Learning material law from displacement fields by artificial neural network

The recently developed data-driven approach can establish the material law for nonlinear elastic composite materials(especially newly developed materials)by the generated stress-strain data under different loading paths(Computational Mechanics,2019).Generally,the displacement(or strain)fields can be obtained relatively easier using digital image correlation(DIC)technique experimentally,but the stress field is hard to be measured.This situation limits the applicability of the proposed data-driven approach.In this paper,a method based on artificial neural network(ANN)to identify stress fields and further obtain the material law of nonlinear elastic materials is presented,which can make the proposed data-driven approach more practical.A numerical example is given to prove the validity of the method.The limitations of the proposed approach are also discussed.

3-D rheologic model of earthquake preparation (I)—Displacement field

Based on the three-dimensional ela stic inclusion model proposed by Dobrovolskii, we developed a three-dimensional rheologic inclusion model and theory to study the earthquake preparation process. By using correspondence principle in the theory of rheologic mechanics, we derived the analytic expression of the viscoelas-tic displacement at an arbitrary point (x, y, z) in three directions of x, y and z-axes (i. e., U(r, t), V*(r, t) and W(r, t)) produced by a three-dimension inclusion in the semi-infinite rheologic medium defined by the standard linear rheologic model.

THE APPLICATION OF MOIRE INTERFEROMETRY IN THE MEASUREMENT OF DISPLACEMENT FIELD AND STRAIN FIELD AT NOTCH-TIP AND CRACK-TIP

This paper presents the application of Moire interferometry in measuring the displacement and strain field at notch-tip and crack-tip before and after crack propagation.The experiment is carried out using a three point bending beam with a notch.The N_x and N_y fringe patterns representing displacement field,and the ΔN_x/Δx and ΔN_y/Δy fringe patterns representing the strain field are obtained.The sensitivity of the meas- ured displacement is 0.417μm per fringe order.The displacement and strain distribution along the section x=0 have been worked out according to N_x and N_y fringe patterns.

Processes of the displacement field change of the 2009 April 6 M_W6.3 L'Aquila earthquake using persistent scatterer and small baseline methods

Using a time series method that combines both the persistent scatterer and small baseline approaches, we analyzed 9 scenes Envisat ASAR data over the L＇Aquila earthquake, and obtained a Shocke＇s displacement field and its evolution processes. The results show that： （1） Envisat ASAR clearly detected the whole processes of displacement field of the L＇Aquila earthquake, and distinct variations at different stages of the displacement field. （2） Preseismic creep displacement → displacement mutation when faulting → constantly slowed down after the earthquake. （3） The area of the strongest deformation and ground rupture was a low-lying oval depression region to the southeast. Surface faulting within a zone of about 22 km× 14 km, with an orientation of 135°, occurred along the NW-striking and SW-dipping Paganica-S. Demetrio normal fault. （4） In analyzing an area of about 54 km x 59 km, bounded by north-south axis to the epicenter, the displacement field has significant characteristics of a watershed： westward of the epicenter shows uplift with maximum of 130 mm in line-of-sight （LOS）, and east of the epicenter was a region with 220 mm of maximum subsidence in the LOS, concentrating on the rupture zone, the majority of which formed in the course of faulting and subsequence.

Study on displacement field generated by aftershocks in Landers earthquake fault zone and its adjacent areas

The displacement field generated by aftershocks in Landers earthquake fault zone and its adjacent areas is calculated in this study. The result is compared with the displacement field of the main shock calculated by co-seismic slip model of Wald and Heaton (1994). The result shows that the direction of displacement generated by aftershocks in Landers seismic fault plane and its adjacent areas is consistent with that generated by main shock. The rupture of aftershock is generally inherited from main shock. The displacement generated by aftershocks is up to an order of centimeter and can be measured by GPS sites nearby. So when we use geodetic data measured after earthquake to study the geophysical problems such as crustal viscosity structure, afterslip distribution, etc., only the displacement field generated by aftershocks considered, can uncertainty be reduced to minimum and realistic result be obtained.

