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Nanoindentation is a useful technique to measure material properties at microscopic level. However, the intrinsically multiscale nature makes it challenging for large-scale simulations to be carried out. It is shown that in molecular statics simulations of nanoindentation, the separated dislocation loops (SDLs) are trapped in simulation box which detrimentally affects the plastic behavior in the plastic zone (PZ); and the long-distance propagation of SDLs consumes much computational cost yet with little contribution to the variation of tip force. To tackle the problem, the dislocation loop erasing (DLE) method is proposed in the work to alleviate the influence of artificial boundary conditions on the SDL–PZ interaction and improve simulation efficiency. Simulation results indicate that the force–depth curves obtained from simulations with and without DLE are consistent with each other, while the method with DLE yields more reasonable results of microstructural evolution and shows better efficiency. The new method provides an alternative approach for large-scale molecular simulation of nanoindentation with reliable results and higher efficiency and also sheds lights on improving existing multiscale methods.

Unlike obviously topological defects in crystals, “defect” identification in metallic glasses (MGs) is still controversial and under investigation. Based on molecular simulations and analysis of MG samples, a structural parameter related to the Laplacian of local equivalent stiffness is proposed for prediction of localized shear deformation in MGs. It is found that local regions with the parameter of positive and relatively large value represent several particular modes of “stiffness valleys” in initial configuration which will strengthen local shear deformation and lead to the formation of shear transformation zones (STZs). More than 80% of the locations where STZs are formed in six types of MG samples under athermal quasi-static shear deformation match well with the regions predicted by the parameter calculated from initial configuration of the samples. The parameter not only reveals the relationship among local heterogeneity, nonaffine displacement, and shear localization, but also provides an efficient way for predicting the activation of STZs in MGs.

As a simple and robust minimization algorithm with high efficiency, the fast inertial relaxation engine (FIRE) method has been widely applied in various fields. Different from the viewpoint of previous reports, the present study found out that integration formulations in the FIRE method have huge influence on its convergence performance and capability of critical analysis. Specifically, the Forward Euler (FE) integration is found ill-suited for all the trial applications due to the outdated velocity update; the Velocity Verlet (VV) integration shows robust convergence and superior efficiency, but loses the ability of critical analysis; the Semi-implicit Euler (SE) integration endows the FIRE method with the critical analysis ability as well as good efficiency, but its convergence is conditional. It is also found that the FIRE method using a modified energy monitor shows more robust convergence than using the original power monitor. Further investigation indicates that the SE integration combined with the energy monitor should be the first choice for the FIRE method in general molecular statics simulations. These findings extend the capability of FIRE and provide practical suggestions for selecting minimization algorithms in molecular simulations.

Severe acute respiratory syndrome (SARS) is a serious disease with many puzzling features. We present a simple, dynamic model to assess the epidemic potential of SARS and the effectiveness of control measures. With this model, we analysed the SARS epidemic data in Beijing. The data fitting gives the basic case reproduction number of 2.16 leading to the outbreak, and the variation of the effective reproduction number reflecting the control effect. Noticeably, our study shows that the response time and the strength of control measures have significant effects on the scale of the outbreak and the lasting time of the epidemic.

The acceleration precursor of catastrophic rupture in rock-like materials is usually characterized by a power-law relationship, but the exponent exhibits a considerable scatter in practice. In this paper, based on experiments of granites and marbles under quasi-static uniaxial and unconfined compression, it is shown that the power-law exponent varies between −1 and −1/2. Such a changeable power-law singularity can be justified by the energy criterion and a power function approximation. As the power-law exponent is close to the lowest value of −1, rocks are prone to a perfect catastrophic rupture. Furthermore, it is found that the fitted reduced power-law exponent decreases monotonically in the vicinity of a rupture point and converges to its lower limit. Therefore, the upper bound of catastrophic rupture time is constrained by the lowest value of the exponents and can be estimated in real-time. This implies that, with the increase of real-time sampling data, the predicted upper bound of catastrophic rupture time can be unceasingly improved.

