Large Deformation Problems Research Articles

Philosophical Reflection on the Problem of Large Deformation of Weak Surrounding Rocks under High Ground Stress

Philosophical Reflection on the Problem of Large Deformation of Weak Surrounding Rocks under High Ground Stress

Modeling Brittle Failure in Rock Slopes Using Semi‐Lagrangian Nonlocal General Particle Dynamics

ABSTRACTThe nonlocal general particle dynamics (NGPD) has been successfully developed to model crack propagation and large deformation problems. In this paper, the semi‐Lagrangian nonlocal general particle dynamics (SL‐NGPD) is proposed to solve brittle failure in rock slopes. In SL‐NGPD, the interaction between particles due to deformation is calculated in the initial configuration, while the friction contact interaction from discontinuities is calculated in the current configuration. The Van der Waals force model is utilized for friction contact. The bond‐level energy‐based failure criterion is developed to predict tensile/compressive‐shear mix‐mode cracks. The artificial viscosity and damage correction are used to enhance the numerical stability and accuracy when modeling brittle failure. The SL‐NGPD paradigm is numerically implemented through adaptive dynamic relaxation and predictor–corrector schemes for stable numerical solutions. The stability and accuracy of SL‐NGPD are verified by simulating compression tests. Thereafter, the crack coalescence patterns of double‐flaw specimens are investigated to understand the triggering failure mechanism of jointed rock slopes. Finally, the progressive failure process of the rock slope with step‐path joints is simulated to demonstrate its validity and robustness in modeling brittle failure in rockslides. The numerical results illustrate that the proposed SL‐NGPD is promising and performant for analyzing brittle failure problems in geotechnical engineering.

Nonlinear analysis of three-dimensional hyperelastic problems using radial point interpolation method

Hyperelastic materials are primarily common in real life as well as in industry applications, and studying this kind of material is still an active research area. Naturally, the characteristic of hyperelastic material will be expressed when it undergoes large deformation, so the geometrical nonlinear effect should be considered. To analyze the behavior of hyperelastic material, the Neo-Hookean model is imposed in this study because of its simplicity. The model shows the nonlinear behavior when the deformation becomes large due to the nonlinear displacement-strain relation. This constitutive relation also gives a good correlation with experimental data. This study performs a meshless method, namely the radial point interpolation method (RPIM), to analyze the nonlinear behavior of Neo-Hookean hyperelastic material under a finite deformation state in three-dimensional space. The standard Newton-Raphson technique is applied to obtain the nonlinear solutions. Unlike mesh-based approaches, the meshless method shows its advantages in large deformation problems due to its mesh independence. In this paper, the numerical results of three-dimensional problems that undergo large deformation will be calculated and validated with solutions derived from previous studies. By investigating the obtained results, the superior ability of RPIM in hyperelastic problems can be proved.

Finite element analysis of large deformation for progressive failure of soil based on Cosserat continuum theory

The large deformation accompanied by strain softening and strain localization of the material is usually encountered in geotechnical engineering. Integrating the RITSS method and the Cosserat continuum theory, a large deformation Cosserat-RITSS finite element method is developed to tackle this issue. Based on the second development interfaces of UEL and SDVINI offered by the finite element software ABAQUS, the Cosserat-RITSS method adopting the MUEM interpolation and mapping method is realized automatically and used to simulate the problem of progressive failure and large deformation characterized by strain localization. The accuracy and effectiveness of the proposed method are verified by the comparison of the small deformation and the large deformation analysis of the penetration process of a rigid strip foundation. Further, the Cosserat-RITSS method is used to analyze the large deformation of a retaining wall resisting on the soil with non-associated plastic flow and strain-softening properties. Compared with the classical RITSS method, it is demonstrated that the proposed method has better performancy of simulating large deformation and overcoming the pathological mesh-dependent problem usually suffered in the classical FEA of large deformation accompanied by strain localization.

Implementation of the Zienkiewicz–Pande Model into a Four‐Dimensional Lattice Spring Model for Plasticity and Fracture

ABSTRACTPlasticity and fracture problems have always been hot topics in numerical methods. In this work, a universal implementation procedure for the elasto‐plastic constitutive model is developed in the four‐dimensional lattice spring model (4D‐LSM), in which the Jaumann stress rate is incorporated to exclude the influence of the rigid rotation in the particle stress, expanding the ability of 4D‐LSM to deal with large elastic deformation problems by its own to large plastic deformation problems. As an example, the Zienkiewicz–Pande (ZP) constitutive model is implemented. Several numerical examples are carried out to check the performance of the implemented model. Through a comparison with analytical solutions, available experimental data, and other numerical results, the stability of the developed plastic framework and the correctness of the stress calculation scheme are verified. Meanwhile, numerical results show that the developed code is capable of solving elasto‐plastic large deformation problems. With the advantage of 4D‐LSM in handling fracture problems, the ability of the embedded model to solve plastic fracture problems is verified with a simple maximum deformation failure criterion.

