order to simulate the progressive failure process of the hard brittle surrounding rockmass, a continuous discontinuous deformation analysis method that couples the finite element and discrete element is adopted. Taking the URL test tunnel in Canada as an engineering case, the constitutive model of the contact considering the effects of cohesion weakening and friction strengthening is applied, and the 2D approximation to 3D excavation by applying elastic modulus reduction technology is adopted to simulate the range and depth of crack growth of the surrounding rockmass. Then, the comparison between simulated results and on-site monitoring results is performed, which shows good consistency. At the same time, the key factors in the numerical simulation of progressive failure in hard brittle rockmass are identified, including the number of elements, excavation effects, and constitutive models. The results show that the constitutive model determines the basic form of crack propagation, but in order to accurately simulate the progressive propagation of cracks, the number of elements must be sufficient enough and the effects of 3D excavation must be considered. The analysis accurately simulates the progressive failure characteristics of hard brittle surrounding rockmass under high stress, achieving the purpose of reasonably grasping the degree of damage to the surrounding rockmass, and provides technical reference and support on how to accurately simulate the failure of hard brittle surrounding rockmass using the finite discrete element method.

A bound water model for numerical simulation of SWCC in the wide suction range based on DDA

In this study, Discontinuous Deformation Analysis (DDA) method is extended to simulate Soil-Water Characteristic Curve (SWCC) by considering both capillary water and bound water at the micro-scale. First, a simple and practical bound water model is proposed and incorporated into DDA program to simulate SWCC in the high suction range. Then, to prove the availability of the developed program, the extended DDA is used to simulate the SWCCs of two types of fine sand with kaolin clay in a wide suction range. The simulation results agree with the experimental results, which demonstrate that the extended DDA is an alternative method for simulating and analyzing SWCC of both cohesionless soil and cohesive soil. Finally, one of the influential factors specific surface area is theoretically analyzed. This study provides an approach to simulate the matric suction of unsaturated soil, and the extended DDA could be a potential tool for unsaturated soil research.

Application of the HF, DRA and DCDA technologies for in situ stress determination in Iron Quadrangle rock masses

ABSTRACT This study presents an unprecedented campaign of measurements (magnitudes and orientations) of the in situ stresses in itabirite rocks of the Brazilian Iron Quadrangle region using the hydraulic fracturing (HF), deformation rate analysis (DRA) and diametrical core deformation analysis (DCDA) methods. The previous studies of this rock mass consider estimated values of k, and the practice of using in situ stress tests to support geotechnical analyses of the rock mass of this region has not been adopted. The study site is located at a depth of up to 400 m around a pit. The rock mass under study shows the presence of different geological structures, which made performing the tests difficult. The DRA results show a marked difference compared to the HF and DCDA results; the horizontal stresses were greater than the vertical stresses, which is a finding that may occur due to local geodynamic influences. The results contribute to the understanding of the strains and stresses induced by mining activities in the Brazilian Iron Quadrangle. For a better determination of the regional in situ stresses in the rock mass of the Brazilian Iron Quadrangle, new HF tests, as well as hydraulic testing of pre-existing fractures are recommended.

Large deformation finite element analyses in TBM tunnel excavation: CEL and auto-remeshing approach

Analyzing tunnel excavation behavior involves large deformation issues. For this reason, large deformation analysis method is required to rigorously investigate the actual effect of excavation on surrounding ground. Two major numerical approaches capable of considering large deformations are applied to investigating the effect of tunnel boring machine excavation: coupled Eulerian-Lagrangian (CEL) and the automatic remeshing after small strain approach. The theoretical basis and application of the methods will be discussed before their relative performance is evaluated through the ground response due to TBM excavation. The ground response will be quantified by estimating the range of the excavation damaged zone (EDZ). By comparing the results, the range of the size of the EDZ will be suggested along the vertical and horizontal direction along the TBM advancement. Based on the computed results, it was found that the size of EDZ around the excavation surface and the tendencies was in good agreement among the two methods. Numerical results clearly show that the size of the EDZ around the tunnel tends to be bigger for harder rocks. The size of the EDZ is found to be direct proportional to the tunnel diameter, whereas the depth of the tunnel is inversely proportional due to higher confinement stress around the excavation surface.