Editorial for Multiscale&Multifield Coupling in Geomechanics

We are delighted to serve as guest editors for this special issue in the Journal of Rock Mechanics and Geotechnical Engineering.The purpose of this special issue is dedicated to gathering the latest research work on Multiscale&Multifield Coupling in Geomechanics,where we delve into the intricate interplay of various fields and scales that govern the behavior of geomaterials.In total,30 manuscripts from USA,China,UK,Germany,Canada,India and United Arab Emirates are selected to be included in this issue.

Multi-Physics Coupled Acoustic-Mechanics Analysis and Synergetic Optimization for a Twin-Fluid Atomization Nozzle

Fine particulate matter produced during the rapid industrialization over the past decades can cause significant harm to human health.Twin-fluid atomization technology is an effective means of controlling fine particulate matter pollution.In this paper,the influences of the main parameters on the droplet size,effective atomization range and sound pressure level(SPL)of a twin-fluid nozzle(TFN)are investigated,and in order to improve the atomization performance,a multi-objective synergetic optimization algorithm is presented.A multi-physics coupled acousticmechanics model based on the discrete phase model(DPM),large eddy simulation(LES)model,and Ffowcs Williams-Hawkings(FW-H)model is established,and the numerical simulation results of the multi-physics coupled acoustic-mechanics method are verified via experimental comparison.Based on the analysis of the multi-physics coupled acoustic-mechanics numerical simulation results,the effects of the water flow on the characteristics of the atomization flow distribution were obtained.A multi-physics coupled acoustic-mechanics numerical simulation result was employed to establish an orthogonal test database,and a multi-objective synergetic optimization algorithm was adopted to optimize the key parameters of the TFN.The optimal parameters are as follows:A gas flow of 0.94 m^(3)/h,water flow of 0.0237 m^(3)/h,orifice diameter of the self-excited vibrating cavity(SVC)of 1.19 mm,SVC orifice depth of 0.53 mm,distance between SVC and the outlet of nozzle of 5.11 mm,and a nozzle outlet diameter of 3.15 mm.The droplet particle size in the atomization flow field was significantly reduced,the spray distance improved by 71.56%,and the SPL data at each corresponding measurement point decreased by an average of 38.96%.The conclusions of this study offer a references for future TFN research.

Deep Learning Applied to Computational Mechanics:A Comprehensive Review,State of the Art,and the Classics

Three recent breakthroughs due to AI in arts and science serve as motivation:An award winning digital image,protein folding,fast matrix multiplication.Many recent developments in artificial neural networks,particularly deep learning(DL),applied and relevant to computational mechanics(solid,fluids,finite-element technology)are reviewed in detail.Both hybrid and pure machine learning(ML)methods are discussed.Hybrid methods combine traditional PDE discretizations with ML methods either(1)to help model complex nonlinear constitutive relations,(2)to nonlinearly reduce the model order for efficient simulation(turbulence),or(3)to accelerate the simulation by predicting certain components in the traditional integration methods.Here,methods(1)and(2)relied on Long-Short-Term Memory(LSTM)architecture,with method(3)relying on convolutional neural networks.Pure ML methods to solve(nonlinear)PDEs are represented by Physics-Informed Neural network(PINN)methods,which could be combined with attention mechanism to address discontinuous solutions.Both LSTM and attention architectures,together with modern and generalized classic optimizers to include stochasticity for DL networks,are extensively reviewed.Kernel machines,including Gaussian processes,are provided to sufficient depth for more advanced works such as shallow networks with infinite width.Not only addressing experts,readers are assumed familiar with computational mechanics,but not with DL,whose concepts and applications are built up from the basics,aiming at bringing first-time learners quickly to the forefront of research.History and limitations of AI are recounted and discussed,with particular attention at pointing out misstatements or misconceptions of the classics,even in well-known references.Positioning and pointing control of a large-deformable beam is given as an example.

