Displacement Field Research Articles

Activation of Ms 6.9 Milin Earthquake on Sedongpu Disaster Chain, China with Multi-Temporal Optical Images

In recent years, disaster chains caused by glacier movements have occurred frequently in the lower Yarlung Tsangpo River in southwest China. However, it is still unclear whether earthquakes significantly contribute to glacier movements and disaster chains. In addition, it is difficult to measure the high-frequency and large gradient displacement time series with optical remote sensing images due to cloud coverage. To this end, we take the Sedongpu disaster chain as an example, where the Milin earthquake, with an epicenter 11 km away, occurred on 18 November 2017. Firstly, to deal with the cloud coverage problem for single optical remote sensing analysis, we employed multiple platform optical images and conducted a cross-platform correlation technique to invert the two-dimensional displacement rate and the cumulative displacement time series of the Sedongpu glacier. To reveal the correlation between earthquakes and disaster chains, we divided the optical images into three classes according to the Milin earthquake event. Lastly, to increase the accuracy and reliability, we propose two strategies for displacement monitoring, that is, a four-quadrant block registration strategy and a multi-window fusion strategy. Results show that the RMSE reduction percentage of the proposed registration method reaches 80%, and the fusion method can retrieve the large magnitude displacements and complete displacement field. Secondly, the Milin earthquake accelerated the Sedongpu glacier movement, where the pre-seismic velocities were less than 0.5 m/day, the co-seismic velocities increased to 1 to 6 m/day, and the post-seismic velocities decreased to 0.5 to 3 m/day. Lastly, the earthquake had a triggering effect around 33 days on the Sedongpu disaster chain event on 21 December 2017. The failure pattern can be summarized as ice and rock collapse in the source area, large magnitude glacier displacement in the moraine area, and a large volume of sediment in the deposition area, causing a river blockage.

Spin-orbit proximity in MoS2/bilayer graphene heterostructures

Van der Waals heterostructures provide a versatile platform for tailoring electronic properties through the integration of two-dimensional materials. Among these combinations, the interaction between bilayer graphene and transition metal dichalcogenides (TMDs) stands out due to its potential for inducing spin–orbit coupling (SOC) in graphene. Future devices concepts require the understanding of the precise nature of SOC in TMD/bilayer graphene heterostructures and its influence on electronic transport phenomena. Here, we experimentally confirm the presence of two distinct types of SOC – Ising (ΔI = 1.55 meV) and Rashba (ΔR = 2.5 meV) – in bilayer graphene when interfaced with molybdenum disulfide. Furthermore, we reveal a non-monotonic trend in conductivity with respect to the electric displacement field at charge neutrality. This phenomenon is ascribed to the existence of single-particle gaps induced by the Ising SOC, which can be closed by a critical displacement field. Our findings also unveil sharp peaks in the magnetoconductivity around the critical displacement field, challenging existing theoretical models.

Mesh topology-based spurious pressure stabilization in 3D finite elasticity using Voronoi tessellations

AbstractIn this paper, we present a mesh topology-based stabilization approach to suppress spurious pressure modes in 3D nearly-incompressible finite elasticity. The focus lies on a mixed formulation with lowest-order approximation for the displacement and pressure fields. Motivated by the fact that the popular H1/P0 element does not fulfill the inf-sup condition, all possible local spurious pressure modes are derived on a patch of elements. The nullspace method is used to determine all spurious pressure solutions. From this, the topological requirements of the finite element mesh are established. We conclude that no more than four elements are allowed to intersect in the same vertex to overcome local checkerboarding. To fulfill this requirement, we employ non-degenerate 3D Voronoi diagrams with several different site distributions. These result in random, centroidal, and honeycomb Voronoi meshes. The resulting convex polyhedral elements are discretized by a polyhedral mixed finite element based on the lowest possible interpolation pair. The numerical examples illustrate that spurious pressure modes do not occur for any degree of mesh refinement as long as the topological mesh requirements are met. Furthermore, it is shown that the numerical inf-sup test is passed. By violating the topological requirements, it is shown that a stable pressure field cannot be guaranteed and the checkerboard phenomenon is provoked.

