Displacement Boundary Research Articles

Effect of Particle Size Distributions (PSDs) on ground responses induced by tunnelling in dense coarse-grained soils: A DEM investigation

Tunnelling-induced ground responses in coarse-grained soils often exhibit complex behaviours such as soil arching and progressive ground instability. However, the effect of particle size distributions (PSDs) on ground responses in tunnelling remains largely unexplored. This study provides new insights into PSD’s effect on tunnelling ground response and the underlying mechanism based on granular skeleton quantification. The coarse-grained soils with 9 typical PSDs were modelled by the discrete element method (DEM) with varied granular skeleton structures. A representative volume element (RVE) assembly method, with a novel iteration-based specimen generation method, is developed to build ground models incorporating millions of soil grains, where an eccentric displacement boundary was embedded for reproducing the tunnel volume losses. The results demonstrated that the change in skeleton structures from fine-grains to coarse-grains dominated leads to the acceleration of soil arch emergence and the deceleration of soil arch collapse-rebuilding. With an increase in ded, the strengthened soil arch leads to a more evident deformation localization in ground, and results in more significant hysteresis of ground instability from the tunnel to the surface. The effect of PSDs on ground responses becomes prominent as the overburden thickness decreases and the tunnel volume loss increases, and a decrease in ded would increase the risk of overall failure in tunnelling.

Effect of the density ratio on the oscillatory Saffman–Taylor instability in vertical conical Hele–Shaw cell

The stability of an oscillating interface between two immiscible liquids with a high viscosity contrast in an axisymmetric conical Hele–Shaw cell in dependence on the density ratio is studied experimentally. The symmetry axis of the cell is vertical, while the tangential component of the gravy acts on the axisymmetric interface. The contact line is almost motionless, while the low-viscosity liquid penetrates a high-viscosity one in the form of an axisymmetric “tongue” in the course of an oscillating cycle. The increase in the oscillation amplitude leads to the development of azimuthal patterns (fingers) at the interface. Fingers of a low-viscosity liquid appear when a viscous liquid is being squeezed out of the cell and reach their maximum length at the maximum displacement of the interface. Then, the fingers decrease and are replaced by small depressions penetrating into the low-viscosity liquid in the phase of maximum boundary displacement toward the low-viscosity liquid. The increase in the density ratio of liquids has a stabilizing effect on the interface: The instability threshold is shifted to the higher oscillation amplitudes. Also, the stability threshold is independent of whether the high-viscosity or low-viscosity liquid is denser than the other one. We propose a new dimensionless parameter that controls the stability of the interface—the multiplication of the square root of the capillary number and the dimensionless amplitude of interface oscillations. It is revealed that the critical value of the stability parameter increases linearly with an increase in the density ratio of liquids.

Назначение рациональных режимов электроэрозионной обработки деталей из титанового сплава ВТ5 на основе решения тепловой задачи о перемещении границы фазового превращения материала

The paper presents results of theoretical studies of the VT5 titanium alloy machinability by the electrodischarge machining method based on solving the thermal problem of the material phase transformation boundary displacement (Stefan problem). It proposes a method for determining parameters of electrical pulses for the VT5 alloy electrodischarge machining in order to increase the process productivity; recommendations are provided for that purpose. Density of the heat flux and its duration were determined necessary for implementation of the VT5 alloy electrodischarge machining process. Dependences were established of the minimum value of the heat flux pulse duration, when the VT5 alloy electrodischarge machining process was possible, and of maximum value of the heat flux pulse duration ensuring maximum removal of the VT5 alloy from the workpiece in one pulse, on the heat flux density. It is shown that for the maximum productivity of the VT5 alloy electrodischarge machining at the heat flux density used, it is necessary to assign effective duration of such a flux. Dependences of the heat flux effective duration on its density were established. Besides, to assign rational modes of VT5 ally electrodischarge machining, relationships were established and provided between the VT5 alloy machinability curves (dependences of the material penetration depth on the pulse duration) and other materials, including those for which rational modes are currently defined