PDE Standardization Analysis and Solution of TypicalMechanics Problems

A numerical approach is an effective means of solving boundary value problems(BVPs).This study focuses on physical problems with general partial differential equations(PDEs).It investigates the solution approach through the standard forms of the PDE module in COMSOL.Two typical mechanics problems are exemplified:The deflection of a thin plate,which can be addressed with the dedicated finite element module,and the stress of a pure bending beamthat cannot be tackled.The procedure for the two problems regarding the three standard forms required by the PDE module is detailed.The results were in good agreement with the literature,indicating that the PDE module provides a promising means to solve complex PDEs,especially for those a dedicated finite element module has yet to be developed.

Modeling asymmetric fracture mechanics of Mg alloy wire in drawing process

In this study,a numerical analysis was conducted on the ductile fracture of a 2-mm diameter Mg-1Zn-0.5Mn-0.5Sr-0.1Ca alloy wire during drawing.The hexagonally close-packed crystal structure of Mg alloys causes asymmetric fracture behavior,especially in the compression region.The aim of this study is to develop a comprehensive damage model for Mg alloy wire that accurately predicts ductile fracture,with a focus on the compression region.A novel experimental method was introduced to measure the ductile fracture of Mg alloy wires under different stress states.The wire drawing process was simulated using the Generalized Incremental Stress-State dependent damage(GISSMO)Model and the Semi-Analytical Model for Polymers(SAMP)model.The damage model's prediction and the experimental results were found to be in excellent agreement,especially in determining crack initiation.Computational analysis established a safe zone diagram for die angle and reduction ratio,and experimental validation confirmed the feasibility of this approach.The proposed damage model can provide a practical and reliable analysis for optimizing the drawing process of Mg alloy wire.

Investigation of the Micro-Mechanics of an Extruded Precipitation-Strengthened Magnesium Alloy under Cyclic Loading

Precipitation strengthening is a crucial microscopic mechanism for enhancing the strength of magnesium alloys. In order to elucidate the influence of precipitation on the microscopic deformation mechanisms and macroscopic mechanical response of magnesium alloys under cyclic loading conditions, we employed a crystal plasticity model to analyze the stress-strain curves, specific crystal plane diffraction intensities, and the temporal evolution of various microscopic deformation mechanisms and twinning volume fractions for an extruded magnesium alloy, AXM10304, containing coherent precipitates. The research findings indicate that precipitation does not fundamentally alter the microscopic mechanisms of this alloy. However, it hinders twinning during the compression stage, mildly promotes detwinning during the tension stage, and enhances tension secondary hardening by elevating the difficulty of activation of the prismatic slip.

A generalized nonlinear three-dimensional failure criterion based on fracture mechanics

Based on fracture mechanics theory and wing crack model,a three-dimensional strength criterion for hard rock was developed in detail in this paper.Although the basic expression is derived from initiation and propagation of a single crack,it can be extended to microcrack cluster so as to reflect the macroscopic failure characteristic.Besides,it can be derived as HoekeBrown criterion when the intermediate principal stress σ_(2) is equal to the minimum principal stress σ_(3)(Zuo et al.,2015).In addition,the opening direction of the microcrack cluster decreases with the increase of the intermediate principal stress coefficient,which could be described by an empirical function and verified by 10 kinds of hard rocks.Rock strength is influenced by the coupled effect of stress level and the opening direction of the microcrack clusters related to the stress level.As the effects of these two factors on the strength are opposite,the intermediate principal stress effect is induced.

Effective data sampling strategies and boundary condition constraints of physics-informed neural networks for identifying material properties in solid mechanics

Material identification is critical for understanding the relationship between mechanical properties and the associated mechanical functions.However,material identification is a challenging task,especially when the characteristic of the material is highly nonlinear in nature,as is common in biological tissue.In this work,we identify unknown material properties in continuum solid mechanics via physics-informed neural networks(PINNs).To improve the accuracy and efficiency of PINNs,we develop efficient strategies to nonuniformly sample observational data.We also investigate different approaches to enforce Dirichlet-type boundary conditions(BCs)as soft or hard constraints.Finally,we apply the proposed methods to a diverse set of time-dependent and time-independent solid mechanic examples that span linear elastic and hyperelastic material space.The estimated material parameters achieve relative errors of less than 1%.As such,this work is relevant to diverse applications,including optimizing structural integrity and developing novel materials.