The Method of the Natural Frequency of the Offshore Wind Turbine System Considering Pile–Soil Interaction

Accurately and efficiently evaluating the influence of pile–soil interaction on the overall natural frequency of wind turbines is one of the difficulties in current offshore wind power design. To improve the structural safety and reliability of the offshore wind turbine (OWT) systems, a new closed-form solution method of the overall natural frequency of OWTs considering pile–soil interactions with highly effective calculations is established. In this method, Hamilton’s principle and the equivalent coupled spring model (ECS model) were firstly combined. In Hamilton’s theory, the Timoshenko beam assumption and continuum element theory considering the three-dimensional displacement field of soil were used to simulate the large-diameter monopile–soil interaction under lateral load in multilayer soil. Case studies were used to validate the proposed method’s correctness and efficiency. The results show that when compared with the data of 13 offshore wind projects reported in existing research papers, the difference between the overall natural frequency calculated by the proposed method and that reported in this study is within ±10%. This calculation method achieves the goal of convenient, fast and accurate prediction of the overall natural frequency of offshore wind systems.

Experimental study on the compression and shear deformation evolution of coal pillar dam samples

To understand the mechanical properties and deformation failure patterns of coal pillar dams in gently inclined coal seam mine underground reservoirs, compression-shear coupling tests with variable angles were conducted on coal pillar dam samples under different saturation states. The digital image correlation (DIC) technique was utilized to obtain the deformation patterns of the displacement field throughout the compression-shear failure process of the samples. Numerical simulations were used to perform a comparative analysis and validation of the experimental results. The results indicated that the load-bearing capacity of the coal pillar dam samples decreased by 12.8–17.4% under water-saturated conditions. For every 5° increase in the inclination angle, the load-bearing capacity of the coal pillar dam samples decreased by an average of 3.53%. The normal stress and shear stress on the shear surface of the saturated samples were both lower than those of the natural samples, and both exhibited a linear variation with increasing inclination angle. The deformation evolution of the coal pillar dam samples under different test conditions exhibited similarity. The initial positive and negative displacement extremities in the horizontal direction were located at the lower right and upper left corners of the samples, respectively. Ultimately, the displacement field of the samples showed a pattern of smaller displacements at the top and larger displacements at the bottom, with negative values at the top and positive values at the bottom, distributed along the direction of the sample’s bedding. The saturated state and the increase in inclination both had a weakening effect on the load-bearing performance of the samples but had a relatively small impact on the differences in the displacement field deformation patterns. The research results can provide a reference for the study of the stability of coal pillar dams under similar conditions.

Investigation on fatigue damage of buton rock asphalt mixtures using semi-circular bending (SCB) and digital image correlation (DIC) techniques

The fatigue performance evaluation indices of Buton rock asphalt (BRA) modified asphalt mixture struggles to accurately characterize damage evolution process under repeated loads of the traffic. This study employs digital image correlation (DIC) technology to assess the fatigue behavior of BRA modified asphalt mixture, quantify the correlation between macroscopic response and local deformation, and verify the accuracy of evaluation indices. By capturing strain and displacement fields, the fatigue damage evolution of BRA modified asphalt is analyzed. Based on fracture mechanics theory, BRA’ s improvement of fatigue performance is quantified. Results show that vertical displacement captured by DIC can divide the three stages of fatigue cracking. The global horizontal strain(GExx)and cumulative horizontal strain(CExx) proposed in this study better characterize the nonlinear fatigue damage evolution compared to horizontal strain(Exx). Adding BRA delays crack initiation, reduces propagation rate, and enhances fatigue performance. Strain field evolution was quantitatively analyzed, and horizontal strain density(DE) and global horizontal strain density(GDE) were proposed as fatigue damage indicators. At the same load level, these indicators in BRA modified asphalt mixture, both pre- and post-aging, exceeded those of neat asphalt mixture. These findings provide a novel and accurate approach for evaluating the fatigue damage behavior of BRA modified asphalt mixture, laying the foundation for future performance-based designs.

