A gated recurrent unit model to predict Poisson’s ratio using deep learning

Static Poisson’s ratio(vs)is crucial for determining geomechanical properties in petroleum applications,namely sand production.Some models have been used to predict vs;however,the published models were limited to specific data ranges with an average absolute percentage relative error(AAPRE)of more than 10%.The published gated recurrent unit(GRU)models do not consider trend analysis to show physical behaviors.In this study,we aim to develop a GRU model using trend analysis and three inputs for predicting n s based on a broad range of data,n s(value of 0.1627-0.4492),bulk formation density(RHOB)(0.315-2.994 g/mL),compressional time(DTc)(44.43-186.9 μs/ft),and shear time(DTs)(72.9-341.2μ s/ft).The GRU model was evaluated using different approaches,including statistical error an-alyses.The GRU model showed the proper trends,and the model data ranges were wider than previous ones.The GRU model has the largest correlation coefficient(R)of 0.967 and the lowest AAPRE,average percent relative error(APRE),root mean square error(RMSE),and standard deviation(SD)of 3.228%,1.054%,4.389,and 0.013,respectively,compared to other models.The GRU model has a high accuracy for the different datasets:training,validation,testing,and the whole datasets with R and AAPRE values were 0.981 and 2.601%,0.966 and 3.274%,0.967 and 3.228%,and 0.977 and 2.861%,respectively.The group error analyses of all inputs show that the GRU model has less than 5% AAPRE for all input ranges,which is superior to other models that have different AAPRE values of more than 10% at various ranges of inputs.

Topology Optimization of Metamaterial Microstructures for Negative Poisson’s Ratio under Large Deformation Using a Gradient-Free Method

Negative Poisson’s ratio(NPR)metamaterials are attractive for their unique mechanical behaviors and potential applications in deformation control and energy absorption.However,when subjected to significant stretching,NPR metamaterials designed under small strain assumption may experience a rapid degradation in NPR performance.To address this issue,this study aims to design metamaterials maintaining a targeted NPR under large deformation by taking advantage of the geometry nonlinearity mechanism.A representative periodic unit cell is modeled considering geometry nonlinearity,and its topology is designed using a gradient-free method.The unit cell microstructural topologies are described with the material-field series-expansion(MFSE)method.The MFSE method assumes spatial correlation of the material distribution,which greatly reduces the number of required design variables.To conveniently design metamaterials with desired NPR under large deformation,we propose a two-stage gradient-free metamaterial topology optimization method,which fully takes advantage of the dimension reduction benefits of the MFSE method and the Kriging surrogate model technique.Initially,we use homogenization to find a preliminary NPR design under a small deformation assumption.In the second stage,we begin with this preliminary design and minimize deviations in NPR from a targeted value under large deformation.Using this strategy and solution technique,we successfully obtain a group of NPR metamaterials that can sustain different desired NPRs in the range of[−0.8,−0.1]under uniaxial stretching up to 20% strain.Furthermore,typical microstructure designs are fabricated and tested through experiments.The experimental results show good consistency with our numerical results,demonstrating the effectiveness of the present gradientfree NPR metamaterial design strategy.

Model test of negative Poisson’s ratio cable for supporting super-largespan tunnel using excavation compensation method

In recent years,there is a scenario in urban tunnel constructions to build super-large-span tunnels for traffic diversion and route optimization purposes.However,the increased size makes tunnel support more difficult.Unfortunately,there are few studies on the failure and support mechanism of the surrounding rocks in the excavation of supported tunnel,while most model tests of super-large-span tunnels focus on the failure characteristics of surrounding rocks in tunnel excavation without supports.Based on excavation compensation method(ECM),model tests of a super-large-span tunnel excavation by different anchor cable support methods in the initial support stage were carried out.The results indicate that during excavation of super-large-span tunnel,the stress and displacement of the shallow surrounding rocks decrease,following a step-shape pattern,and the tunnel failure is mainly concentrated on the vault and spandrel areas.Compared with conventional anchor cable supports,the NPR(negative Poisson’s ratio)anchor cable support is more suitable for the initial support stage of the super-large-span tunnels.The tunnel support theory,model test materials,methods,and the results obtained in this study could provide references for study of similar super-large-span tunnels。