Porosity, permeability and rock mechanics of Lower Silurian Longmaxi Formation deep shale under temperature-pressure coupling in the Sichuan Basin, SW China

To investigate the porosity, permeability and rock mechanics of deep shale under temperature-pressure coupling, we selected the core samples of deep shale from the Lower Silurian Longmaxi Formation in the Weirong and Yongchuan areas of the Sichuan Basin for porosity and permeability experiments and a triaxial compression and sound wave integration experiment at the maximum temperature and pressure of 120 ℃ and 70 MPa. The results show that the microscopic porosity and permeability change and the macroscopic rock deformation are mutually constrained, both showing the trend of steep and then gentle variation. At the maximum temperature and pressure, the porosity reduces by 34%–71%, and the permeability decreases by 85%–97%. With the rising temperature and pressure, deep shale undergoes plastic deformation in which organic pores and clay mineral pores are compressed and microfractures are closed, and elastic deformation in which brittle mineral pores and rock skeleton particles are compacted. Compared with previous experiments under high confining pressure and normal temperature,the experiment under high temperature and high pressure coupling reveals the effect of high temperature on stress sensitivity of porosity and permeability. High temperature can increase the plasticity of the rock, intensify the compression of pores due to high confining pressure, and induce thermal stress between the rock skeleton particles, allowing the reopening of shale bedding or the creation of new fractures along weak planes such as bedding, which inhibits the decrease of permeability with the increase of temperature and confining pressure. Compared with the triaxial mechanical experiment at normal temperature, the triaxial compression experiment at high temperature and high pressure demonstrates that the compressive strength and peak strain of deep shale increase significantly due to the coupling of temperature and pressure. The compressive strength is up to 435 MPa and the peak strain exceeds 2%, indicating that high temperature is not conducive to fracture initiation and expansion by increasing rock plasticity. Lithofacies and mineral composition have great impacts on the porosity, permeability and rock mechanics of deep shale. Shales with different lithologies are different in the difficulty and extent of brittle failure. The stress-strain characteristics of rocks under actual geological conditions are key support to the optimization of reservoir stimulation program.

Recent advances in the mechanics of 2D materials

The exceptional physical properties and unique layered structure of two-dimensional(2D)materials have made this class of materials great candidates for applications in electronics,energy conversion/storage devices,nanocomposites,and multifunctional coatings,among others.At the center of this application space,mechanical properties play a vital role in materials design,manufacturing,integration and performance.The emergence of 2D materials has also sparked broad scientific inquiry,with new understanding of mechanical interactions between 2D structures and interfaces being of great interest to the community.Building on the dramatic expansion of recent research activities,here we review significant advances in the understanding of the elastic properties,in-plane failures,fatigue performance,interfacial shear/friction,and adhesion behavior of 2D materials.In this article,special emphasis is placed on some new 2D materials,novel characterization techniques and computational methods,as well as insights into deformation and failure mechanisms.A deep understanding of the intrinsic and extrinsic factors that govern 2D material mechanics is further provided,in the hopes that the community may draw design strategies for structural and interfacial engineering of 2D material systems.We end this review article with a discussion of our perspective on the state of the field and outlook on areas for future research directions.