Crack propagation analysis of slewing bearings in wind turbines applying a modified sub-model technology

As slewing bearings in wind turbines are exposed to complex operational environments, they are prone to crack initiation, propagation and evolution that can lead to contact fatigue problems. Reliable crack extension prediction is a critical requirement. With the goal of obtaining more accurate crack characteristics, this study proposes a crack initiated contact finite element model (CI-CFEM) targeted at the raceway of slewing bearings by introducing a modified sub-model. In the application of the global finite element model (G-FEM) to the slewing bearing system, the rolling displacements of the ball and the boundary displacements are employed in CI-CFEM to take account of external ring deformations and the support conditions. The crack is embedded using FRANC3D, and the stress intensity factor distribution and propagation characteristics of the crack front are investigated. Furthermore, the effect of external load and the design parameters of the slewing bearing on crack propagation are explored, providing insight for optimizing the design of slewing bearings to extend service life. The results reveal that changing external loads and bearing parameters are an effective means of retarding crack propagation rate, while have relatively minor influence on crack growth angle.

Free Vibration Analyses of Stiffened Functionally Graded Graphene-Reinforced Composite Multilayer Cylindrical Panel

In this paper, the free vibration response of a stiffened functionally graded graphene nanoplatelet (GPL)-reinforced composite multilayer cylindrical shell panel is studied for the first time. The shell is stiffened by both stringers and rings. Additionally, the effect of reinforcing the shell panel, ring and stinger with GPLs is independently studied. Halpin–Tsai relations are employed to evaluate the mechanical properties of the shell panel, rings and stringers. The first-order shear deformation shell theory, accompanied by the Lekhnitsky smeared stiffener model, using the numerical finite element method and Hamilton principle, is employed to develop the governing motion equations of the shell panel. Four different types of GPL patterns, including FG-A, FG-X, FG-O and UD, are assumed across the thickness of the shell panel, rings and stringers. The effects of different factors, including various weight fractions and patterns of GPLs nanofillers, the geometry of the shell panel and stiffeners and two displacement boundary conditions, on the natural frequencies of the shell panel, have been studied.

Modeling isovolumetric phases in cardiac flows by an Augmented Resistive Immersed Implicit Surface method.

A major challenge in the computational fluid dynamics modeling of the heart function is the simulation of isovolumetric phases when the hemodynamics problem is driven by a prescribed boundary displacement. During such phases, both atrioventricular and semilunar valves are closed: consequently, the ventricular pressure may not be uniquely defined, and spurious oscillations may arise in numerical simulations. These oscillations can strongly affect valve dynamics models driven by the blood flow, making unlikely to recovering physiological dynamics. Hence, prescribed opening and closing times are usually employed, or the isovolumetric phases are neglected altogether. In this article, we propose a suitable modification of the Resistive Immersed Implicit Surface (RIIS) method (Fedele et al., Biomech Model Mechanobiol 2017, 16, 1779-1803) by introducing a reaction term to correctly capture the pressure transients during isovolumetric phases. The method, that we call Augmented RIIS (ARIIS) method, extends the previously proposed ARIS method (This et al., Int J Numer Methods Biomed Eng 2020, 36, e3223) to the case of a mesh which is not body-fitted to the valves. We test the proposed method on two different benchmark problems, including a new simplified problem that retains all the characteristics of a heart cycle. We apply the ARIIS method to a fluid dynamics simulation of a realistic left heart geometry, and we show that ARIIS allows to correctly simulate isovolumetric phases, differently from standard RIIS method. Finally, we demonstrate that by the new method the cardiac valves can open and close without prescribing any opening/closing times.

Computational study of the mechanical behavior of the astrocyte network and axonal compartments in the mouse optic nerve head.

