Deformation Coupling Research Articles

Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number

Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The resulting fluid–structure interaction is formulated for both vanishing and finite flow inertia. At the leading-order in the small aspect ratio, the lubrication approximation implies that the pressure only varies in the streamwise direction. Meanwhile, the compliant wall's slenderness makes the fluid–solid interface behave like a Winkler foundation, with the displacement fully determined by the local pressure. Coupling flow and deformation and averaging across the cross section leads to a one-dimensional reduced model. In the case of vanishing flow inertia, an effective deformed channel height is defined rigorously to eliminate the spanwise dependence of the deformation. It is shown that a previously used averaged height concept is an acceptable approximation. From the one-dimensional model, a friction factor and the corresponding Poiseuille number are derived. Unlike the rigid duct case, the Poiseuille number for a compliant duct is not constant but varies in the streamwise direction. Compliance can increase the Poiseuille number by a factor of up to four. The model for finite flow inertia is obtained by assuming a parabolic vertical variation of the streamwise velocity. To satisfy the displacement constraints along the edges of the channel, weak tension is introduced in the streamwise direction to regularize the Winkler-foundation-like model. Matched asymptotic solutions of the regularized model are derived.

Study on the Deformation Characteristics of Fractured Basalt Under Coupling of Three-Dimensional Stress and Water Pressure Cycling

The seepage-stress coupling of fractured rock masses is a physical, chemical and mechanical process that depends strongly on the lithological conditions, structural state, initial stress level and stress path for the hydraulic coupling during water storage. A newly developed true triaxial hydraulic coupling test system named HMTS-1200 was used to carry out triaxial hydromechanical coupling deformation tests on fractured basalt under water pressure along a cyclic loading and unloading path. The following test results were obtained. During cyclic water pressure loading and unloading, the additional axial deformation exhibits the characteristic fluctuations of compression-expansion-compression, whereas the lateral deformation exhibits the characteristic fluctuations of expansion-compression-expansion. Under hydraulic-mechanical coupling, the coupling of the axial pressure and the water pressure is noticeable. The lower the axial pressure is, the more noticeable the additional specimen deformation is. The deformation modulus of the fractured basalt under triaxial stress-hydraulic pressure coupling depends strongly on the loading-unloading of the water pressure and the confining pressure. The deformation modulus is logarithmic in the number of cycles and linear in the water pressure. The abovementioned test results serve as an important reference for the study of hydraulic coupling characteristics of and time effects on bank rock mass deformation parameters during reservoir operation.

Shaking table test of acceleration response of surrounding rock of the 3D cross tunnel under earthquake

Taking the 3D cross-engineering of Caomeigou No.1 Tunnel and Pandaoling Tunnel as an example, a shaking table test was carried out to study the effect of tunnel spatial position on seismic wave propagation characteristics and acceleration response of surrounding rock under earthquake seismic excitation. Based on the influence of the spatial position of the tunnel, the characteristic form of the surrounding rock between the cross section and non-cross section is divided, and the accelerometer layout scheme is designed. Based on statistical probability, the ratio of peak ground velocity to peak ground acceleration (PGA) was introduced to quantitatively characterize the characteristics of seismic wave propagation spectrum. Furthermore, the SPECTR calculation was used to obtain the regional difference in the seismic wave propagation potential damage potential displacement parameter (P d ). Under the influence of the spatial location of the 3D cross tunnel, the peak acceleration and motion duration of the seismic wave are mainly reflected in the variation of the section along the elevation direction. Low-frequency (≤20 Hz) seismic waves have a greater impact on the tunnel structure, and peak ground velocity/peak ground acceleration ratio has a positive correlation with the peak input energy of ground motion. The ultra-small net-spacing cross tunnel has a spatially distributed coupling deformation effect. The crown of the upper-span tunnel is highly sensitive to earthquakes and becomes a weak link in seismic design. These results help us provide a theoretical basis for the seismic design of the cross-tunnel.

Design of a Multi-Point Kinematic Coupling for a High Precision Telescopic Simultaneous Measurement System.

This paper covers the design of a new multi-point kinematic coupling specially developed for a high precision multi-telescopic arm measurement system for the volumetric verification of machine tools with linear and/or rotary axes. The multipoint kinematic coupling allows the simultaneous operation of the three telescopic arms that are registered at the same time to a sphere fixed on the machine tool spindle nose. Every coupling provides an accurate multi-point contact to the sphere, avoiding collisions and interferences with the other two multi-point kinematic couplings, and generating repulsion forces among them to ensure the coupling’s fingers interlacing along the machine tool x/y/z travels in the verification process. Simulation presents minimal deformation of the kinematic coupling under load, assuring the precision of the sphere-to-sphere distance measurement. Experimental results are provided to show that the multi-point kinematic coupling developed has repeatability values below ±1.2 µm in the application.