The Impact of Fabric Weave and Anisotropy on the Poisson’s Ratio in Technical Fabrics

Poisson’s ratio changes during the tensile stress of technical fabric samples due to the anisotropy of technical fabrics.This paper examines the effects of the type of weave and the anisotropic characteristics of the technical fabric on maximum tensile force,corresponding elongation,work-to-maximum force,elasticity modulus,and Poisson’s ratio when axial tensile forces are applied to samples cut at various angles in the direction of the weft yarns of the technical fabric.In the lab,3 cotton fabric samples of constant warp and weft density with different structural weave types(plain weave,twill weave,atlas weave)were subjected to the tensile force until they broke at the following angles:0°,15°,30°,45°,60°,75°,90°.Based on the different measured values of technical fabric stretching in the longitudinal direction and lateral narrowing,Poisson’s ratio is calculated.The Poisson’s ratio was calculated up to a relative elongation of the fabric of 8%,as the buckling of the fabric occurs according to this elongation value.According to the results presented in this paper,the type of weave of the fabric,the direction of tensile force,and the relative narrowing of the technical fabrics all play important roles in the Poisson’s ratio value.The Poisson’s ratio curve of a technical fabric under tensile stress(i.e.elongation)is primarily determined by its behaviour in the opposite direction of the elongation.The change in the value of the Poisson’s ratio is represented by a graph that first increases nonlinearly and then decreases after reaching its maximum value.

Design, Characterization, and 3D Printing of Cardiovascular Stents with Zero Poisson’s Ratio in Longitudinal Deformation

Inherent drawbacks associated with drug-eluting stents have prompted the development of bioresorbable cardiovascular stents.Additive manufacturing(3-dimentional(3D)printing)has been widely applied in medical devices.In this study,we develop a novel screw extrusion-based 3D printing system with a new designed mini-screw extruder to fabricate stents.A stent with a zero Poisson’s ratio(ZPR)structure is designed,and a preliminary monofilament test is conducted to investigate appropriate fabrication parameters.3D-printed stents with different geometric structures are fabricated and analyzed by observation of the surface morphology.An evaluation of the mechanical properties and a preliminary biological evaluation of 3D-printed stents with different parameters are carried out.In conclusion,the screw extrusion-based 3D printing system shows potential for customizable stent fabrication.

Multidisciplinary Design Optimization of Crash Box with Negative Poisson’s Ratio Structure

To improve the crashworthiness and energy absorption performance,a novel crash box negative Poisson’s ratio(NPR)structure is proposed according to the characteristics of low speed collision of bumper system.Taking the peak collision force and the average collision force as two subsystems,a multidisciplinary collaborative optimization design is carried out,and its optimization results are compared with the ones optimized by NSGA-II algorithm.Simulation results show that the crashworthiness and energy absorption performance of the novel crash box is improved effectively based on the multidisciplinary optimization method.

Topological Design of Microstructures of Materials Containing Multiple Phases of Distinct Poisson’s Ratios

A methodology for achieving the maximum bulk or shear modulus in an elastic composite composed of two isotropic phases with distinct Poisson’s ratios is proposed.A topology optimization algorithm is developed which is capable of finding microstructures with extreme properties very close to theoretical upper bounds.The effective mechanical properties of the designed composite are determined by a numerical homogenization technique.The sensitivities with respect to design variables are derived by simultaneously interpolating Young’smodulus and Poisson’s ratio using different parameters.The so-called solid isotropicmaterial with penalizationmethod is developed to establish the optimization formulation.Maximum bulk or shearmodulus is considered as the objective function,and the volume fraction of constituent phases is taken as constraints.Themethod ofmoving asymptotes is applied to update the design variables.Several 3D numerical examples are presented to demonstrate the effectiveness of the proposed structural optimization method.The effects of key parameters such as Poisson’s ratios and volume fractions of constituent phase on the final designs are investigated.A series of novel microstructures are obtained fromthe proposed approach.It is found that the optimized bulk and shearmoduli of all the studied composites are very close to the Hashin-Shtrikman-Walpole bounds.