Using the reverse geometry method for warpage compensation on changing meshes with interpolation methods

AbstractIn the manufacturing process of injection molding, the geometric accuracy of the produced part is affected by shrinkage and warpage. To support efforts to compensate for these effects, this paper presents an extension of the numerical compensation approach known as the reverse geometry method. The reverse geometry method is based on the numerical forward simulation of the displacement field resulting from shrinkage and warpage. It is an iterative method that performs node‐based compensation in each step. The mention of node‐based compensation already indicates that the method is associated with a computational mesh. In particular, in its basic version, it is linked to a specific mesh that must be kept identical during all iteration steps. This requirement is not always compatible with commercial simulation tools for injection molding, which enforce automatic remeshing between simulations. We present an interpolation method that allows to handle changing meshes and illustrate the method with two practical examples.

A novel framework for elucidating the effect of mechanical loading on the geometry of ovariectomized mouse tibiae using principal component analysis

IntroductionMurine models are used to test the effect of anti-osteoporosis treatments as they replicate some of the bone phenotypes observed in osteoporotic (OP) patients. The effect of disease and treatment is typically described as changes in bone geometry and microstructure over time. Conventional assessment of geometric changes relies on morphometric scalar parameters. However, being correlated with each other, these parameters do not describe separate fractions of variations and offer only a moderate insight into temporal changes.MethodsThe current study proposes a novel image-based framework that employs deformable image registration on in vivo longitudinal images of bones and Principal Component Analysis (PCA) for improved quantification of geometric effects of OP treatments. This PCA-based model and a novel post-processing of score changes provide orthogonal modes of shape variations temporally induced by a course of treatment (specifically in vivo mechanical loading).Results and DiscussionErrors associated with the proposed framework are rigorously quantified and it is shown that the accuracy of deformable image registration in capturing the bone shapes (∼1 voxel = 10.4 μm) is of the same order of magnitude as the relevant state-of-the-art evaluation studies. Applying the framework to longitudinal image data from the midshaft section of ovariectomized mouse tibia, two mutually orthogonal mode shapes are reliably identified to be an effect of treatment. The mode shapes captured changes of the tibia geometry due to the treatment at the anterior crest (maximum of 0.103 mm) and across the tibia midshaft section and the posterior (0.030 mm) and medial (0.024 mm) aspects. These changes agree with those reported previously but are now described in a compact fashion, as a vector field of displacements on the bone surface. The proposed framework enables a more detailed investigation of the effect of disease and treatment on bones in preclinical studies and boosts the precision of such assessments.

Fractional Viscoelastic Analysis of Transversely Isotropic Surrounding Rock Along Shallow Buried Elliptical Tunnel

ABSTRACTThis study introduces the fractional order Merchant model to analytically solve the stress and displacement fields of the transversely isotropic viscoelastic surrounding rock along shallow elliptical tunnels. First, the stress and displacement solutions of fractional order viscoelastic and transversely isotropic half planes under arbitrary loads are obtained using the Laplace transform and the elastic‐viscoelastic correspondence principle. Second, based on the above half plane solution and the solution of the deep buried elliptical tunnel problem, the Schwarz alternating method is introduced to obtain the analytical solution of the shallow buried elliptical tunnel. A MATLAB program is developed, and the accuracy of the theory and program in this study is verified by comparing it with the results of ABAQUS. Finally, the effects of transversely isotropic parameters, tunnel burial depth, and viscoelastic parameters on the stress and displacement of tunnel surrounding rock are analyzed.