Large deformation problem of hyperbolic shallow shells with bimodular effect: A perturbation‐variation method

AbstractAs an important analytical method, the perturbation‐variation method combines the advantages of perturbation method and variational method, and is widely used for the solution of nonlinear plate and shell problems. In this study, the perturbation‐variation method is used to solve the large deformation problem of a flexible hyperbolic thin shallow shells with different moduli in tension and compression (bimodular effect). First, we establish the governing equations expressed in terms of three displacement components, in which the bimodular effect of materials is considered in physical equations and the large deformation of shell is considered in geometrical equations. Next, we use the perturbation‐variation method to solve the governing equations established, obtaining the perturbation‐variation solution up to third‐order. During the application of the method, the displacements are expressed into perturbation formulas of all levels first, and the unknown constants and functions in the perturbation formulas are determined by the extreme value conditions of the functional established (variational principle), hence the perturbation‐variation method gets its name from this practice. The numerical results from FEM basically agree with the perturbation‐variation solution obtained. The method proposed may be extended into the solution of similar partial differential equations established in applied fields.

A continuous-discontinuous coupling computational method for multi-material mixtures

Considering the important role of particle-reinforced composites (PRCs), and to accurately assess the mechanical properties of PRC with arbitrarily complex internal structures, this paper proposes a new continuous-discontinuous coupled computational method, i.e., the multi-material integrated analysis (MIA) method, by combining the advantages of the discontinuous deformation analysis (DDA) method, the numerical manifold method (NMM), and the meshless method, for the continuous-discontinuous dual state of this kind of materials when they are subjected to forces. The core idea of this method is by establishing a single physical cover (PC) on each particle and defining a unified and piecewise approximation function over it to achieve displacement coordination between the particles and the matrix. In this model, the particles can maintain the contact and separation characteristics like the blocks, while the matrix is able to achieve the bonding function by overlapping different covers. Two numerical integration schemes, namely single-point Gaussian integration and Monte Carlo integration, are proposed to address the integration issues in stiffness matrix calculations. Meanwhile by considering the similarity between NMM and meshless method interpolation function construction, this paper combines circular coverage and 0th-order moving least squares to construct the interpolation function to form the displacement approximation function for the whole solution space. Moreover, the method of lattice retrieval (also Nearest Neighbor Search, NNS) is invoked for particle contact determination to improve the efficiency of contact and coverage relationship determination. The validity of the model is verified by taking asphalt mixture, a typical PRC, as a demonstrative case study. The results show that the MIA method solves the one-sided problem that the existing algorithms usually only consider the continuous or discontinuous properties of PRC, and provides a new method for comprehensively analyzing the micromechanical response of PRC and solving its large deformation problem.

Nonlinear NMM analysis for large deformation and contact problems: Using full strain-rotation decomposition algorithm and augmented Lagrangian method enhanced open-closed iteration

Nonlinear analysis deals with problems that involve large displacements, strains, rotations, and contact problems. Accurate results can be obtained by choosing a reasonable method for decomposing strain and rotation to avoid errors and ensure the correct contact force. A novel full strain-rotation (S-R) decomposition and an augmented Lagrangian enhanced contact model are established within the numerical manifold method (NMM) framework. Limitations in simplified S-R NMM are overcome using our redesigned resolution procedure. A new method has been applied to analyse beams with large deflections, block columns under compression, block sliding, rock falling, and semi-ring contact with block problems. Promising results from the analysis indicate that proposed method is more accurate and effective in theory and numerically than prior approaches when resolving contact problems and large deformations.