Numerical study on the effect of the geometry size of multi-chamber infusion bag on its bursting force

This study explored the variation of bursting force of multi-chamber infusion bag with different geometry size, providing guidance for its optimal design. Models of single-chamber infusion bag with different size were established. The finite element based on fluid cavity method was adopted to calculate the fluid-solid coupling deformation process of infusion bag to obtain corresponding critical bursting force. As a result, we proposed an empirical formula predicting the critical bursting force of one chamber infusion bag with specified geometry size. Besides, a theoretical analysis, which determines the force condition of three chamber infusion bag when falling from high altitude, was conducted. The proportion of force loaded on different chamber was gained. The results indicated that critical bursting force is positively related to the length and width of the chamber, and negatively related to the height of the chamber. While the infusion bag falling, the impact force loaded on each chamber is proportional to the total liquid within it. To raise the critical bursting force of in fusion bag, a greater length and width corresponding to reduced height are recommended considering the volume of liquid needed to be filled in.

Underlying SUSY in a generalized Jaynes\u2013Cummings model

We present a general qubit-boson interaction Hamiltonian that describes the Jaynes–Cummings model and its extensions as a single Hamiltonian class. Our model includes non-linear processes for both the free qubit and boson field as well as non-linear, multi-boson excitation exchange between them. It shows an underlying algebra with supersymmetric quantum mechanics features allowing an operator based diagonalization that simplifies the calculations of observables. As a practical example, we show the evolution of the population inversion and the boson quadratures for an initial state consisting of the qubit in the ground state interacting with a coherent field for a selection of cases covering the standard Jaynes–Cummings model and some of its extensions including Stark shift, Kerr-like, intensity dependent coupling, multi-boson exchange and algebraic deformations.

Multi-field coupling deformation of rock and multi-scale flow of gas in shale gas extraction

Shale is a kind of multi-scale medium to store shale gas. The analysis of its structural changes during gas extraction is helpful to increase shale gas production. In this study, the shale reservoir is divided into three systems according to the scale: kerogen system, pore system and fracture system. Based on the fractal geometry theory, the fractal permeability models of the pore system and fracture system are established according to the fracture length and pore diameter geometric characteristics. The diffusion model of kerogen system was established according to the nano-pore structure characteristic of kerogen with adsorption and desorption mechanism. A multi-scale fluid-solid coupling model was established by combining the gas mass transfer equation with the matrix deformation equation. The accuracy of the model is verified by the horizontal well gas production data. The results show that:(1) the effective stress causes the evolution of reservoir internal structure and permeability; (2) local mechanical property changes of the reservoir will spread to the entire reservoir; (3) adsorption effect dominates the storage capacity of shale structure. This study provides a new method for revealing the mechanism of gas flow in rock and improving gas extraction rate.

Residual stress modeling considering microstructure evolution in metal additive manufacturing

Metal additive manufacturing (AM) process induces residual stress which can hinder the applicability of AM. Residual stress build-up causes part failure due to the crack initiation and growth, and also distortion during or after fabrication. Consequently, it is of great importance to accurately and rapidly predict residual stress within the AM parts. During the thermal loading, the grain size is altered at the subsurface through dynamic recrystallization (DRx) and subsequent recovery. The yield strength of the alloys is largely determined by the size of nucleated grains, and it has a substantial influence on residual stress build-up. In this work, a physics-based analytical model is proposed to predict the residual stress considering the microstructure of the additively manufactured part. The thermal signature of this process is predicted using a transient moving point heat source. Due to the high-temperature gradient innate in this process, material may experience high thermal stress which often exceeds the yield strength. The thermal stress is obtained from Green’s functions of stresses due to the point body load. The modified Johnson-Cook flow stress model is used to predict the yield surface. In this flow stress model, the yield strength parameter is modified to incorporate the effect of grain size using Hall-Petch equation. The dynamic recrystallization and the resultant grain size are predicted by utilizing the Johnson–Mehl–Avrami–Kolmogorov (JMAK) model for IN718 alloy. Moreover, a grain refinement model is used to include the effect of the rapid solidification on grain size. Then, as a result of the cyclic heating and cooling and the fact that the material is yielded, the residual stress build-up is precited from incremental plasticity and kinematic hardening behavior of the metal according to the property of volume invariance in plastic deformation in coupling with equilibrium and compatibility conditions. Results from the analytical residual stress model showed good agreement with X-ray diffraction measurements used to determine the residual stresses in the IN718 specimens. Moreover, the phases present in the IN178 samples built via direct metal disposition (DMD) are evaluated using X-ray diffraction.