An electro-elastic contact problem with an internal state variable

We consider a mathematical model which describes the quasistatic process of contact between a piezoelectric body and an electrically conductive foundation. General models for elastic materials with piezoelectirec effect, called electro-elastic materials. This paper is devoted to the study of the model involving a frictionless contact between an electro-elastic body characterized by long memory and a conductive adhesive foundation. The process is mechanically quasistatic and electrically static. We model the material with a general nonlinear electro-elastic constitutive law with internal state variable and the contact with normal compliance and unilateral constraint, where the adhesion is taken into account and a regularized electrical conductivity condition. The main feature of these models consists of the fact that their variational formulation is given by a history-dependent quasivariational inequality for the displacement field and a linear variational equation for the electric potential. A weak formulation for the model is given in the form of a coupled system for the displacement, the stress, the electric displacement, the electric potential, the bonding and the variable state internal fields. We derive a variational formulation for the problem and then, under a smallness assumption on the data, we prove the existence of a unique weak solution to the model. We also investigate the behavior of the solution with respect the electric data on the contact surface and prove its unique weak solution. The proof is based on nonlinear evolution equations with monotone operators, differential equations and Banach fixed point arguments.

Engineering band structures of two-dimensional materials with remote moiré ferroelectricity.

The stacking order and twist angle provide abundant opportunities for engineering band structures of two-dimensional materials, including the formation of moiré bands, flat bands, and topologically nontrivial bands. The inversion symmetry breaking in rhombohedral-stacked transitional metal dichalcogenides endows them with an interfacial ferroelectricity associated with an out-of-plane electric polarization. By utilizing twist angle as a knob to construct rhombohedral-stacked transitional metal dichalcogenides, antiferroelectric domain networks with alternating out-of-plane polarization can be generated. Here, we demonstrate that such spatially periodic ferroelectric polarizations in parallel-stacked twisted WSe2 can imprint their moiré potential onto a remote bilayer graphene. This remote moiré potential gives rise to pronounced satellite resistance peaks besides the charge-neutrality point in graphene, which are tunable by the twist angle of WSe2. Our observations of ferroelectric hysteresis at finite displacement fields suggest the moiré is delivered by a long-range electrostatic potential. The constructed superlattices by moiré ferroelectricity represent a highly flexible approach, as they involve the separation of the moiré construction layer from the electronic transport layer. This remote moiré is identified as a weak potential and can coexist with conventional moiré. Our results offer a comprehensive strategy for engineering band structures and properties of two-dimensional materials by utilizing moiré ferroelectricity.

Uncovering the Fracturing Mechanism of Granite Under Compressive–Shear Loads for Sustainable Hot Dry Rock Geothermal Exploitation

Shear-dominated hazards, such as induced earthquakes, pose an escalating threat to the sustainability and safety of the geothermal exploitation. Variations in fault orientations and compression–shear stress ratios exert a profound influence on the failure processes underlying these disasters. To better understand these effects on the shear failure mechanisms of hot dry rocks, mode-II fracturing tests on granites were conducted at varying loading angles (specifically, 55°, 60°, 65°, and 70°). These tests were accompanied by a comprehensive analysis of the mechanical properties, energy dissipation behavior, acoustic emission (AE) responses, and digital image correlation (DIC)-extracted displacement fields. The tensile–shear properties of stress-induced microcracks were discerned via AE characteristic parameter analysis and DIC displacement decomposition, and the mode-II fracture energy release rate was quantitatively characterized. The results reveal that with increasing compression–shear loading angles, the mechanical properties of granites are weakened, and the elastic strain energy at peak stress gradually decreases, while the slip-related dissipated energy increases. Throughout the fracturing process, the AE count progressively climbs and reaches a peak near catastrophic failure, with an upsurge in low-frequency and high-amplitude AE events. Microcrack distribution concentrates aggregation along the shear plane, reflecting the emergent displacement discontinuities evident in DIC contours. Both the AE characteristic parameter analysis and DIC displacement decomposition demonstrate that shear-sliding constitutes the paramount mechanism, and the fraction of shear-oriented microcracks and the ratio of tangential versus normal displacement escalate with increases in shear stress. This analysis is supported by the heightened propensity for transgranular microcracking events observed through scanning electron microscopy. As the shear-to-compression stress increases, the energy concentration along the shear band intensifies, with the gradient of the fitting line between cumulative AE energy and slip displacement steepening, indicative of a heightened mode-II energy release rate. These results contribute to a deeper understanding of the mode-II fracture mechanism of rocks, thereby providing a foundational basis for early warnings of shear-dominant geomechanical disasters, and improving the safety and sustainability of subsurface rock engineering.