In-Plane and Out-of-Plane Mechanical Properties of Zero Poisson’s Ratio Cellular Structures for Morphing Application

Intelligent structures like zero Poisson’s ratio(ZPR)cellular structures have been widely applied to the engineering fields such as morphing wings in recent decades,owing to their outstanding characteristics including light weight and low effective modulus. In-plane and out-of-plane mechanical properties of ZPR cellular structures are investigated in this paper. A theoretical method for calculating in-plane tensile modulus,in-plane shear modulus and out-of-plane bending modulus of ZPR cellular structures is proposed,and the impacts of the unit cell geometrical configurations on in-plane tensile modulus,in-plane shear modulus and out-of-plane bending modulus are studied systematically based on finite element(FE)simulation. Experimental tests validate the feasibility and effectiveness of the theoretical and FE analysis. And the results show that the in-plane and out-of-plane mechanical properties of ZPR cellular structures can be manipulated by designing cell geometrical parameters.

Elastic and Viscoelastic Poisson’s Ratios: The Theoretical Mechanics Perspective

A recent review publication presented an extensive and comprehensive assessment of the phenomenological relations of Poisson’s ratios (PRs) to the behavior and responses of contemporary materials under specific loading conditions. The present review and analysis paper is intended as a theoretical mechanics complement covering mathematical and physical modeling of a single original elastic and of six time and process (i.e. path and stress) dependent viscoelastic PR definitions as well as a seventh special path independent one. The implications and consequences of such models on material characterization are analyzed and summarized. Indeed, PRs based on experimentally obtained 2-D strains under distinct creep and/or relaxation processes exhibit radically different time responses for identical material specimen. These results confirm the PR’s implicit path dependence in addition to their separate intrinsic time reliance. Such non-uniqueness of viscoelastic PRs renders them unsuitable as universal material descriptors. Analytical formulations and experimental measurements also examine the physical impossibility of instantaneously achieving time independent loads or strains or their rates thus making certain PR definitions based on constant state variables, while mathematically valid, physically unrealistic and unachievable. A newly developed theoretical/experimental protocol for the determination of the time when loading patterns reach stead-state conditions based on strain accelerations demonstrates the capability to measure this time from experimental data. Due to the process dependent PRs, i.e. stress and stress history paths, the non-existence of a unique viscoelastic PR and of a universal elastic-viscoelastic correspondence principle or analogy (EVCP) in terms of PRs is demonstrated. Additionally and independently, the required double convolution integral construction of linear viscoelastic constitutive relations with the inclusion of PRs is cumbersome analytically and computationally needlessly highly CPU intensive. Furthermore, there is no theoretical fundamental hint as to what loading path is required to produce a unique universal viscoelastic PR definition necessary for formulating a PR based constitutive relation or an EVCP protocol. The analysis associated with an additional Class VII viscoelastic PR establishes it as a universal representation which is loading path and strain independent while still remaining time dependent. This Class PR can be the one used if it is desired to express constitutive relations in terms of PRs, subject to the caveat applying to all PR Classes regarding the CPU intensiveness in the time space due to triple product and double convolution integral constitutive relations. However, the use PRs is unnecessary since any set of material behavior can be uniquely and completely defined in terms of only moduli and/or compliances. The mathematical model of instantaneous initial loading paths, based on Heavi-side functions, is examined in detail and shown to lead to infinite velocities and accelerations. Additionally, even if non-instantaneous gradual loading functions are employed the resulting PRs are still load and load history dependent. Consequently, they represent specialized PR responses applicable and limited to those particular load and history combinations. Although the analyses contained herein are generalized to non-homogeneous linear viscoelastic materials, the main focus is on PR time and process dependence. The non-homogeneous material results and conclusions presented herein apply equally to homogeneous viscoelasticity and per se do not influence the results or conclusions of the analytical development regarding viscoelastic PRs. In short, these PR analyses apply to all linear viscoelastic material characterization.

