Solution of structural mechanic’s problems by machine learning

This article proposes analysis procedure of structural mechanic’s problem as integral formulation. The analysis procedure was proposed as stressed-based analysis procedure as before plying the procedure, it is required to define stress distribution within the structural body by proper modelling and structural idealization assumptions. The methodology can suitable be applied for finding the solution of engineering applications with required accuracy. The methodology exploits the unfolded part of the structural analysis problems which were not so easy to solve such as geometric and material nonlinearity together with simple integration technique [11]. It has already unfolded the misery of physically exploiting plastic behaviour structures before the start of fracture of elastic materials [13]. The formulation is integral formulation rather than differential formulation in which whole stress –strain behaviour is utilised in the analysis procedure by using neural network as regression tool. In this article, one dimensional problem of uniaxial bar and plane strain axis symmetric problem of cylinder subjected to internal pressure is solved. The results are compared with the classical differential formulation or linear theory.

Origin and Application of the Twinned Calcite Strain Gauge

This paper is a personal account of the origin and development of the twinned-calcite strain gauge, its experimental verification, and its relationship to stress analysis. The method allows the calculation of the three-dimensional deviatoric strain tensor based on five or more twin sets. A minimum of about 25 twin sets should provide a reasonably accurate result for the magnitude and orientation of the strain tensor. The opposite-signed strain axis orientation is the most accurately located. Where one strain axis is appreciably different from the other two, that axis is generally within about 10° of the correct value. Experiments confirm a magnitude accuracy of 1% strain over the range of 1–12% axial shortening and that samples with more than 40% negative expected values imply multiple or rotational deformations. If two deformations are at a high angle to one another, the strain calculated from the positive and negative expected values separately provides a good estimate of both deformations. Most stress analysis techniques do not provide useful magnitudes, although most provide a good estimate of the principal strain axis directions. Stress analysis based on the number of twin sets per grain provides a better than order-of-magnitude approximation to the differential stress magnitude in a constant strain rate experiment.

Residual lattice strain in quartzites as a potential palaeo-piezometer

SUMMARY If a crystal lattice is subjected to a stress, it becomes distorted and no longer represents the ideal crystal symmetry, and if the stress introduces defects such as dislocations, some of this distortion is preserved after the applied stress is removed. In this study, we investigate lattice distortion in quartz at the micron scale with synchrotron X-ray Laue diffraction. From Laue images the local deviatoric strain tensor is derived and corresponding stresses are calculated based on elastic properties. The method is applied to metasedimentary quartzites from the Bergell Alps that were deformed at conditions of greenschist facies metamorphism. The residual palaeostrain is represented in maps of the deviatoric strain tensor components and with deviatoric strain axis pole figures. Data suggest overall shortening perpendicular to the schistosity plane but with considerable asymmetry relative to foliation and lineation, probably attributed to simple shear. Crystallographic pole figures from Laue diffraction agree with neutron diffraction and EBSD measurements and display quartz c-axes girdle distributions with maxima also perpendicular to schistosity. The method shows promise to be used as a palaeo-piezometer to unravel the stress field during tectonic deformation.

Effects of Uniaxial Strain on the Structures of Vacancy Clusters in FCC Metals

The effects of [001] uniaxial strain on the stable structures and structural evolution of vacancy clusters in fcc metals, Cu, Ni, Al and Fe, have been studied and compared. Under uniaxial strain, the clusters in all these metals tend to align parallel or perpendicular to the strain axis under tensile or compressive strain. Moreover, both the body cluster and the {001} planar cluster become the dominant types. In addition, the stacking fault tetrahedron cluster becomes another dominant type in Al under compressive strain. The cluster structures in Fe are disordered under strain possibly because the pure fcc Fe is thermodynamically unstable under the current simulation condition.

Parametric resonance in the dynamics of an elliptic vortex in a periodically strained environment

The model of an elliptic vortex evolving in a periodically strained background flow is studied in order to establish the possible unbounded regimes. Depending on the parameters of the exterior flow, there are three classical regimes of the elliptic vortex motion under constant linear deformation: (i) rotation, (ii) nutation, and (iii) infinite elongation. The phase portrait for the vortex dynamics features critical points which correspond to the stationary vortex not changing its form and orientation. We demonstrate that, given superimposed periodic oscillations to the exterior deformation, the phase space region corresponding to the elliptic critical point experiences parametric instability leading to locally unbounded dynamics of the vortex. This dynamics manifests itself as the vortex nutates along the strain axis while continuously elongating. This motion continues until nonlinear effects intervene near the region associated with the steady-state separatrix. Next, we show that, for specific values of the perturbation parameters, the parametric instability is effectively suppressed by nonlinearity in the primal parametric instability zone. The secondary zone of the parametric instability, on the contrary, produces an effective growth of the vortex's aspect ratio.