Coupled deformation behavior analysis for the glass panel in unitized hidden-frame supported glass curtain wall system

As a kind of building envelope, glass panel has been emerging and widely employed in unitized hidden-frame supported (UHFS) glass curtain wall system in modern construction engineering. In practical service conditions, the large area of glass panels involved in the all-glass facades of UHFS glass curtain wall system usually expose to external wind loads, thus it is quite essential to focus on the coupled deformation of the glass panel caused by complex boundary constraints stemming from connected components and their interactions in UHFS glass curtain wall system. In this paper, the optical measurement system associated with the standard air-tight test chamber of UHFS glass curtain wall samples for DIC analysis of the glass panel was first established based on the theory of stereo vision and digital image correlation. Then, the conventional digital indicators and finite element analysis (FEA) models were employed to provide the actual and theoretical deformation information of the panel, which were used to demonstrate that the adopted DIC method had the unique advantage of characterizing full-field coupled deformation behavior of the glass panel affected by complicated boundary conditions. Consequently, the spatiotemporal deformation behavior of the glass panel in practical service conditions was investigated and thus the principal strain, maximum relative deflection (MRD) as well as strain energy density on the panel surface were accordingly evaluated. The above metrics could be used for failure risk evaluation and providing safety design suggestions for the glass panel in UHFS curtain wall system.

A novel temperature-strain synchronous measurement method

Thermal-mechanical coupling deformation is inevitable in the operation of materials and structures. Traditional deformation researches have mainly focused on temperature or deformation measurement at a specific temperature, but few studies have investigated the coupling relationship between temperature and deformation in a non-uniform thermal environment. This study presents a novel method of measuring the temperature and strain distribution of an object synchronously. A calibration object and its calibration method were designed to be utilized in the synchronous calibration of both the infrared and visible cameras, and a matching method of the infrared image and the visible image was proposed. The data in the non-uniform temperature field and the non-uniform strain field corresponded accurately using the proposed method. A simulation experiment and actual thermal coupling deformation experiments were utilized to verify the effectiveness and accuracy of the proposed method. The proposed method can realize the accurate correspondence of the temperature and strain fields in the measurement area and provide technical support for studying the actual thermal-mechanical coupling deformation of materials and structures.

Finite element method simulating bursting process of multi-chamber flexible package infusion bag

This study aims to overcome the shortcomings such as low efficiency, high cost and difficult to carry out multi-parameter research, which limited the optimization of infusion bag configuration and manufacture technique by experiment method. We put forward a fluid cavity based finite element method, and it could be used to simulate the stress distribution and deformation process of infusion bag under external load. In this paper, numerical models of infusion bag with different sizes was built, and the fluid-solid coupling deformation process was calculated using the fluid cavity method in software ABAQUS subject to the same boundary conditions with the burst test. The peeling strength which was obtained from the peeling adhesion test was used as failure criterion. The calculated resultant force which makes the computed peeling stress reach the peeling strength was compared with experiment data, and the stress distribution was analyzed compared with the rupture process of burst test. The results showed that considering the errors caused by the difference of weak welding and eccentric load, the flow cavity based finite element method can accurately model the stress distribution and deformation process of infusion bag. It could be useful for the optimization of multi chamber infusion bag configuration and manufacture technique, leading to cost reduction and study efficiency improvement.

Key Aquiclude Strata Reconstruction and Fluid–Solid Coupled Deformation Mechanism Study for Backfill Coal Mining

Key Aquiclude Strata Reconstruction and Fluid–Solid Coupled Deformation Mechanism Study for Backfill Coal Mining

A novel chiral metamaterial with multistability and programmable stiffness

Chiral metamaterials are widely studied for their unique mechanical properties, but still have problems such as low stiffness and few available scenarios. Based on the tetra-chiral metamaterial, a type of metamaterial with programmable stiffness and multistability is designed in this paper. The stiffness of two-dimensional (2D) metamaterial can be adjusted programmatically by changing its geometric parameters. The equivalent elastic modulus and Poisson’s ratio were obtained by using an analytical solution and finite element method. Then the 2D metamaterials were extended to cylindrical tubes with multistability. The deformation patterns of the 2D metamaterials and cylindrical tubes with different geometric parameters were investigated. It is found that the cylindrical tubes can exhibit compression–torsion coupling and multistability deformation characteristics. This work can provide a valuable reference for designs of novel metamaterials with coupled deformation, as well as further expanding the field of application.