Static and free vibration response of FGM plates using higher order shear deformation theory and strain-based finite element formulation

The primary objective and novelty of this work lie in the development of a new four-node quadrilateral finite element based on strain-based high-order shear deformation theory (HSDT). This is the first study to apply this innovative approach to analyze both the static and free vibration behaviors of functionally graded (FG) plates. Another key novelty is the reduction in the number of unknowns to five, unlike other high-order shear deformation theories that employ a larger number of unknowns. This reduction is achieved by applying the condition of zero transverse shear stress at the top and bottom free surfaces of the FG plate and by assuming that the transverse shear strains are sinusoidally distributed through the thickness. The material properties of FG plates are modeled to vary according to a simple power law based on the volume fractions of their constituents. The developed finite element possesses five degrees of freedom (DOFs) per node, resulting from the combination of two strain-based elements: the first is a membrane with two DOFs, and the second is a bending plate with three DOFs. The displacement fields of the proposed element are expressed using high-order terms based on the strain approach, which satisfy compatibility equations and rigid body modes. Furthermore, the concept of the neutral surface is introduced to eliminate membrane-bending coupling. The elementary stiffness and mass matrices are derived using both the total potential energy principle and Hamilton’s principle. The performance and convergence of the proposed element are validated through examples from the literature.

Early crack resistance and life cycle assessment of seawater-mixed sintered sludge cement paste

Due to the accelerating effect of chloride and sulfate on the hydration of clinker, seawater-mixed cement (SC) paste is more prone to brittle cracking. Herein, this research systematically investigates the early crack resistance of seawater-mixed sintered sludge cement (SSSC) paste based on splitting tensile test and restrained squared eccentric ring test. The microstructure characteristics characterized by mercury intrusion porosimetry and scanning electron microscopy are combined to reveal the enhancement mechanism of sintered sludge ash (SSA) on SC paste, and a life cycle assessment is conducted around its carbon footprint. The results indicate that the SSA incorporation causes a continuous increase of 24.4 % in the splitting tensile strength of SSSC paste. Meanwhile, the digital image correlation technology accurately captures the strain and displacement fields composed of crack propagation, which tends to be symmetrically distributed and reduces the crack width by 30 %. During the inhomogeneous restrained shrinkage process, as the SSA increases, the crack deviation of the SSSC paste first magnifies and then reduces, the crack width decreases, and the cracking time extends. The pozzolanic activity of SSA is more active in SC paste, which significantly promotes the secondary accumulation of C-S-H and the increase of gel pore volume. This effectively reduces the risk of brittle cracking caused by uneven distribution of paste stiffness due to hydration acceleration during seawater mixing. In addition, replacing 50 % cement with SSA only results in a total of 4.1 % carbon emissions in SSSC paste and a 47.8 % reduction in global warming potential from sludge transportation to activation treatment, demonstrating significant environmental advantages.

Size-dependency and lattice-discreetness effect on fracture toughness in 2D crystals under antiplanar loading

AbstractFracture toughness is the material property characterizing resistance to failure. Predicting its value from the solid structure at the atomistic scale remains elusive, even in the simplest situations of brittle fracture. We report here numerical simulations of crack propagation in two-dimensional fuse networks of different periodic geometries, which are electrical analogs of bidimensional brittle crystals under antiplanar loading. Fracture energy is determined from Griffith’s analysis of energy balance during crack propagation, and fracture toughness is determined from fits of the displacement fields with Williams’ asymptotic solutions. Significant size dependencies are evidenced in small lattices, with fracture energy and fracture toughness both converging algebraically with system size toward well-defined material-constant values in the limit of infinite system size. The convergence speed depends on the loading conditions and is faster when the symmetry of the considered lattice increases. The material constants at infinity obey Irwin’s relation and properly define the material resistance to failure. Their values are approached up to $$\sim 15\%$$ ∼ 15 % using the recent analytical method proposed in Nguyen and Bonamy (Phys Rev Lett 123:205503, 2019). Nevertheless, the deviation remains finite and does not vanish when the system size goes to infinity. We finally show that this deviation is a consequence of the lattice discreetness and decreases when the super-singular terms of Williams’ solutions (absent in a continuum medium but present here due to lattice discreetness) are taken into account.