MEASUREMENT OF WELDING DYNAMIC DISPLACEMENT FIELDS BY ELECTRONIC SPECKLE PATTERN INTERFERENCE

In order to effectively control the stress and distortion which produced in welding process, the dynamic change laws of displacement field is the most important factor. The characteristics of the welding dynamic displacement field is high temperature, high strain velocity, thus ordinary methods such as resistance strain gauge or Moiré method can not be used for the measurement of the zone of high temperature. Speckle interference method has the merits of non-contact, resistance to the disturbance of impure lights, high accuracy of measurement (half of wavelength).The paper represents the measurement of dynamic displacement field of argon-arcspot welding, by which it shows that the method of speckle interference is feasible for the measurement of welding dynamic displacement.

Analyis on the indirect tension displacement and strain field of asphalt mixture based on ABAQUS and DICM

In order to study the damage mechanism of asphalt mixture,it is important to obtain the distribution of displacement and strain of its sample in the indirect tension mode.As a result,the digital image correlation method (DICM) was used to evaluate the displacement field and strain field of asphalt mixture.The results showed that the displacement fields under DICM and ABAQUS are similarly;the strain fields are different due to the different modulus of mastic and aggregate;and DICM is an practical method to study the indirect tension displacement and stain.

Ultrasonic displacement field generated by laser pulse line source

Applying the Fourier transform to the wave equations of elastic medium at its surface a laser pulse line source is acted, the integral representations of solutions are obtained. Displacement waveforms are calculated numerically by using double FFT. The calculated results include the displacements of the elastic half space of Aluminum medium, and epicenter and off-epicenter of an Aluminum plate. The two exciting sources of thermoelastic and ablating generation are considered respectively. The experiment was made on the Aluminum medium with a Nd:YAG laser and the normal displacement signals are detected by a laser interferometer. The numerical results are quite in agreement with experiments.

Nonlinear Transient Response of Functionally Graded Material Sandwich Doubly Curved Shallow Shell Using New Displacement Field

In this paper, the nonlinear transient dynamic response of functionally graded material （FGM） sandwich doubly curved shell with homogenous isotropic material core and functionally graded face sheet is analyzed using a new displacement field on the basis of Reddy＇s third-order shear theory for the first time. The equivalent material properties for the FGM face sheet are assumed to obey the rule of simple power law function in the thickness direction. Based on Reddy＇s theory of higher shear deformation, a new displacement field is developed by introducing the secant function into transverse displacement. Four coupled nonlinear differential equations are obtained by applying Hamilton＇s principle and Galerkin method. It is assumed that the FGM sandwich doubly curved shell is subjected to step loading, air-blast loading, triangular loading, and sinusoidal loading, respectively. On the basis of double-precision variable- coefficient ordinary differential equation solver, a new program code in FORTRAN software is developed to solve the nonlinear transient dynamics of the system. The influences of core thickness, volume fraction, core-to-face sheet thickness ratio, width-to-thickness ratio and blast type on the transient response of the shell are discussed in detail through numerical simulation.

Displacement Field due to Nonuniform Slip along a Long Dip-Slip Fault in Two Welded Half-Spaces

The solution of static deformation of two homogeneous, isotropic, and perfectly elastic half-spaces in welded contact due to a long dip-slip fault with uniform slip is well known. The aim of the present article is to obtain the static deformation of two homogeneous, isotropic, and perfectly elastic half-spaces in welded contact due to nonuniform slip along a long dip-slip fault. The fault is vertical and lies entirely in the lower half-space, extending up to the interface. Four slip profiles are considered： lin- ear, parabolic, elliptic, and cubic. Closed-form expressions for the elastic residual field have been ob- tained for the different slip profiles. The displacement field due to four nonuniform slip profiles is com- pared with the displacement field due to uniform slip. For comparison, we have assumed the source potency for different slip profiles to be the same, which is achieved by taking the fault slip at the inter- face constant and varying the fault width. It is found that the displacement field varies significantly at the fault width rather than at the interface. Moreover, uniform slip along the fault makes the edges singular. This singularity at the lower edge is not present in the case of nonuniform slip along a long dip-slip fault.