Achieving complete reaction while the solid volume increases: A numerical model applied to serpentinisation

Solid volume increases during the hydration of mantle rocks. The fluid pathways necessary to feed the reaction front with water can be filled by the low density reaction products. As a result, the reaction front dries out and the reaction stops at low reaction progress. This process of porosity clogging is generally predicted to dominate in reactive transport models, even when processes such as reaction-induced fracturing are considered. These predictions are not consistent with observations at mid-ocean ridges where dense mantle rocks can be completely replaced by low density serpentine minerals. To solve this issue, we develop a numerical model coupling reaction, fluid flow and deformation. High extents of reaction can only be achieved when considering that the increase in solid volume during reaction is accommodated through deformation rather than porosity clogging. The model can generate an overpressure that depends on the extent of reaction and on the boundary conditions. This overpressure induces viscoelastic compaction that limits the extent of the reaction. The serpentinisation rate is therefore controlled by the accommodation of volume change during reaction, and thus by deformation, either induced by the reaction itself or by tectonic processes.

Seismic Optimization of High Cantilever Multianchor Pile Strengthening Soil Slopes against Earthquakes

To explore the optimal seismic performance of multianchor pile, we carried out a series of shaking table tests. Based on the special form of multianchor piles’ reinforcement, we put forward the optimal design scheme of using EPS foam as damping layers and energy-dissipation springs for improving the self-coordinating devices of anchor head. By measuring acceleration and dynamic soil-pressure response under different intensities of vibration, we analyzed the correlation between acceleration caused by seismic wave action and damage characterized by time-domain and spectral characteristics of dynamic soil-pressure. We discuss in detail the relationship between frequency and specific period of dynamic soil-pressure and acceleration. We then used the SPECTR program to calculate the energy spectrum. Under the reciprocating action of seismic waves of different intensities, our slope model showed the continuous effect of spatial coupling deformation leading to regional damage and failure. Furthermore, the spatial distribution for amplitude of acceleration and dynamic soil-pressure showed the outstanding response of lateral amplitude of pile structures without optimization. The energy-spectrum distribution of acceleration seismic input was orderly, while the dynamic soil-pressure distribution of piles was disordered. Low-frequency (≤10 Hz) seismic waves have a great influence on these structures. The difference of acceleration hysteresis along the elevations was mainly caused by the propagation stage after the main earthquake. The correlation between dynamic soil-pressure and acceleration response in each group before the pile occurred in the same earthquake area was very weak, showing a low correlation. The optimization effect of optimized structures is related to the position of the shock-absorbing layer. Under high acceleration, multianchor piles easily cause bulge failures or shear failures at the positions of sliding surfaces. These results are helpful for improvements to reliably optimize designs in pile structure dynamic parameters.

Anisotropic behaviors of helically corrugated cylindrical shells: Homogenized in-plane stiffness

Thin-walled corrugated structures have been widely used in engineering applications for centuries, because corrugation enables engineers to tailor directional dependent properties despite the structures being made of isotropic materials. However, the vast majority of research has paid attention to corrugated plates and relatively scarce studies are on corrugated shells. This paper, therefore, aims to investigate elastic behaviors of thin cylindrical shells that possess sinusoidal corrugating patterns in the helical direction. Elastic responses of undulated shells under three types of deformation, namely, axial elongation, axial torsion, and radial expansion are thoroughly investigated by using the finite-element method (FEM) via ABAQUS™. The effective stiffness of the corrugated cylinders is determined by a homogenization technique in a representative unit cell element. A variety of FEM models are created according to four groups of dimensionless parameters, i.e. radius-to-thickness ratio, radius-to-corrugating depth ratio, helical angle and the number of waveform (thread) in a cylinder cross section. The results show that the degree of anisotropy induced by the corrugated shells is different from that of a fiber-reinforced composite material, significantly sensitive to their configurations, and can be extraordinarily higher than the perfect round shell made of the same parent material. Unorthodox coupling quantities of torsional-axial, torsional-radial, and axial-radial coupling deformations are encountered at some specific geometries. Anisotropy design space in the form of spherical maps is given as a guideline to effectively design or select a proper helically corrugated cylindrical shell with the desired stiffness properties.