MA-VoxelMorph: Multi-scale attention-based VoxelMorph for nonrigid registration of thoracoabdominal CT images

This paper aims to develop a nonrigid registration method of preoperative and intraoperative thoracoabdominal CT images in computer-assisted interventional surgeries for accurate tumor localization and tissue visualization enhancement. However, fine structure registration of complex thoracoabdominal organs and large deformation registration caused by respiratory motion is challenging. To deal with this problem, we propose a 3D multi-scale attention VoxelMorph (MA-VoxelMorph) registration network. To alleviate the large deformation problem, a multi-scale axial attention mechanism is utilized by using a residual dilated pyramid pooling for multi-scale feature extraction, and position-aware axial attention for long-distance dependencies between pixels capture. To further improve the large deformation and fine structure registration results, a multi-scale context channel attention mechanism is employed utilizing content information via adjacent encoding layers. Our method was evaluated on four public lung datasets (DIR-Lab dataset, Creatis dataset, Learn2Reg dataset, OASIS dataset) and a local dataset. Results proved that the proposed method achieved better registration performance than current state-of-the-art methods, especially in handling the registration of large deformations and fine structures. It also proved to be fast in 3D image registration, using about 1.5 s, and faster than most methods. Qualitative and quantitative assessments proved that the proposed MA-VoxelMorph has the potential to realize precise and fast tumor localization in clinical interventional surgeries.

Large deformation problems arising from deep excavation in silt strata: A case study in Shenzhen, China

Deep excavations in silt strata can lead to large deformation problems, posing risks to both the excavation and adjacent structures. This study combines field monitoring with numerical simulation to investigate the underlying mechanisms and key aspects associated with large deformation problems induced by deep excavation in silt strata in Shenzhen, China. The monitoring results reveal that, due to the weak property and creep effect of the silt strata, the maximum wall deflection in the first excavated section (Section 1) exceeds its controlled value at more than 93% of measurement points, reaching a peak value of 137.46 mm. Notably, the deformation exhibits prolonged development characteristics, with the diaphragm wall deflections contributing to 39% of the overall deformation magnitude during the construction of the base slab. Subsequently, numerical simulations are carried out to analyze and assess the primary factors influencing excavation-induced deformations, following the observation of large deformations. The simulations indicate that the low strength of the silt soil is a pivotal factor that results in significant deformations. Furthermore, the flexural stiffness of the diaphragm walls exerts a notable influence on the development of deformations. To address these concerns, an optimization study of potential treatment measures was performed during the subsequent excavation of Section 2. The combined treatment approach, which comprises the reinforcement of the silt layer within the excavation and the increase in the thickness of the diaphragm walls, has been demonstrated to offer an economically superior solution for the handling of thick silt strata. This approach has the effect of reducing the lateral wall displacement by 83.1% and the ground settlement by 70.8%, thereby ensuring the safe construction of the deep excavation.

Anchoring mechanical characteristics of Ductile-Expansion bolt

The application of ductile rock bolts has been a crucial method for solving the problems of large deformations, energy absorption and stability control issues in deep rock masses. To study the anchoring mechanism of the key expansive structure, this paper proposes a novel type of bolt — the Ductile-Expansion bolt, and conducts research on anchoring mechanics, energy absorption characteristics, and failure modes of the bolt. In addition, this paper defines the concept of load-volume ratio of metal rock bolts and proves the Ductile-Expansion bolt is capable of better improving the unit volume bearing capacity of the bolt material. Furthermore, laboratory and field tests verify the Ductile-Expansion bolt had better anchoring effect than the traditional rebar bolt, with the expansion structure favorably enhancing the ductility and energy absorption performance of the bolt. Finally, this paper microscopically analyzes the crack propagation and distribution morphology of the bolts by establishing a 3D coupled numerical model based on FDM-DEM. Numerical results illustrate the interface at the variable diameter of the Ductile-Expansion bolt serves as the transition zone between high and low stress levels. The expansion structure can impose radial compression on the medium around the bolt, which can improve the bolt anchorage performance.

Comparison of elements and state-variable transfer methods for quasi-incompressible material behaviour in the particle finite element method

AbstractThe Particle Finite Element Method (PFEM) is attractive for the simulation of large deformation problems, e.g. in free-surface fluid flows, fluid–structure interaction and in solid mechanics for geotechnical engineering and production processes. During cutting, forming or melting of metal, quasi-incompressible material behaviour is often considered. To circumvent the associated volumetric locking in finite element simulations, different approaches have been proposed in the literature and a stabilised low-order mixed formulation (P1P1) is state-of-the-art. The present paper compares the established mixed formulation with a higher order pure displacement element (TRI6) under 2d plane strain conditions. The TRI6 element requires specialized handling, involving the deletion and re-addition of edge-mid-nodes during triangulation remeshing. The robustness of both element formulations is analysed along with different state-variable transfer schemes, which are not yet widely discussed in the literature. The influence of the stabilisation factor in the P1P1 element formulation is investigated, and an equation linking this factor to the Poisson ratio for hyperelastic materials is proposed.