Determination of the full-field stress and displacement using photoelasticity and sampling moirémethod in a 3D-printed model

The quantitative characterization of the full-field stress and displacement is significant for analyzing the failure and instability of engineering materials.Various optical measurement techniques such as photoelasticity,moiréand digital image correlation methods have been developed to achieve this goal.However,these methods are difficult to incorporate to determine the stress and displacement fields simultaneously because the tested models must contain particles and grating for displacement measurement;however,these elements will disturb the light passing through the tested models using photoelasticity.In this study,by combining photoelasticity and the sampling moirémethod,we developed a method to determine the stress and displacement fields simultaneously in a three-dimensional(3D)-printed photoelastic model with orthogonal grating.Then,the full-field stress was determined by analyzing 10 photoelastic patterns,and the displacement fields were calculated using the sampling moirémethod.The results indicate that the developed method can simultaneously determine the stress and displacement fields.

Simulation of surface displacement and strain field of the 2011 Japan Mw9. 0 earthquake

Based on dislocation theory of 0kada, we adopted a finite-element fault model inverted by Gavin Hayes from seismic data for the 2011 Japan Mw9.0 earthquake, and obtained the corresponding surface displacement and strain fields. The calculated displacement field is consistent with the observed GPS results in the trend of changes. Also the surface displacement and strain fields both show large variations in space.

Effect of dynamic loading orientation on fracture properties of surrounding rocks in twin tunnels

For expedited transportation,vehicular tunnels are often designed as two adjacent tunnels,which frequently experience dynamic stress waves from various orientations during blasting excavation.To analyze the impact of dynamic loading orientation on the stability of the twin-tunnel,a split Hopkinson pressure bar(SHPB)apparatus was used to conduct a dynamic test on the twin-tunnel specimens.The two tunnels were rotated around the specimen’s center to consider the effect of dynamic loading orientation.LS-DYNA software was used for numerical simulation to reveal the failure properties and stress wave propagation law of the twin-tunnel specimens.The findings indicate that,for a twin-tunnel exposed to a dynamic load from different orientations,the crack initiation position appears most often at the tunnel corner,tunnel spandrel,and tunnel floor.As the impact direction is created by a certain angle(30°,45°,60°,120°,135°,and 150°),the fractures are produced in the middle of the line between the left tunnel corner and the right tunnel spandrel.As the impact loading angle(a)is 90°,the tunnel sustains minimal damage,and only tensile fractures form in the surrounding rocks.The orientation of the impact load could change the stress distribution in the twin-tunnel,and major fractures are more likely to form in areas where the tensile stress is concentrated.

Analysis of the Wenchuan Ms8.0 Earthquake's Co-seismic Stress and Displacement Change by Using the Finite Element Method

The variation of in situ stress before and after earthquakes is an issue studied by geologists. In this paper, on the basis of the fault slip dislocation model of Wenchuan Ms8.0 earthquake, the changes of co-seismic displacement and the distribution functions of stress tensor around the Longmen Shan fault zone are calculated. The results show that the co-seismic maximum surface displacement is 4.9 m in the horizontal direction and 6.5 m in the vertical direction, which is almost consistent with the on-site survey and GPS observations. The co-seismic maximum horizontal stress in the hanging wall and footwall decreased sharply as the distance from the Longmen Shan fault zone increased. However, the vertical stress and minimum horizontal stress increased in the footwall and in some areas of the hanging wall. The study of the co-seismic displacement and stress was mainly focused on the long and narrow region along the Longmen Shan fault zone, which coincides with the distribution of the earthquake aftershocks. Therefore, the co-seismic stress only affects the aftershocks, and does not affect distant faults and seismic activities. The results are almost consistent with in situ stress measurements at the two sites before and after Wenchuan Ms8.0 earthquake. Along the fault plane, the co-seismic shear stress in the dip direction is larger than that in the strike direction, which indicates that the faulting mechanism of the Longmen Shan fault zone is a dominant thrust with minor strike-slipping. The results can be used as a reference value for future studies of earthquake mechanisms.

Numerical Simulation of Non-linear Joint Using Displacement Discontinuity Method

An iterative algorithm for modeling of non-linear joint by the displacement discontinuity method (DDM) was described, and the effect of the non-linear joint on the in-situ stress field was investigated in this paper. The Barton-Bandis (BB) non-linear joint model and failure criterion were adopted in the new DDM program. Using this program, the stress field around the non-linear joint was obtained, the parameters analysis of the joint was carried out, and the deformation and stress distribution of the joint were studied. The simulation results show that: (1)the in-situ stress is significantly affected by the joint; (2)the increase of stiffness, friction angle, and thickness of the joint affect the stress concentration in different ways; (3)the influence distance of the joint changes with the angle of the joint; (4)the deformation and stress of the joint change with the point position.