Trans-scale mechanics: looking for the missing links between continuum and micro/nanoscopic reality

Problems involving coupled multiple space and time scales offer a real challenge for conventional frame-works of either particle or continuum mechanics. In this paper, four cases studies （shear band formation in bulk metallic glasses, spallation resulting from stress wave, interaction between a probe tip and sample, the simulation of nanoindentation with molecular statistical thermodynamics） are provided to illustrate the three levels of trans-scale problems （problems due to various physical mechanisms at macro-level, problems due to micro-structural evolution at macro/micro-level, problems due to the coupling of atoms/ molecules and a finite size body at micro/nano-level） and their formulations. Accordingly, non-equilibrium statistical mechanics, coupled trans-scale equations and simultaneous solutions, and trans-scale algorithms based on atomic/molecular interaction are suggested as the three possible modes of trans-scale mechanics.

Preface: machine-learning approaches for computational mechanics

Machine-learning(ML) approaches have gained significant attention in recent years for their potential to revolutionize various scientific research fields,including computational mechanics,materials science,and biomedical engineering.In the field of computational mechanics,various neural network models such as feedforward neural networks,convolutional neural networks.

Mineralogy,microstructures and geomechanics of rock salt for underground gas storage

Rock salt has excellent properties for its use as underground leak‐proof containers for the storage of renewable energy.Salt solution mining has long been used for salt mining,and can now be employed in the construction of underground salt caverns for the storage of hydrogen gas.This paper presents a wide range of methods to study the mineralogy,geochemistry,microstructure and geomechanical characteristics of rock salt,which are important in the engineering of safe underground storage rock salt caverns.The mineralogical composition of rock salt varies and is linked to its depositional environment and diagenetic alterations.The microstructure in rock salt is related to cataclastic deformation,diffusive mass transfer and intracrystalline plastic deformation,which can then be associated with the macrostructural geomechanical behavior.Compared to other types of rock,rock salt exhibits creep at lower temperatures.This behavior can be divided into three phases based on the changes in strain with time.However,at very low effective confining pressure and high deviatoric stress,rock salt can exhibit dilatant behavior,where brittle deformation could compromise the safety of underground gas storage in rock salt caverns.The proposed review presents the impact of purity,geochemistry and water content of rock salt on its geomechanical behavior,and thus,on the safety of the caverns.

Deep-sea rock mechanics and mining technology:State of the art and perspectives

The review covers the development and the state of the art in deep-sea mining rock mechanics,equipment and challenges.It begins by introducing the significance of deep-sea mining,the types and geographical distribution of deep-sea resources.Section 2 reviews the mechanical properties and fracture mechanism of seabed and related continental rocks,which contributes to the advancement of relevant technologies and theories.Deep-sea mining systems developed by coastal countries are presented in Section 3.Seabed mineral collection systems are critically assessed in Section 4.Subsea mining vehicle is reviewed by walking mechanism and controlling system in Section 5.In Section 6,the development of subsea lifting system is detailed by dividing it into hydraulic and pneumatic lifting modes,and some technical problems in the lifting system are described.An in-depth description of surface support systems is presented in Section 7,which includes the deep-sea mining ship,dynamic positioning system,heave compensation system,launch and retrieval system,mineral disposing system as well as the storage and transferring systems.Section 8 discusses the challenges in the deep-sea mining,in terms of natural occurrence conditions,international legal framework and cooperative mining,environmental protection and economic benefits,etc.Finally,a brief summary and some aspects of prospective research are presented in Section 9.

Assembly and disassembly mechanics of a spherical snap fit

The snap fit is a common mechanical mechanism.We have studied the spherical snap fit carefully for its physical asymmetry,which is easy to assemble but difficult to disassemble.Because of the complexity of spherical snap fit,it is difficult to get a theoretical formula to describe its physical asymmetry.In this paper,the pushing assembly and pulling disassembly of spherical snap fit are studied by both finite element analysis and experiments.The theoretical formulaes of spherical snap fit have been obtained based on numerical simulations and theoretical results of cylindrical snap fit.

Machine learning in mechanics

Machine learning has attracted much attention in various fields of mechanics. It can represent high-dimensional complex nonlinear systems and has powerful optimization algorithms. So far, machine learning has achieved much success in various mechanical simulation problems, including reconstruction and reduced-order modeling of complex mechanical systems, turbulence modeling and simulation, aerodynamic optimization design for wings, flow control,etc.