The comparative simulations of dislocation evolution in nanoindentation are carried out in terms of both molecular dynamics (MD) and energy minimization (EM) methods, to explore what really govern the computational efficiency and fidelity in molecular simulations relevant to dislocation evolutions. It is found that although all simulations can present similar relationship between indentation force and depth, there still might be some significant differences in the simulated dislocation patterns and computational efficiency. Firstly, the EM simulations show more complicated dislocations. Secondly, the necessary computational effort of EM increases nonlinearly with indentation depth, compared to the linear dependence in MD simulations, namely EM shows higher efficiency than MD in shallow indentation, but vice versa in deeper ones. More importantly, it is revealed that the time consumption of the minimization iteration is strongly dependent on the moving of dislocation loops and increases greatly when dislocation loops move long distances. Whereas MD simulations of complicated dislocations patterns may need less time cost but present immature dislocation evolutions, since the relaxation steps in MD simulations are fixed beforehand, regardless of the dislocation loops moving to equilibrium state or not. (C) 2017 Elsevier B.V. All rights reserved.

Polymer or glass films impregnated with quantum dots (QDs) have potential applications for mesoscale stress/strain sensing in the interior of materials under mechanical loading. One requirement in the development of such nanocomposite sensor materials is the establishment of calibrated relations between shifts in the emission spectrum of QD systems and the input stress/strain on the composites. Here, we use a multiscale computational framework to quantify the strain-dependent blueshift in the emission spectrum of CdTe QDs uniformly distributed in a matrix material under loading of a range of strain triaxiality. The framework, which combines the finite element method, molecular dynamics simulations and the empirical tight-binding method, captures the QD/matrix interactions, possible deformation-induced phase transformations and strain-dependent band structures of the QDs. Calculations reveal that the response of the QDs is strongly dependent on state of input strain. Under hydrostatic compression, the blueshift increases monotonically with strain. Under compression with lateral/axial strain ratios between 0.0 and 0.5, the blueshift initially increases, reaches a peak at an intermediate strain, and subsequently decreases with strain. This trend reflects a competition between increases in the energy levels associated with the conduction and valence bands of the QDs. The deformation-induced blueshift is also found to be dependent on QD orientations. The averaged blueshift over all orientations for the composite under uniaxial strain condition explains the blueshift variation trend observed in laser-driven shock compression experiments. Based on the simulation result, guidelines for developing QD composites as stress/strain sensing materials are discussed.

In numerous cases, the failure of disordered heterogeneous brittle media under external loading emerges as an abrupt, unstable transition of evolution mode from the globally stable accumulation of microdamages to catastrophic rupture. The microdamages are initiated at the atomic scale, then they display inverse cascade from smaller scales to larger scales presenting a coupling process across multiple scales.

Broadly speaking, all macroscopically time-dependent processes may result from the evolution of various microstructures as shown in the figures at the very beginning of this chapter.

Roughly speaking, mechanics seems to be a mature discipline, however, so far the conventional mechanics still can not give answers to a number of practical problems, such as

A new type of quaternary D flip-flop based on multiple-valued current-mode is presented for high-speed sequential circuit in VLSI systems. It employs master-slave mode and dynamic multiple-valued source-coupled logic. A distinguishable multiple-valued interval, fast switch speed and compact structure are obtained by combining source-coupled logic with differential-pair circuit. The performance evaluation is carried out with HSPICE using 0.18μm CMOS process. A performance comparison with those issued in some references is conducted. The delay in our design is about 74% reduced by comparison with the corresponding binary implementation. The circuitry proposed is simplicity, regularity, and modularity, so well suited for VLSI implementation. Quaternary logic seems to be a potential and feasible method of high-performance VLSI systems.

GaAs is brittle at room temperature at the macro-scale; however, ductility emerges when its characteristic dimension reduces to the nano-scale. Using molecular dynamics simulations, we reveal that there is a brittle-to-ductile transition in GaAs nano-rods due to the competition between generation of cracks and initiation of dislocations. Such a competition is sensitive to aspect ratios of nano-rods. These results well explain experimentally observed ductility of GaAs nano-rods and have important implications for the design of semiconductor materials with tailored mechanical properties. (C) 2015 Elsevier Ltd. All rights reserved.

Although it has been well known that hardness of metals obtained with conical indenter remains a constant of about 3 times yield strength in conventional tests, and hardness will show a size effect of increasing hardness with decreasing indentation depth in micro-scale beyond 100 nm, the nano-indentation hardness experiments within 100 nm indentation depth usually show a large deviation and unclear trends. We report the cross-validated experimental and numerical results of two opposite depth-dependences of hardness at real nano-scale. That is to say, the indentation size effect (ISE) of hardness of single-crystal copper shows a rapid increase and then a slow decrease with increasing indentation depth within 100 nm depth. All of the results were coss-checked by means of both elaborated nano-indentation experiments with calibrated indenter tips and large scale molecular dynamics (MD) simulations. Further analysis of the MD results and experimental data reveal that the two opposite ISE of nano-hardness should be attributed to the finite roundness of the indenter tip and the intrinsic transition governing property of the material.