Glaucoma is a blinding disease characterized by the degeneration of the retinal ganglion cell (RGC) axons at the optic nerve head (ONH). A major risk factor for glaucoma is the intraocular pressure (IOP). However, it is currently impossible to measure the IOP-induced mechanical response of the axons of the ONH. The objective of this study was to develop a computational modeling method to estimate the IOP-induced strains and stresses in the axonal compartments in the mouse astrocytic lamina (AL) of the ONH, and to investigate the effect of the structural features on the mechanical behavior. We developed experimentally informed finite element (FE) models of six mouse ALs to investigate the effect of structure on the strain responses of the astrocyte network and axonal compartments to pressure elevation. The specimen-specific geometries of the FE models were reconstructed from confocal fluorescent images of cryosections of the mouse AL acquired in a previous study that measured the structural features of the astrocytic processes and axonal compartments. The displacement fields obtained from digital volume correlation in prior inflation tests of the mouse AL were used to determine the displacement boundary conditions of the FE models. We then applied Gaussian process regression to analyze the effects of the structural features on the strain outcomes simulated for the axonal compartments. The axonal compartments experienced, on average, 6 times higher maximum principal strain but 1800 times lower maximum principal stress compared to those experienced by the astrocyte processes. The strains experienced by the axonal compartments were most sensitive to variations in the area of the axonal compartments. Larger axonal compartments that were more vertically aligned, closer to the AL center, and with lower local actin area fraction had higher strains. Understanding the factors affecting the deformation in the axonal compartments will provide insights into mechanisms of glaucomatous axonal damage.

The strong stabilization of a 1-D conservative wave equation by boundary displacement only

In this paper, we consider the stabilization of a 1-D conservative wave equation by collocated boundary displacement signal only. We first design an observer for the original system, in which we introduce an ordinary differential equation so that the unavailable velocity can be recovered. Then we use the C0-semigroup theory to verify the well-posedness and stability of the error system. Next we propose a feedback law in terms of the observer. Consequently, we obtain the asymptotic stability of the closed-loop system. Finally, using the finite element method, the numerical simulations show that the open-loop system is conservative and the closed-loop system is asymptotically stable.

Microstructure-Based Two-Scale Simulation of Deformation and Fracture of SiCp/2009Al Composite

Accurately predicting the formability of composites is quite important for designing the materials and optimizing the processing parameters of such components. This paper presents a microstructure-based two-scale model to analyze the deformation behavior of the SiCp/2009Al composite during upsetting. The microstructure-based micro-scale model with a displacement boundary condition that was obtained from a macro-scale model can predict particle cracking, interface failure and matrix fracture by introducing the normal stress criterion, the maximum stress ratio criterion and the shear fracture model. The simulation results show that, during unidirectional upsetting, the crack initiates in the matrix, and then propagates in the matrix, the interface and the particle. Comparing with the unidirectional upsetting, the bidirectional upsetting results in a more uniform stain distribution and a smaller maximum strain, which prevent the initiation of the crack in the matrix. The simulation results compare well with the deformation and fracture patterns observed in experiment, indicating an effective way to optimise the plastic working and designing of composites.

Displacements and stresses around a circular tunnel in an elastic medium with pseudo-static horizontal earthquake body forces

This manuscript presents an analytical solution based on the complex variable approach for computing displacements and stresses around a single circular tunnel in a linear elastic medium in the presence of pseudo-static horizontal earthquake body forces. The solution has been obtained with the imposition of uniform as well as non-uniform radial displacement boundary conditions along the tunnel’s periphery taking the ground volume loss (GVL) as a governing input parameter. The non-uniform radial displacements’ boundary condition along the tunnel periphery has been modelled by using the Gaussian distribution function. The effects of the distribution of the tunnel’s peripheral displacements, Poisson’s ratio of the continuum and the depth to radius of the tunnel on the results have been examined. Necessary validation exercise, in the presence of horizontal earthquake acceleration, has also been carried out by comparing the obtained results with that computed on the basis of the finite element method. The results were also compared with that reported in literature. It was observed that with an increase in the pseudo static acceleration, there is (i) a significant increase in the horizontal displacements, (ii) a generation of non-symmetric displacement and stress pattern, (iii) an increase in the shear stresses, and (iv) the development of high deviatoric stress zones around the tunnel periphery.