Artificial boundary condition for Klein-Gordon equation by constructing mechanics structure

An innovative local artificial boundary condition is proposed to numerically solve the Cauchy problem of the Klein-Gordon equation in an unbounded domain.Initially,the equation is considered as the axial wave prop-agation in a bar supported on a spring foundation.The numerical model is then truncated by replacing the half-infinitely long bar with an equivalent mechanical structure.The effective frequency-dependent stiffness of the half-infinitely long bar is expressed as the sum of rational terms using Pade approximation.For each term,a corresponding substructure composed of dampers and masses is constructed.Finally,the equivalent mechan-ical structure is obtained by parallelly connecting these substructures.The proposed approach can be easily implemented within a standard finite element framework by incorporating additional mass points and damper elements.Numerical examples show that with just a few extra degrees of freedom,the proposed approach effec-tively suppresses artificial reflections at the truncation boundary and exhibits first-order convergence.

Recent advances in theoretical models of respiratory mechanics

As an important branch of biomedical engineering, respiratory mechanics helps to understand the physiology of the respiratory system and provides fundamental data for developing such clinical technologies as ventilators. To solve different clinical problems, researchers have developed numerous models at various scales that describe biological and mechanical properties of the respiratory system. During the past decade, benefiting from the continuous accumulation of clinical data and the dramatic progress of biomedical technologies （e.g. biomedical imaging）, the theoretical modeling of respiratory mechanics has made remarkable progress regarding the macroscopic properties of the respiratory process, complexities of the respiratory system, gas exchange within the lungs, and the coupling interaction between lung and heart. The present paper reviews the advances in the above fields and proposes potential future projects.

NANO SCIENCE AND ENGINEERING IN SOLID MECHANICS

According to National Science Foundation （NSF） Director A. Bement, ‘Transformative research is... research driven by ideas that stand a reasonable chance of radically changing our understanding of an important existing scientific concept or leading to the creation of a new paradigm or field of science is also characterized by its challenge to current understanding or its pathway to new frontiers.＇ Nanotechnology is one of such frontiers. It is the creation of new materials, devices and systems at the molecular level--phenomena associated with atomic and molecular interactions strongly influence macroscopic material properties with significantly improved mechanical, optical, chemical, electrical... properties. Former NSF Director Rita Colwell in 2002 declared, ‘nanoscale technology will have an impact equal to the Industrial Revolution＇. The transcendent technologies include nanotechnology, microelectronics, information technology and biotechnology as well as the enabling and supporting mechanical and civil infrastructure systems and materials. These technologies are the primary drivers of the twenty first century and the new economy. Mechanics is an essential eleraent in all of the transcendent technologies. Research opportunities, education and challenges in mechanics, including experimental, numerical and analytical methods in nanomechanics, carbon nano-tubes, bio-inspired materials, fuel cells, as well as improved engineering and design of materials are presented and discussed in this paper.

A Modified Molecular Structural Mechanics Method for Analysis of Carbon Nanotubes

A modified molecular structural mechanics method, based on molecular mechanics and similar to the finite element method, was developed. The energy of a system was expressed by the force field functions of the molecular mechanics. Under the small deformation assumption and by the principle of minimum potential energy, the system function was established. The properties of tension and bending of single-walled carbon nanotubes were analyzed. The Young＇s modulus is about 0.36 TPa nm, which agrees perfectly with the results of previous analysis by other researchers. It is found, for the first time, that the Young＇s moduli, for Zigzag nanotubes, are different from each other when the system energy was expressed as the sum of two or three individual energy terms in molecular mechanics. Whereas, the Young＇s moduli were the same for the Armchair nanotubes. It is found, when simulating the bending, that the deflections are closer to the theoretical ones, of the classical elasticity, when the diameter of the carbon nanotube increases.