Implementation of the non-reflection boundary for the seismic response analysis in the framework of non-local general particle dynamics

A thorough understanding of the seismic response of geotechnical structures has always been an aspiration for all engineers. Recently, the non-local general particle dynamics (NLGPD), which considers the variation of material density, has exhibited excellent promise in modelling extremely large deformation and dynamic problems. To extend the capacity of NLGPD to carry out seismic response analysis, four non-reflection boundaries are newly added in the framework of NLGPD in this paper. The viscous boundary allows wave energy to be absorbed by dashpot, in which a stress input method is proposed to input the seismic motion. The viscous-spring boundary can capture the elasticity recovery ability of the far-field medium. The free-field boundary achieves the free-field motion at lateral boundaries in the process of absorbing wave, and the corresponding relation between the points of the main model and the free-field column is determined. The static-dynamic unified boundary is introduced to model the transformation process from fixed boundary conditions in a static state to free field boundary conditions in dynamic analysis. Several representative numerical examples are solved to validate the feasibility of the proposed method. The numerical results show that the NLGPD method provides robustness and broad applicability for the seismic response analysis.

General particle dynamics: On the correlation of nonlocal and local theories for large deformation problems

This paper presents a detailed investigation on the General Particle Dynamics (GPD) method and its implications for addressing challenges in large deformation mechanics and fracture modeling. The GPD method integrates nonlocal interactions and nonlocal differential operators to overcome limitations of classical continuum mechanics in capturing long-range interactions and material behaviors under extreme deformation conditions. Through a systematic examination of the physical and mathematical foundations of GPD, including its governing equations and constitutive relations, we elucidate the robust and applicability of the proposed method in simulating complex deformation phenomena. Furthermore, the relationships among GPD, conventional mechanical theories (Smoothed Particle Hydrodynamics), nonlocal theory (Peridynamics) and Molecular Dynamic theories are discussed. Numerical examples related to large deformation and fracture problems are tested to verify the ability of the proposed method. The numerical results show that GPD inherits the advantages of the classical method and also has its unique properties in solid fracture mechanics and large deformation problems, making it a promising approach in computational mechanics.

Research on stress field inversion and large deformation level determination of super deep buried soft rock tunnel

Understanding the characteristics and distribution patterns of the initial geo-stress field in tunnels is of great significance for studying the problem of large deformation of tunnels under high geo-stress conditions. This article proposes a ground stress field inversion method and large deformation level determination based on the GS-XGBoost algorithm and the Haba Snow Mountain Tunnel of the Lixiang Railway. Firstly, the hydraulic fracturing method is used to conduct on-site testing of tunnel ground stress and obtain tunnel ground stress data. Then, a three-dimensional model of the Haba Snow Mountain Tunnel will be established, and it will be combined with the GS-XGBoost regression algorithm model to obtain the optimal boundary conditions of the model. Finally, the optimal boundary condition parameters are substituted into the three-dimensional finite-difference calculation model for stress calculation, and the distribution of the in-situ stress field of the entire calculation model is obtained. Finally, the level of large deformation of the Haba Snow Mountain Tunnel will be determined. The results show that the ground stress of the tunnel increases with the increase of burial depth, with the maximum horizontal principal stress of 38.03 MPa and the minimum horizontal principal stress of 26.07 MPa. The Haba Snow Mountain Tunnel has large deformation problems of levels I, II, III, and IV. Level III and IV large deformations are generally accompanied by higher ground stress (above 28 MPa) and smaller surrounding rock strength. The distribution of surrounding rock strength along the tunnel axis shows a clear "W" shape, opposite to the surface elevation "M" shape. It is inferred that the mountain may be affected by geological structures on both sides of the north and south, causing more severe compression of the tunnel surrounding rock at the peak.