Shape optimization of non-rigid origami leading to emerging bistability

Origami structures are a type of thin-walled flexible structures that undergo large deformation. Their inherent non-rigid characteristic empowers them with great potential for applications in space structures, metamaterials, and robotics. To understand the large deformation of origami structures, consideration of nonlinear mechanics is necessary. However, most origami structures are still designed by pure geometric approaches without considering their non-rigid behavior. In this work, we propose a computational design framework that incorporates nonlinear mechanics into the design procedure of origami. Guided by minimization of stored energy, under prescribed displacement boundary conditions, we optimize the configuration of origami structures. Difficulties arise due to the complex energy landscape of origami structures that inevitably induces bifurcation. We develop strategies to keep track of a stable deformation branch during the optimization process. A surprising outcome is that our approach naturally leads to self-emerging bistable structures, which is demonstrated by a series of numerical examples. We believe that our new approach would make substantial contribution to computational design of non-rigid origami structures, benefiting applications in origami-inspired solutions for science and engineering.

A multiple-data-based direct method for inverse problem in three-dimensional linear elasticity

Estimating the unknown Young’s modulus and boundary conditions of an elastic object from locally observed boundary data is an inverse problem which is usually solved by iterative methods. In this paper, a multiple-data-based direct (MD) method is proposed to solve this inverse problem without iterations. The proposed method applies a global normalized objective function and a global regularization coefficient τg for energy-like regularization to ensure the convergence of the unknown displacement boundary conditions. A coarse-mesh based preprocessing algorithm is proposed to speed up the determination of the regularization coefficient. A multi-force-position method is proposed to obtain observation data, which improves accuracy of the MD method when the number of experiments is limited. Both numerical and physical experiments were conducted. Compared with the single-data-based direct (SD) methods proposed in our previous work, the MD method yields more accurate estimation of Young’s modulus and boundary conditions in both numerical and physical experiments.

EVALUATION OF Zr, Ni-Cr, And Au-Ag APPLIED MATERIALS USING FEM ON PROSTHETIC CROWNS

The crown is a steady prosthesis designed to restore the functionality of a damaged tooth along, with its shape and size. They are also used to reinforce the tooth that poses long-term risk due to wide cavities and accidental injuries. The crowns are fixed using dental cement made of different materials such as porcelain cement, ceramics, etc. The present work aims to assess the mechanical properties – stiffness and strength, of the single molar crown prosthetic tooth materials to determine the efficacy of each material under typical masticatory load observed in clinical settings. To this end, the finite element method (FEM) is used to analyze the mechanical behavior of the molar crowns made of Zirconium (Zr), Nickel Chromium (Ni-Cr), and Gold alloy (Au-Ag). The crown models were created in Solidworks and exported to the ANSYS FE package. The exported three-dimensional models were subjected to varying loading conditions – vertical and oblique forces to the tooth axis under suitable displacement boundary conditions. Due to a relatively high elastic modulus, the Zr and Ni-Cr alloy exhibited a higher stress concentration and lower deformation on the crown’s intaglio surface compared to the Au-Ag alloy.