Effect of Poisson’s ratio on stress state in the Wenchuan M_S8.0 earthquake fault

The Wenchuan Ms8.0 earthquake occurred on the Longmenshan fault which inclines at a dip angle exceeding 60 degrees. Since most thrust earthquakes occur on faults with dip angles of about 30 degrees, it is enigmatic why the Wenchuan earthquake occurred on such a steep fault. In this study we use a simple finite element model to investigate how the stress state in the fault changes with the variation of Poisson＇s ratio. The results show that, with the Poisson＇s ratio in the fault increasing, the magnitudes of the principal stresses increase and the maximum Shear stress decrease, and, especially, the angle between the maximum principal stress and the fault plane decreases, which will enhance the driving force to overcome the frictional resistance on the fault. The increase of Poisson＇s ratio in the fault may be an important factor to affect the occurrence of the fault earthquakes with large angles between maximum principal stress and fault plane.

EFFECTS OF POISSON’S RATIO ON SCALING LAW IN HERTZIAN FRACTURE

In this paper the Auerbach＇s scaling law of Hertzian fracture induced by a spherical indenter pressing on a brittle solid is studied. In the analysis, the singular integral equation method is used to analyze the fracture behavior of the Hertzian contact problem. The results show that the Auerbach＇s constant sensitively depends on the Poisson＇s ratio, and the effective Auerbach＇s domain is also determined for a given value of the Poisson＇s ratio.

Poisson’s Ratio of Surface Soils and Shallow Sediments Determined from Seismic Compressional and Shear Wave Velocities

This paper presents the results of seismic compressional, P- and shear, S-wave measurements carried out on the unconsolidated top-soil at the different locations of the study area to determine Poisson’s ratio. In this work, seismic refraction data is used to determine Poisson’s ratio as an aid to engineering foundation. A 12-channel seismograph with signal stacking ability was used together with high frequency (100 Hz) geophones on the top-soil. The geophone intervals were set to 5 m at the all locations. In all the locations, Vp/Vs ratio ranged from 1.0289 to 1.4185 for the top layer. Vp/Vs ratio in the second layer ranged from 1.0512 to 1.5834. The Poisson’s ratio for the first layer ranged from -8.0324 to 0.2060. For the second layer, the Poisson’s ratio ranged from -0.7567 to 0.1683. The values of Vp/Vs ratio less than in the first layer and in some locations in the second layer resulted in negative Poisson’s ratio. The low and negative values of Poisson’s ratio are symptomatic of occurrence of ripable anisotropic materials in the locations where they occur, which suggests that indicated average depth should be removed and refilled with geomaterials that may be resilient to carry engineering loads.

A Note on the Effect of Negative Poisson’s Ratio on the Deformation of a Poroelastic Half-Space by Surface Loads

The aim of this note is to study the effect of negative Poisson’s ratio on the quasi-static deformation of a poroelastic half-space with anisotropic permeability and compressible fluid and solid constituents by surface loads. Two particular cases considered are: two-dimensional normal strip loading and axisymmetric normal disc loading. It is found that a negative Poisson’s ratio makes the Mandel-Cryer effect more prominent. It also results in an increase in the magnitude of the surface settlement.

Mechanical design and analysis of bio-inspired reentrant negative Poisson’s ratio metamaterials with rigid-flexible distinction

Aiming at achieving tunable reentrant structures with rigidity and uniformity,respectively,the C-shaped and S-shaped reentrant metamaterials were proposed by the bionic design of animal structures.Utilizing beam theory and energy methodology,the analytical expressions of the equivalent elastic modulus of the metamaterials were derived.Differences in deformation modes,mechanical properties,and energy absorption capacities were characterized by using experiments and the finite element analysis method.The effects of ligament angle and thickness on the mechanical characteristics of two novel metamaterials were investigated by using a parametric analysis.The results show that the stiffness,deformation mode,stress-strain curve,and energy absorption effects of three metamaterials are significantly different.This design philosophy can be extended from 2D to 3D and is applicable at multiple dimensions.