An efficient shape-based procedure for strain hardening identification in the post-necking phase

Nowadays, finite element (FE) codes are increasingly employed for simulating large deformation problems. Thus, to reliably represent the strain hardening behavior, a proper calibration of constitutive laws is essential. Focusing on tensile tests, the main issue with ductile metals is necking occurrence, because of the consequent triaxiality and non-uniformity of the strain and stress states. Over the past decades many strain hardening identification approaches have been proposed. Among them, FE-based inverse methods are widely used, but computationally expensive and time consuming. Hence, the authors propose an efficient method which exploits a database for relating the plastic flow rule and the specimen necking profile. The explicit solver of the nonlinear FE code LS-DYNA was used to build the database, whose size could be limited thanks to physical considerations. The developed methodology was applied to experimental quasi-static tensile tests performed on different metals. The predicted hardening laws showed good agreement with those identified with FE-based inverse methods, thus verifying the applicability of the proposed strategy. This study paves the way for machine learning tools having as main input the necking shape: indeed, the present work suggests their feasibility and provides insights into how to establish datasets for a proper and efficient training.

A Multi-Time-Step Parallel Computing Method based on Overlapping Particles for DEM

The application of the discrete element method (DEM) to continuous medium problems is becoming increasingly widespread. In this work, a parallel computing method with multiple time steps based on overlapping particles is proposed. The domain decomposition method (DDM) with overlapping particles method is used to increase the speed up and shorten the computation time and meet the consistency requirements during data transmission. The multi-time-step method (MTSM) is adopted to tackle the matching of asynchronous step boundary. Data are exchanged at the boundaries in each subdomain with a message passing interface (MPI). The computational efficiency of different step ratios in both serial and parallel computing is studied respectively. Numerical examples show that the DEM can effectively handle large structure deformation problems, and provides a shorter calculation time than that of the finite element method (FEM). The DEM with multiple time steps in different subdomains effectively reduces the computation time than that with a single time step in the entire domain. Under fixed step ratio conditions, using parallel computing can save more time than serial computing. This work develops ideas for expanding the application of DEM for large engineering problems.

Data transfer within a finite cell remeshing approach applied to large deformation problems

AbstractThe present work is a comparative study of different data transfer techniques in the context of the finite cell method (FCM) in combination with remeshing for hyperelastic problems undergoing large deformations. The FCM is an immersed-boundary method that uses Cartesian grids for the discretization so as to avoid the generation of boundary conforming meshes. To overcome problems with heavily distorted meshes at large deformation states, we apply a remeshing procedure. During the remeshing, the data containing the deformation history has to be transferred between the meshes. In the present study, different methods are considered and compared: radial basis functions without and with polynomial extension, inverse distance weighting, and $$\textit{L}_\text {2}$$ L 2 -projection applying the shape functions used in the FCM for the trial and test functions.

Model tests and numerical simulations of deformation repair effect for operating shield tunnels under horizontal lateral grouting

To address the large deformation problem of operating straight-joint assembled shield tunnels in soft soil, horizontal lateral grouting is often used. Using an independently designed and developed lateral grouting test device, a horizontal lateral grouting model test was conducted to study the tunnel force state and deformation repair law under the action of lateral grouting. The mechanical responses of tunnel under single-hole grouting (SHG) and two double-holes grouting (DHG) cases were comparatively analyzed, and the test results were further validated via numerical simulations. The results indicate that several key indicators of tunnel behavior, including additional pressure, bending moment, radial displacement, convergence deformation, and ellipticity, exhibit a positive correlation with the grouting volume and a negative correlation with the distance to the grouting point when implementing SHG. Expect for radial displacement, all of these metrics caused by DHG were greater than those caused by SHG. The horizontal radial displacement increases under same-side DHG but decreases under different-side DHG. Interestingly, same-side DHG is more favorable for reducing internal force and repairing tunnel deformation, and effectively improves tunnel differentiated deformation state along the longitudinal direction. However, different-side DHG can provide a better effect for transverse convergence deformation repair under the premise of minimizing tunnel overall displacement.

Multiphysics simulation of freezing and thawing granular media using material point method

In this paper, a fully coupled thermo-hydro-mechanical material point method, applicable to liquid-saturated porous systems undergoing large deformations and phase transitions, is presented. A mathematical framework was established based on multiphasic mixture theory and fundamental physical conservation laws, rather than using phenomenological or semi-empirical equations. A fractional-step-based semi-implicit solution scheme was proposed to solve the coupled formulations within the framework of the generalized interpolation material point method. The proposed method was validated using several benchmark examples, including the talik closure and thaw consolidation. Its performance in simulating climate-driven large deformation problems was further demonstrated by simulating the settlement of a rigid footing on thawing ground. This paper presents an innovative and rigorous framework for predicting the impact of climate change on engineering practices.