考虑前屈曲耦合变形时功能梯度圆板的稳定性分析

考虑前屈曲耦合变形时功能梯度圆板的稳定性分析

Analytical Modeling of Residual Stress in Laser Powder Bed Fusion Considering Volume Conservation in Plastic Deformation

Residual stress (RS) is the most challenging problem in metal additive manufacturing (AM) since the build-up of high tensile RS may influence the fatigue life, corrosion resistance, crack initiation, and failure of the additively manufactured components. While tensile RS is inherent in all the AM processes, fast and accurate prediction of the stress state within the part is extremely valuable and results in optimization of the process parameters to achieve a desired RS and control of the build process. This paper proposes a physics-based analytical model to rapidly and accurately predict the RS within the additively manufactured part. In this model, a transient moving point heat source (HS) is utilized to determine the temperature field. Due to the high temperature gradient within the proximity of the melt pool area, the material experiences high thermal stress. Thermal stress is calculated by combining three sources of stresses known as stresses due to the body forces, normal tension, and hydrostatic stress in a homogeneous semi-infinite medium. The thermal stress determines the RS state within the part. Consequently, by taking the thermal stress history as an input, both the in-plane and out of plane RS distributions are found from the incremental plasticity and kinematic hardening behavior of the metal by considering volume conservation in plastic deformation in coupling with the equilibrium and compatibility conditions. In this modeling, material properties are temperature-sensitive since the steep temperature gradient varies the properties significantly. Moreover, the energy needed for the solid-state phase transition is reflected by modifying the specific heat employing the latent heat of fusion. Furthermore, the multi-layer and multi-scan aspects of metal AM are considered by including the temperature history from previous layers and scans. Results from the analytical RS model presented excellent agreement with XRD measurements employed to determine the RS in the Ti-6Al-4V specimens.

Applications of phase field fracture in modelling hydrogen assisted failures

The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of phase field-based multi-physics models in transforming the engineering assessment and design of structural components in hydrogen-containing environments. First, we present a theoretical and numerical framework coupling deformation, diffusion and fracture, which accounts for inertia effects. Several constitutive choices are considered for the crack density function, including choices with and without an elastic phase in the damage response. The material toughness is defined as a function of the hydrogen content using an atomistically-informed hydrogen degradation law. The model is numerically implemented in 2D and 3D using the finite element method. The resulting computational framework is used to address a number of case studies of particular engineering interest. These are intended to showcase the model capabilities in: (i) capturing complex fracture phenomena, such as dynamic crack branching or void-crack interactions, (ii) simulating standardised tests for critical components, such as bolts, and (iii) enabling simulation-based paradigms such as Virtual Testing or Digital Twins by coupling model predictions with inspection data of large-scale engineering components. The evolution of defects under in-service conditions can be predicted, up to the ultimate failure. By reproducing the precise geometry of the defects, as opposed to re-characterising them as sharp cracks, phase field modelling enables more realistic and effective structural integrity assessments.

Core reinforcement design for improving flexural energy-absorption of corrugated sandwich composite structure

To strengthen Specific Energy-Absorption (SEA) behavior of Sandwich Composite Structure (SCS), a kind of light-weight vertical stiffener is proposed for the corrugated core. The vertical stiffener, embedded in the corrugated core, can not only absorb part of energy but also simultaneously enhance Energy-Absorption (EA) of other components. The Hashin damage model considering the shear stress and ductile damage model is adopted to predict the failure of carbon fiber face-sheets and aluminum-core, respectively. The perfect bonding is modeled for interfaces between the face-sheet and core due to little realistic debonding. The finite element model is verified by available data of conventional SCS. To obtain more design ideas, several stiffeners with different thicknesses, numbers, and positions are investigated. From the predicted results, both the flexural load and deformation of SCS correlate well with experimental results. It is highlighted that the SCSs with different vertical stiffeners exhibit 9.74%–58.48% higher SEA than the SCS without stiffener. The complex reinforcement mechanisms are extensively revealed by underlying coupling EA and deformation mechanisms. Structural parameter analysis shows that the thickness and number have significant effects on the flexural behavior and SEA of reinforced SCS.