Exact Dirichlet boundary Physics-informed Neural Network EPINN for solid mechanics

Physics-informed neural networks (PINNs) have been rapidly developed for solving partial differential equations. The Exact Dirichlet boundary condition Physics-informed Neural Network (EPINN) is proposed to achieve efficient simulation of solid mechanics problems based on the principle of least work with notably reduced training time. There are five major building features in the EPINN framework. First, for the 1D solid mechanics problem, the neural networks are formulated to exactly replicate the shape function of linear or quadratic truss elements. Second, for 2D and 3D problems, the tensor decomposition was adopted to build the solution field without the need of generating the finite element mesh of complicated structures to reduce the number of trainable weights in the PINN framework. Third, the principle of least work was adopted to formulate the loss function. Fourth, the exact Dirichlet boundary condition (i.e., displacement boundary condition) was implemented. Finally, the meshless finite difference (MFD) was adopted to calculate gradient information efficiently. By minimizing the total energy of the system, the loss function is selected to be the same as the total work of the system, which is the total strain energy minus the external work done on the Neumann boundary conditions (i.e., force boundary conditions). The exact Dirichlet boundary condition was implemented as a hard constraint compared to the soft constraint (i.e., added as additional terms in the loss function), which exactly meets the requirement of the principle of least work. The EPINN framework is implemented in the Nvidia Modulus platform and GPU-based supercomputer and has achieved notably reduced training time compared to the conventional PINN framework for solid mechanics problems. Typical numerical examples are presented. The convergence of EPINN is reported and the training time of EPINN is compared to conventional PINN architecture and finite element solvers. Compared to conventional PINN architecture, EPINN achieved a speedup of more than 13 times for 1D problems and more than 126 times for 3D problems. The simulation results show that EPINN can even reach the convergence speed of finite element software. In addition, the prospective implementations of the proposed EPINN framework in solid mechanics are proposed, including nonlinear time-dependent simulation and super-resolution network.

Concurrent Build Direction, Part Segmentation, and Topology Optimization for Additive Manufacturing Using Neural Networks

Abstract Without an explicit formulation to minimize support structures, topology optimization may create complex shapes that require an intensive use of support material when additively manufactured. We propose a neural network-based approach to topology optimization that aims to reduce the use of support structures in additive manufacturing. Our approach uses a network architecture that allows the simultaneous determination of an optimized: (1) part segmentation, (2) the topology of each part, and (3) the build direction of each part that collectively minimize the amount of support structure. Through training, the network learns a material density and segment classification in the continuous 3D space. Given a problem domain with prescribed load and displacement boundary conditions, the neural network takes as input 3D coordinates of the voxelized domain as training samples and outputs a continuous density field. Since the neural network for topology optimization learns the density distribution field, analytical solutions to the density gradient can be obtained from the input–output relationship of the neural network. We demonstrate our approach on several compliance minimization problems with volume fraction constraints, where support volume minimization is added as an additional criterion to the objective function. We show that simultaneous optimization of part segmentation along with the topology and print angle optimization further reduces the support structure, compared to a combined print angle and topology optimization without segmentation.

Moore–Gibson–Thompson model with the influence of moisture diffusivity of semiconductor materials during photothermal excitation

In the present work, the semiconductor material is used to study the moisture diffusivity when a modified Moore–Gibson–Thompson (MGT) model is taken into account. The influence of moisture concentration is included in the governing equations throughout the photothermal transfer process. Based on the dissimilar relaxation durations of the coupled optoelectronic and thermoelastic waves, the MGT model is used to investigate the issue at hand. The method of the Laplace transform is used to obtain analytical solutions for the physical quantities, constitutive relationships, elastic waves, carrier density, heat equation conduction, and moisture diffusivity for the thermo-elastic medium. To extract the primary physical quantities in the space–time domain, the boundary conditions, temperature, plasma, displacement, and mechanical stress are inverted numerically using the Laplace transform. The effect of the new parameter like the reference moisture parameter with various values is discussed graphically on the primary physical quantities. The comparison between silicon and germanium is taken into account to achieve numerical computations.