The strain rate dependency of materials’ failure has been widely observed in experiments and simulations, yet its microscopic mechanism is still elusive due to the complexity of failure processes. In this work, modified molecular dynamics simulations are carried out to investigate the strain rate effect over a wide strain rate range. The results demonstrate three typical failure modes induced by the competition of two timescales involved. The transition of mechanisms underlying these failure modes is discussed with a simplified model. The corresponding analysis indicates that the thermal activation model offers a good prediction for the variation of failure strain with respect to applied strain rate for failure mode I; the coupled evolution of atomic motions and potential landscapes governs the failure mode II; and the failure mode III is a result of the rapid separation between loading and deformation parts of the sample.

Since rate effect of materials plays a key role in impact engineering, the microscopic mechanism of rate effect is investigated at molecular level in this paper. The results show that rate effect on the strength of atomic system is closely related to the coupled evolution of atomic motions and potential landscapes. Accordingly, it becomes possible to develop a new algorithm of molecular simulation, which could properly and efficiently demonstrate strain rate effect under a wide range of loading rates and unveil the mechanisms underlying the strain rate effects.

This paper briefly reviews our recent analytical and experimental results on 3 interrelated features beyond the peak load in heterogeneous media: continuous bifurcation, damage localization and catastrophic rupture (CR). Firstly, an Elastic Statistically-Brittle model (ESB) was introduced to formulate the basic features of a kind of heterogeneous media, like rocks and cements. The global mean field approximation (GMF) shows that the measure of heterogeneity, like the Weibull modulus m in the distribution of meso-strength plays a key role to distinguish CR from gradual failure. Then, with the ESB model and corresponding experimental results, continuous bifurcation and damage localization are discussed. In accord with these, regional mean field approximation (RMF) is adopted and it shows that any scale of damage localization can satisfy the conservation laws in continuum mechanics. This implies that catastrophic rupture could appear at any state beyond the peak load, depending on the unknown evolution of damage localization zone. Hence, catastrophic rupture seems to occur stochastically at macroscopic level. On the other hand, both experimental and analytic studies demonstrate that a robust power law singularity (-1/2) appears ahead of CR. Preliminary applications of these ideas are briefly described.

Molecular dynamics simulations are performed to investigate a spontaneous self-healing process in fractured GaAs nanowires with a zinc blende structure. The results show that such self-healing can indeed occur via rebonding of Ga and As atoms across the fracture surfaces, but it can be strongly influenced by several factors, including wire size, number of healing cycles, temperature, fracture morphology, oriented attachment and atomic diffusion. For example, it is found that the self-healing capacity is reduced by 46% as the lateral dimension of the wire increases from 2.3 to 9.2 nm, and by 64% after 24 repeated cycles of fracture and healing. Other factors influencing the self-healing behavior are also discussed.

Oxygen vacancy, a kind of native point defects in ferroelectric ceramics, usually causes an increase of the dielectric loss. Based on experimental observations, it is believed that all of the oxygen vacancies are an unfavorable factor for energy saving. By using molecular dynamics simulations, we show that the increase of coercive and saturated electric fields is due to the difficulty to switch local polarization near an oxygen vacancy, and so that a ferroelectric device has to sustain the rising consumption of energy. The simulation results also uncover how oxygen vacancies influence ferroelectric properties.

This paper briefly reviews a distinct and efficient numerical approach to quasi-static analysis of nanomaterials at finite temperature: molecular statistical thermodynamics (MST), especially its various applications and efficiency. Different from molecular dynamics (MD) based on Newton equations, MST is a half-analytical numerical method based on the minimization of Helmholtz free energy. The applications of MST to compression of nanorods, nanoindentations and tension of nanowires show that MST is capable of characterizing the nucleation, propagation and interaction of dislocations as well as phase transformations involved in quasi-static deformations. Not only the mechanical responses and properties calculated with MST are in agreement with MD simulations, but the size effect of Young’s modulus of zinc oxide nanowires calculated with MST are also in good consistency with experimental results. All these results justify the reliability of MST. Furthermore, the efficiency analysis indicates that MST is dramatically faster than MD for quasi-static processes and is expected to be capable of simulating nanomaterials at larger scales with high efficiency.