Structural and kinematic analyses of the basement window within the hinterland fold-and-thrust belt of the Zagros orogen, Iran

The Zagros hinterland fold-and-thrust belt is located in the central portion of the Zagros Thrust System and consists of the exhumed basement windows associated with NW-striking and NE-dipping flexural duplex structures that contain in-sequence thrusting and related folds. Mylonitic nappes of the basement were exhumed along deep-seated sole thrusts of the Zagros Thrust System. Lattice preferred orientation (LPO) c-axes of quartz show asymmetric type-1 crossed girdles that demonstrate a non-coaxial deformation under plane strain conditions. Based on the opening angles of quartz c-axis fabric skeletons, deformation temperatures vary from 425±50°C to 540±50°C, indicating amphibolite facies conditions. The estimated mean kinematic vorticity evaluated from quartz c-axis of the quartzo-feldspathic mylonites (Wm = 0.55±0.06) indicates the degree of non-coaxiality during mylonite exhumation. The estimated angle θ between the maximum instantaneous strain axis (ISA1) and the transpressional zone boundary is 17°, and the angle of oblique convergence is 57° in the M2 nappe of the basement involved. This indicates that the mylonitic nappe was formed by a combination of 62% pure shear and 38% simple shear during oblique convergence.

Parametric resonance in the dynamics of an elliptic vortex in a periodically strained environment

The model of an elliptic vortex evolving in a periodically strained background flow is studied in order to establish the possible unbounded regimes. Depending on the parameters of the exterior flow, there are three classical regimes of the elliptic vortex motion under constant linear deformation: (i) rotation, (ii) nutation, and (iii) infinite elongation. The phase portrait for the vortex dynamics features critical points, which correspond to the stationary vortex not changing its form and orientation. We demonstrate that, given superimposed periodic oscillations to the exterior deformation, the phase space region corresponding to the elliptic critical point experiences parametric instability leading to locally unbounded dynamics of the vortex. This dynamics manifests itself as the vortex nutates along the strain axis while continuously elongating. This motion continues until nonlinear effects intervene near the region associated with the steady-state separatrix. Next, we show that for specific values of the perturbation parameters, the parametric instability is effectively suppressed by nonlinearity in the primal parametric instability zone. The secondary zone of the parametric instability, on the contrary, produces an effective growth of the vortex's aspect ratio.

A Step Forward in the Understanding of the Strain Reversal Effect on the Recrystallization Kinetics after Hot Working

A reversion of the strain produces a modification of the static recrystallization kinetics. Initially, the reversion increases the recrystallization time, that reaches a maximum at a certain strain, and decreases again for increasing reverse strains. This transient on recrystallization kinetics develops over a strain interval similar to that of the microstructural and stress-strain transients. At strains beyond the transient, the reversion can be regarded as a shift on the strain axis. However, at the authors knowledge there is no formulation able to describe the material behaviour during the transient. The present work introduces an equivalent strain concept based on the substructural dissolution/build-up processes taking place as a result of the strain reversal. This formulation allows including the effect of the strain path on recrystallization models.

Investigation of Nanometric Thin-Film Bismuth Piezoresistors Deposited on Silicon Substrates

ABSTRACTThin film bismuth piezoresistors, defined on oxidized silicon wafers, are investigated as a function of their orientation for their eventual integration on micro-electro-mechanical (MEMS) microsensors. Bismuth’s piezoresistance (or elasto-resistance) is experimentally investigated to accurately determine its longitudinal and transverse strain sensitivities. Whisker-shaped resistive elements defined on different orientations (from 0o, the beam’s main strain axis, to 90o, perpendicular to that axis) undergo changes of resistance (ΔR), associated with the induced strains on silicon cantilevers beam’s surface when these are mechanically loaded under pure bending stress conditions. For Bi-resistors, the traditional gage factor concept, (ΔR/Ro)/εl, is found to be equal to +16 and +33, for elements oriented along 0 and 90o, respectively, considerably larger than those for metals or metal alloys. These high sensitivity values and the “unusual” positive, higher value for the 90o (perpendicular) resistors can be of considerable interest for microsensors applications. The results of this study enable us to precisely determine the bismuth’s longitudinal and transverse strain sensitivities that are calculated to be equal to +26 and +40.5 respectively. This experimental study is extended to explore the Bi-films’ response to bi-axial strain fields.