Research into the thermal expansion behavior of spread tow woven pierced carbon/carbon composites at high temperature

Textile-reinforced carbon/carbon composites are frequently used for thermal safety due to their superb thermophysical properties. The coefficient of thermal expansion (CTE) is a fundamental performance metric of spread tow woven pierced carbon/carbon composites (STWPs). The multiscale representative volume element (RVE) models constructed as part of this work were used for investigating the CTEs of STWPs at high temperature. The temperature displacement coupling analysis step was established to predict the CTEs of STWPs considering the high-temperature environment. In addition, periodic displacement boundary conditions were adopted as node constraints with the spatial periodicity of RVE models. The influences of pore positions and configurations on the CTEs of the matrix were considered through two different matrix RVE model. The CTEs of the spread tow (ST) and fiber rod were computed using two microscale RVE models with an unequal fiber volume fraction. A novel modeling strategy for the mesoscale RVE model was put forth in order to calculate the CTEs of the STWPs due to the remarkable lightness and thinness of the ST. Only 9.64% and 7.92% errors in the in-plane and out-of-plane directions were found when the experimental findings were compared to those predicted by numerical models, demonstrating the accuracy and effectiveness of the multiscale RVE models. Moreover, the impacts of areal density of ST woven fabric on the CTEs of STWPs were discussed. The fundings demonstrated that the in-plane and out-of-plane CTEs both decreased as the areal density increased.

Parameter level set method for identifying 2D and 3D void using boundary displacement information

In this paper, the parameter level set method for 2D and 3D void identification is established uniformly by adopting boundary displacement information. Among them, the level set function is used to describe the evolution of the void interface. To avoid mesh reconstruction during the identification process, the ersatz material model associated with the level set function is developed to solve the forward problem. Simultaneously, considering further improving the optimization efficiency and reducing the identification cost, the compactly supported radial basis function is used to approximately expand the level set function. This scheme transforms the optimization of level set function into the optimization of the expansion coefficients, which reduces the optimization variables to some extent. In addition, the L-M algorithm with a certain regularization capability is employed to optimize the objective function. Finally, voids with various shapes in 2D and 3D structures are uniformly identified including complex multi-void structures such as structures similar to the human face and I-beam. The identification results show that the proposed identification method is effective and reliable even after introducing noise.

Fracture Toughness Characteristics of Stacked Bilayer Graphene via Far-Field Displacement Measurements.

Mechanical properties of graphene, e.g., strength, modulus, and fracture toughness are extremely sensitive to flaws. Here the fracture properties of stacked bilayer graphene sheets (SBLG) are reported, obtained via stacking two individually grown graphene sheets. The SBLG is presented here as a building block for flaw-resilient nanomaterials. The fracture properties of freestanding SBLG sheets, suspended on transmission electron microscope (TEM) grids, are characterized by stretching the TEM grid inside an scanning electron microscope (SEM) chamber and monitoring the local displacements in real-time. The fracture toughness is measured and expressed as a function of the critical displacement required to propagate existing cracks in the experiment via computational models. This approach decouples force and displacements measurements, and utilizes the known elastic modulus along with the known displacement boundary conditions at the onset of crack growth to estimate the far field force and stress. This strategy represents a breakthrough in nanoscale fracture mechanics for statistical analysis and high throughput experimens on multiple samples at a time. Results demonstrate that the SBLG is markedly tougher than as-grown single or multilayer graphene, with a mode I fracture toughness of ≈28.06±7.5 MPa . The mechanisms leading to a higher toughness of SBLG are also analyzed and discussed.

Parameter estimation and velocity signal extraction for one-dimensional wave equation with harmonic corrupted boundary observation

Abstract In this paper, we consider parameter estimation and velocity signal extraction from a disturbed boundary velocity signal for an unstable wave equation. Firstly, an adaptive observer is designed based on the boundary displacement and the corrupted boundary velocity. Then the design of the feedback law adopts the backstepping method of infinite dimensional system. Finally, as time approaches infinity, the estimated parameters converge to the unknown parameters, the initial value disturbance can be obtained, and the velocity signal can be asymptotically recovered. Meanwhile, the asymptotic stability of the closed-loop system can be proved by $C_{0}$-semigroup theory and Lyapunov method. Numerical simulation shows that the proposed scheme is reasonable.