“Off the Pacific coast of Tohoku Earthquake” (M9.0, on March 11th, 2011) is the greatest one in Japanese seismic record. The hypocenter is located 130 km ESE off the Pacific coast of Tohoku with the focal depth of 24 km. The quake-triggered tsunami afterward seriously damaged the nuclear reactors and caused severe consequences to the society [1]. The main shock of the Tohoku Earthquake lasted for about 140 s [2] and hundreds of aftershocks occurred during the next couple of days [1]. On March 25th, 2011, Okada, the president of NESC, gave a preliminary report on the earthquake as follows [1]. This earthquake is of thrust type, caused by the rebound of a continental plate (North American) against a subducting oceanic plate (Pacific) at the Japan Trench. The rupture (offset of rock) is initiated from a hypocenter and spreads to make a planar cut surface. But, the gigantic energy of M9.0 earthquake was never radiated only from the hypocenter and the amount of offset determines the magnitude of the earthquake [1]. If so, what specific amount of rock offset the gigantic energy comes from and how large the relevant region is become the two key issues in understanding the earthquake. According to our experimental and theoretical study of catastrophic rupture in heterogeneous media, such as rocks, catastrophic rupture should be a self-sustainable process. That is to say, during a catastrophic rupture, the elastic energy released from the unloading zone should afford all dissipations in the rupture, including the dissipation in rupture zone, radiating stress waves, etc. [3–5]. In this paper, based on the GPS observations available now, the distribution of co-seismic incremental strains are reconstructed first, and then the elastic energy released from an unloading region is calculated and compared to the energy involved in seismic waves. The comparison of the two energies is in reasonable agreement and the reconstructed incremental strain field clearly highlights the region, which makes the major contribution to the earthquake.

Hybrid molecule/cluster statistical thermodynamics (HMCST) method is an efficient tool to simulate nano-scale systems under quasi-static loading at finite temperature. In this paper, a self-adaptive algorithm is developed for this method. Explicit refinement criterion based on the gradient of slip shear deformation and a switching criterion based on generalized Einstein approximation is proposed respectively. Results show that this self-adaptive method can accurately find clusters to be refined or transferred to molecules, and efficiently refine or transfer the clusters. Furthermore, compared with fully atomistic simulation, the high computational efficiency of the self-adaptive method appears very attractive.

Instrumented indentation is a method that has been widely used to obtain material properties at micro and nano scale, yet creditable indentation size effect at real nano-scale and its mechanism are still unsolved. This paper summarizes our recent work on progresses in experimental and simulation approaches to this problem. By confirming the crystalline orientations and the surface roughness of the sample, obtaining the tip radius of the indenters, as well as considering tip radius in large-scale molecular simulation, the gap between the experiment and simulation results is bridged, and these two results can be cross verified with each other, which leads to a reliable hardness trend over the indentation depth at nano-scale. Two opposite size effects are observed, and their different mechanisms are revealed, as the conventional size effect results from the plastic behavior such as dislocation nucleation and propagation in the sample beneath the indenter, while the initial reverse size effect is due to the combined effect of the indenter roundness and elastic behavior of the material. Systematic investigation on the efficiency and fidelity of MD and MS is carried out, on problem of the dislocation evolution during indentation, the influence of the relaxation time and convergence resolution on the load curve and dislocation patterns are studied, and suggestion on choice of two simulation methods and the relaxation time and convergence resolution are given.

Evolution of localized damage zone is a key to catastrophic rupture in heterogeneous materials. In the present article, the evolutions of strain fields of rock specimens are investigated experimentally. The observed evolution of fluctuations and autocorrelations of strain fields under uniaxial compression demonstrates that the localization of deformation always appears ahead of catastrophic rupture. In particular, the localization evolves pronouncedly with increasing deformation in the rock experiments. By means of the definition of the zone with high strain rate and likely damage localization, it is found that the size of the localized zone decreases from the sample size at peak load to an eventual value. Actually, the deformation field beyond peak load is bound to suffer bifurcation, namely an elastic unloading part and a continuing but localized damage part will co-exist in series in a specimen. To describe this continuous bifurcation and localization process observed in experiments, a model on continuum mechanics is developed. The model can explain why the decreasing width of localized zone can lead stable deformation to unstable, but it still has not provided the complete equations governing the evolution of the localized zone.