Interaction among fractures and stress field computation of fracture systems

The interaction problem among fractures under the action of compressional stress is studied in this paper by using the finite element method and boundary element method respectively.The mechanical criteria which differentiate between the independent fractures and fracture systems and their computation methods are presented in this paper.The proportional conditions between length and spacing of fractures that exist interaction for several kinds of fracture groups of different geometric arrangement are given.The effect of interaction among fractures on the displacement field,stress field and strain energy distribution are computed.The relations between the fracture system of conjugate array and conjugate earthquakes are also discussed in this paper.

SCATTERING FAR FIELD SOLUTION OF SH-WAVE BY MOVABLE RIGID CYLINDRICAL INTERFACE INCLUSION

The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.

Unloading damage patterns of rock slopes in open pit mines and analyses of their mechanisms

The stability of slopes is essential for ensuring safe production in open-pit mines.Analyzing and managing the deformation and failure of the slope rock mass becomes more challenging as the slope height increases.To investigate the damage patterns of slopes with varying heights,three slope models were developed based on a rock slope in Dagushan,China.The deformation failure processes of slopes under the influence of excavation and unloading were analyzed using the base friction test method in combination with digital image technology contrasting.The results supported the following findings:(1)Unloading tensile stress caused lateral partitioning in the slope.Both the foot and top of the slope underwent initial tensile cracks.(2)The destabilization mechanism of unloading deformation in slopes of different heights involved a combination of traction at the foot of the slope or pushing at the top of the slope,followed by accelerated deformation,deceleration creep,and overall destabilization.(3)The unloading damage patterns of slopes at different heights were summarized as follows:compression tension cracking,traction,and slip damage for medium and low slopes;compression tension cracking,traction,and slip failure for the upper part of high slopes;and relaxation tension cracking,pushing,traction,and slip failure for the lower part.Moreover,the upper part of ultra-high slopes exhibited compression tension cracking,traction,and slip failure,while the middle and lower parts displayed relaxation tension cracking,pushing,traction,and slip patterns.Finally,numerical simulations were conducted to verify the results of the test analyses,which demonstrated good consistency.These research results were of great engineering value for proposing effective safety management measures for high slopes.

Influence of advanced engineering measures on displacement and stress field of surrounding rock in tunnels crossing active strike-slip faults

Based on significant improvements in engineering materials,three advanced engineering measures have been proposed-super anchor cables,high-strength concrete anti-fault caverns,and grouting modification using high-strength concrete-to resist fault dislocation in the surrounding rock near tunnels crossing active strike-slip faults.Moreover,single-or multiple-joint advanced engineering measures form the local rock mass-anti-fault(LRAF)method.A numerical method was used to investigate the influence of LRAF methods on the stress and displacement fields of the surrounding rock,and the anti-fault effect was evaluated.Finally,the mechanism of action of the anchor cable was verified using a three-dimensional numerical model.The numerical results indicated that the anchor cable and grouting modification reduced the displacement gradient of the local surrounding rock near the tunnels crossing fault.Furthermore,anchor cable and grouting modifications changed the stress field of the rock mass in the modified area.The tensile stress field of the rock mass in the modified anchor cable area was converted into a compressive stress field.The stress field in the modified grouting area changed from shear stress in the fault slip direction to tensile stress in the axial tunnel direction.The anti-fault cavern resisted the dislocation displacement and reduced the maximum dislocation magnitude,displacement gradient,and shear stress.Among the three advanced engineering measures,the anchor cable was the core of the three advanced engineering measures.An anchor cable,combined with other LRAF measures,can form an artificial safety island at the cross-fault position of the rock mass to protect the tunnel.The research results provide a new supporting idea for the surrounding rock of tunnels crossing active strike-slip faults.

Numerical simulation of Dabie orogenicbelt's tectonic evolution

The influence of hot mantle intrusive body on tectonic stress field and displacement field of Dabie orogenic belthave been analyzed by means of finite element method. Numerical simulations show that the intrusion of hot mantle material leads to an extensional stress state in the upper crust of central Da bie mountains, while compressivestress state appears on both sides of orogenic belt under the action of horizontal compression from Yang tze craton.This is in accordance with the actual faulting tectonics in this area. Possible evolution trend in transition area isdiscussed, too.