A closed-form solution for thermally induced affine deformation in unbounded domains with a temporally accelerated anomalous thermal conductivity

Abstract One of the successful mathematical tools in the 21st century is the distributed-order fractional derivative, particularly, the bi-fractional diffusion equation of natural form (Chechkin, Gorenflo, and Sokolov, Phys. Rev. E 2002) and the bi-fractional diffusion equation of the modified form (Sokolov, Chechkin, and Klafter, Acta Phys. Pol. B 2004). The present study adopts the bi-fractional diffusion heat equation of the modified form that uses two Riemann-Liouville time-fractional derivatives with different fractional orders and the Riesz space-fractional derivative, and bears the property of variable thermal conductivity with temporal acceleration; i.e., the material thermal conduction transits from a low value at the small values of time ($t\to 0$) to a larger value at the long-time domain ($t\to \infty$). The corresponding fractional thermoelasticity theory, that uses the bi-fractional diffusion heat equation of the modified form, is exclusively considered in this work. For a quasi-static unbounded Hookean domain, exact solutions for the temperature, hydrostatic stress, and the displacement fields are derived in both short-time and long-time domains, in terms of the Fox \textit{H}-function. The exact solutions for the linearized problem are derived using the inversion of problem variables from the Laplace-Fourier space. Adding a zero initial condition on the normal stress of the unbounded space transforms the conventional Cauchy problem to a mixed initial-boundary value problem in order to derive a generalized form of the displacement. Additionally, thermal energy is not conserved in the presence of space fractality. The effect of such an accelerating transition in the thermal conduction on the displacement component is focused on, and it is found that the displacement inherits a similar transition behavior.

Engaging Data Literacies in Displacement

Data-driven humanitarianism is changing the face of aid. More data potentially enables quicker and more efficient evidence-based responses to situations of conflict and disaster. Yet the proliferation of data also challenges traditional lines of accountability, exacerbates the drive toward extractive relations and processes while deepening communication barriers and asymmetric relations between humanitarians and affected communities. This article reflects on critical data literacy as a transformative method in the context of the datafication of the humanitarian sector. It draws on research carried out with internally displaced persons (IDPs) in Nigeria and South Sudan as part of a collaborative international project examining the practice and ethics of data collection and use. The article discusses the project’s participatory ethos, its engagement of IDPs with the project over time and the importance of developing co-produced tools of critical data literacy together with IDPs. Reflecting on the significance of our findings for humanitarian practitioners as well as for academics working in the field of humanitarianism and displacement, the article argues for a collective commitment to engaging with affected communities while cautioning against viewing data literacy as an easy fix to empowerment challenges, both in the conduct of humanitarian work and in the implementation of research.

Strain-softening model for granite and sandstone based on experimental and discrete element methods