Recently, people are confused with two opposite variations of elastic modulus with decreasing size of nano scale sample: elastic modulus either decreases or increases with decreasing sample size. In this paper, based on intermolecular potentials and a one dimensional model, we provide a unified understanding of the two opposite size effects. Firstly, we analyzed the microstructural variation near the surface of an fcc nanofilm based on the Lennard-Jones potential. It is found that the atomic lattice near the surface becomes looser in comparison with the bulk, indicating that atoms in the bulk are located at the balance of repulsive forces, and the elastic moduli decrease with the decreasing thickness of the film accordingly. In addition, the decrease in moduli should be attributed to both the looser surface layer and smaller coordination number of surface atoms. Furthermore, it is found that both looser and tighter lattice near the surface can appear for a general pair potential and the governing mechanism should be attributed to the surplus of the nearest force to all other long range interactions in the pair potential. Surprisingly, the surplus can be simply expressed by a sum of the long range interactions and the sum being positive or negative determines the looser or tighter lattice near surface respectively. To justify this concept, we examined ZnO in terms of Buckingham potential with long range Coulomb interactions. It is found that compared to its bulk lattice, the ZnO lattice near the surface becomes tighter, indicating the atoms in the bulk are located at the balance of attractive forces, owing to the long range Coulomb interaction. Correspondingly, the elastic modulus of one-dimensional ZnO chain increases with decreasing size. Finally, a kind of many-body potential for Cu was examined. In this case, the surface layer becomes tighter than the bulk and the modulus increases with deceasing size, owing to the long range repulsive pair interaction, as well as the cohesive many-body interaction caused by the electron redistribution.

In this paper, some basic mechanical behaviors of bulk metallic glasses (BMGs) were discussed. It can be found from the discussions that the mechanical behaviors of BMGs are mainly due to the formation and operation of shear bands in BMGs. Furthermore, the relevant mechanics of shear banding were investigated in the paper. The theoretical analysis of deformation coupling thermal softening and free volume creation softening demonstrates that the free volume creation and thermal softening can jointly promote the formation of shear bands in BMGs, and the observed post mortem. shear band width looks more like that governed by free volume creation. (C) 2007 Elsevier Ltd. All rights reserved.

The microstructural heterogeneity and stress fluctuation play important roles in the failure process of brittle materials. In this paper, a generalized driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. As an illustration, the failure process of cement material under explosive loading is analyzed using the model. The result agrees well with the experimental one, which proves the efficiency of the model.

Investigations made by the authors and collaborators into the microstructural aspects of adiabatic shear localization are critically reviewed. The materials analyzed are low-carbon steels, 304 stainless steel, monocrystalline Fe-Ni-Cr, Ti and its alloys, Al-Li alloys, Zircaloy, copper, and Al/SiCp composites. The principal findings are the following: (a) there is a strain-rate-dependent critical strain for the development of shear bands; (b) deformed bands and white-etching bands correspond to different stages of deformation; (c) different slip activities occur in different stages of band development; (d) grain refinement and amorphization occur in shear bands; (e) loss of stress-carrying capability is more closely associated with microdefects rather than with localization of strain; (f) both crystalline rotation and slip play important roles; and (g) band development and band structures are material dependent. Additionally, avenues for new research directions are suggested.

Thoroughly understanding AFM tip-surface interactions is crucial for many experimental studies and applications. It is important to realize that despite its simple appearance, the system of tip and sample surface involves multiscale interactions. In fact, the system is governed by a combination of molecular force (like the van der Waals force), its macroscopic representations (such as surface force) and gravitational force (a macroscopic force). Hence, in the system, various length scales are operative, from sub-nanoscale (at the molecular level) to the macroscopic scale. By integrating molecular forces into continuum equations, we performed a multiscale analysis and revealed the nonlocality effect between a tip and a rough solid surface and the mechanism governing liquid surface deformation and jumping. The results have several significant implications for practical applications. For instance, nonlocality may affect the measurement accuracy of surface morphology. At the critical state of liquid surface jump, the ratio of the gap between a tip and a liquid dome (delta) over the dome height (y(o)) is approximately (n-4) (for a large tip), which depends on the power law exponent n of the molecular interaction energy. These findings demonstrate that the multiscale analysis is not only useful but also necessary in the understanding of practical phenomena involving molecular forces. (c) 2007 Elsevier Ltd. All rights reserved.

Molecular dynamics (MD) simulations are carried out to analyze the diffusion bonding at Cu/Al interfaces. The results indicate that the thickness of the interfacial layer is temperature-dependent, with higher temperatures yielding larger thicknesses. At temperatures below 750 K, the interface thickness is found to increase in a stepwise manner as a function of time. At temperatures above 750 K, the thickness increases rapidly and smoothly. When surface roughness is present, the bonding process consists of three stages. In the first stage, surfaces deform under stress, resulting in increased contact areas. The second stage involves significant plastic deformation at the interface as temperature increases, resulting in the disappearance of interstices and full contact of the surface pair. The last stage entails the diffusion of atoms under constant temperature. The bonded specimens show tensile strengths reaching 88% of the ideal Cu/Al contact strength.

Geological sequestration of CO2 (carbon dioxide) shows great potential to reduce Greenhouse gas emissions. However, CO2 injection into geological formations may give rise to a variety of coupled chemical and physical processes. The thermo-hydro-mechanical (THM) impact of CO2 injection can induce fault instability, even possibly lead to seismic activities in and around the disposal reservoir. A sequential coupling approach under some assumptions was proposed in the numerical study to investigate the THM behavior of the CO2 sequestration system concerning the temperature, initial geological stress, injection pressure and CO2 buoyancy. The fault was treated as a flexible contact model. The effects of CO2 injection on the mechanical behavior of the faults were investigated. The Drucker-Prager model and the cap model were used to model the constitutive relationship of formations. The numerical results show that injection pressure sensitively affects the relative slip change of the fault. At the initial stage of the sequestration process, the injection pressure plays a key role in affecting the pore pressure of the formations. However, as time continues, the influence of CO2-induced buoyancy becomes obvious on the pore pressure of the formations. In general, The THM effects of CO2 geosequestration do not affect the mechanical stability of formations and faults.

It is of utmost importance to understand the spallation behaviour of heterogeneous materials. In this paper, a driven nonlinear threshold model with stress fluctuation is presented to study the effects of microstructural heterogeneity on continuum damage evolution. The spallation behavior of heterogeneity material is analyzed with this model. The heterogeniety of mesoscopic units is characterized in terms of Weibull modulus m of strength distibution and stress fluctuation parameter k. At high stress, the maximum damage increases with m; while at low stress, the maximum damage decreases. In addition, for low stress, severe stress fluctuation causes higher damage; while for high stress, causes lower damage.

The process of damage evolution concerns various scales, from micro- to macroscopic. How to characterize the trans-scale nature of the process is on the challenging frontiers of solid mechanics. In this paper, a closed trans-scale formulation of damage evolution based on statistical microdamage mechanics is presented. As a case study, the damage evolution in spallation is analyzed with the formulation. Scaling of the formulation reveals that the following dimensionless numbers: reduced Mach number M, damage number S, stress wave Fourier number Ψ, intrinsic Deborah number D*, and the imposed Deborah number De*, govern the whole process of deformation and damage evolution. The evaluation of Ψ and the estimation of temperature increase show that the energy equation can be ignored as the first approximation in the case of spallation. Hence, apart from the two conventional macroscopic parameters: the reduced Mach number M and damage number S, the damage evolution in spallation is mainly governed by two microdamage-relevant parameters: the Deborah numbers D* and De*. Higher nucleation and growth rates of microdamage accelerate damage evolution, and result in higher damage in the target plate. In addition, the mere variation in nucleation rate does not change the spatial distribution of damage or form localized rupture, while the increase of microdamage growth rate localizes the damage distribution in the target plate, which can be characterized by the imposed Deborah number De*.

Trans-scale coupling plays a significant role in multiscale problems. Since the mechanisms governing the trans-scale coupling vary from case to case, to identify and characterize the governing mechanisms of trans-scale coupling are the most crucial points in multiscale simulations. The failure of solid media is a typical multiscale process. This paper chooses two model problems, i.e., damage localization in spallation of an Al alloy and the catastrophe transition in a rock under quasi-static loading, to illustrate the trans-scale coupling in different phases of material failure. In the spallation process the governing mechanism of trans-scale effects is the coupling and competition between dynamics at different levels, which can be effectively characterized by two imposed Deborah numbers. In the catastrophe failure of heterogeneous media the governing mechanism of trans-scale coupling is the strong and sensitive coupling between the nonlinear dynamics and the disordered heterogeneity. In addition, the inverse cascade of damage evolution magnifies the effects of microstructures on failure and induces trans-scale sensitivity. Although the concept of critical sensitivity seems to be promising in catastrophe prediction, novel concepts and numerical schemes are still badly needed.