Combing macroscopic experimental method and mesoscopic numerical method, this study analyses the strain-softening behaviours of granite and sandstone. From the macroscopic perspective, the stress–strain curves of granite and sandstone under different confining pressures are studied by laboratory triaxial compression test. Variations of post-peak reduction modulus and critical plastic shear strain versus confining stress are obtained. Evolution of strength parameters at peak, residual and strain-softening stage are proposed. Then a method to develop the strain-softening model of hard and soft rocks is presented. From the mesoscopic perspective, based on the laboratory test results, the parameters of discrete element method PFC for the samples of the granite and sandstone are calibrated. Comparing the basically consistent results of laboratory experiment and numerical simulation, the feasibility of discrete element method is verified. Evolutions of mesoscopic crack propagation and mesoscopic particle displacement field in the complete failure process are analysed. Typical stresses of granite sample and sandstone sample in the failure stage are investigated. Above combined macroscopic experimental method and mesoscopic numerical method systematically analyse the characteristics of hard rock and soft rock in the strain-softening stage. Failure process and mechanical property of hard rock and soft rock are revealed at the macroscopic and mesoscopic levels. The initiation and propagation process of micro-cracks in rock are thoroughly investigated. The research results provide a scientific foundation for the analyse of strain-softening behaviour of hard rock and soft rock. The result shows that both the mesoscopic numerical method and macroscopic experimental method indicate that the failure pattern of sandstone is influenced by both confining pressure and axial stress, while granite is mainly affected by axial stress.

MorphFlow: Estimating Motion in In-Situ Tests of Concrete

Abstract Background In situ Computed Tomography is a valuable tool to investigate failure mechanics of materials in 3D. For brittle materials with sudden fracture like concrete however, state-of-the-art methods such as Digital Volume Correlation fail to produce displacement fields that display the discontinuous behavior of load induced cracking correctly. Objective The main objective is to develop an algorithm that calculates displacement fields for large-scale in situ experiments on concrete. Methods The algorithm presented is based on a 3D Optical Flow method solved by a primal-dual procedure and equipped with a coarse-to-fine scheme based on morphological wavelets. The algorithm is publicly available. Our evaluation focuses on the beneficial use of morphological wavelets over classical ones, and on the ability to produce reliable results with limited data. Applying the primal-dual scheme to in situ tests and using morphological wavelets are novel contributions. Results The results show that our algorithm cannot only cope with large volume images, but also produces discontinuous displacement fields that yield high strain in fractured regions. It does not only perform better than state-of-the-art methods, but also achieves sufficient results on reduced data. The morphological wavelets play a key role in this finding - they even allow to deduce cracks of widths less than a voxel. Conclusion Displacement calculation for in situ tests of brittle materials requires voxel-accurate displacement fields that allow for discontinuities. The presented algorithm fulfills these requirements and therefore is a powerful tool for future understanding of failure mechanics in concrete.

Active control for higher order micro sandwich beam with various cores integrated by piezoelectric layers based on MSGT on the Pasternak foundation

In the present article, the vibration suppression of higher order micro sandwich beams based on modified strain gradient beam theory (MSGT) and Reddy/Timoshenko beam theories is developed. Three types of core, including honeycomb, foam, and porous for a micro sandwich beam, are considered. The core’s top and bottom are integrated by piezoelectric layers as actuator and sensor, respectively. Displacement fields are defined via third-order shear deformation beam theory (TSDBT) (or Reddy beam theory (RBT)) and first-order shear deformation beam theory (FSDBT) (or Timoshenko beam theory (TBT)). The governing equations of motion are derived using MSGT to consider the small-scale effect. To optimal approaches for the controller, state feedback is designed based on a linear quadratic regulator (LQR) in the state-space form. Moreover, the effect of various parameters, including small-scale parameters, three types of core, temperature changes, Pasternak foundation, density of core, dimensionless cell thickness ([Formula: see text]), and internal aspect ratio ([Formula: see text]), angles ([Formula: see text]) of honeycomb, and the porosity parameter is performed on the active control of the smart micro sandwich beam. The numerical results indicate that the parameters mentioned significantly affect the optimal vibration control of the smart micro sandwich beam. It is found that the lightweight cores have more attenuation of the transient response and faster settling time. By analyzing the effect of temperature changes on active vibration control of lighter core, it was found that the frequency decreases as the temperature increases. Also, by considering the Pasternak foundation, it is found that the time period without considering the elastic foundation is longer than when considering the elastic foundation, and the natural frequency is vice versa. Also, the settling time by considering the elastic foundation occurs earlier. In the active control field of smart micro beams, this theoretical investigation developed widely as a benchmark for experimental research and the manufacturing process.