Energy Absorption by 3D-Printed Mesh Structures with a Negative Poisson’s Ratio

A negative Poisson's ratio(NPR)structure represents optimal impact-resistance with applications in various fields,including the crash box in vehicles,which absorbs impact kinetic energy.The crash box is designed to deform in response to impact,increasing local structural density,which enhances impact resistance performance.Current studies have only focused on the NPR effect in the plane dimension at low-speed loads.Few studies have considered high-speed impact loads on three-dimensional NPR structures.We have developed two types of AlSi10Mg alloy energy-absorbing structures with NPR using three-dimensional printing technology,and have compared our systems with a conventional hexagonal mesh structure.Sample testing involved split-Hopkinson pressure bar measurements,which showed good agreement with dynamic numerical simulations.When subjected to an impact load,the NPR structure exhibited better impact resistance and energy absorption compared with the positive Poisson's ratio structure.The proposed dual-layer hexagonal structure ensures an NPR effect while exhibiting higher strength and improved stability relative to the conventional concave hexagon structure.

Negative Poisson’s ratio cable compensation support for 32 m super-large-span highway tunnel:A case study

Although super-large-span tunnels ensure convenient transportation,they face many support challenges.The lack of normative construction guidance and the limited number of reference engineering cases pose a significant challenge to the stability control of superlarge-span tunnels.Based on the geological conditions of a super-large-span tunnel(span=32.17 m)at the bifurcation section of the Shenzhen interchange,this study determined support parameters via theoretical calculation,numerical simulation,and engineering analogy.The support effects of negative Poisson’s ratio(NPR)anchor cables and ordinary anchor cables on super-long-span tunnels were simulated and studied.Further,based on FLAC3D simulations,the surrounding rock stress field of NPR anchor cables was analyzed under different prestressing conditions,and the mechanism of a long-short combination,high-prestress compensation NPR anchor cable support was revealed.On the basis of numerical simulations,to our knowledge,the three-dimensional(3D)geomechanical model test of the NPR anchor cable and ordinary anchor cable support for super-large-span tunnel excavation is conducted for the first time,revealing the stress evolution law of super-large-span tunnels,deformation and failure characteristics of the surrounding rock,and the changing trend of the anchor cable’s axial force,and verifies that NPR anchor cables with high preloads are suitable for super-large-span tunnel support and have advantages over ordinary anchor cables.This study can provide a reliable theoretical reference for the support design and stability control of the surrounding rock of similar shallow-buried super-large-span tunnels.

Underwater cylindrical sandwich meta-structures composed of graded semi re-entrant zero Poisson’s ratio metamaterials with pre-strained wave propagation properties

Zero Poisson’s ratio(ZPR)mechanical metamaterials can yield no transverse displacements when unidi-rectionally compressed,and cylindrical sandwich meta-structures composed of semi re-entrant(SRE)ZPR metamaterials are thus explored for applications on cylindrical shells of underwater equipment or sub-mersible structures.A group of ZPR unit cells with specified pre-strained wave propagation characteristics and adequate load-bearing capabilities is optimally designed based on the periodic boundary condition(PBC)and Bloch’s Theorem.The sound transmission and pressure-resistant performance of cylindrical sandwich meta-structures comprising the homogeneous and graded SRE ZPR unit cells are then investi-gated.The results show that the designed meta-structures can perfectly yield better vibroacoustic atten-uation behavior within the specified frequency regions corresponding to the pre-strained band gaps and safely bear the hydrostatic pressure equivalent to 1000 m depth with low weight-bulk ratios.In addition,the functionally graded metamaterial core can boost vibroacoustic performance within broader frequency ranges.

Negative Poisson’s ratio locally resonant seismic metamaterials vibration isolation barrier

In recent decades,the application of seismic metamaterials to protect civil infrastructures being free of the damage of earthquakes has been attracting extensive attention.Specifically,the proposed locally resonant seismic metamaterials provide the probability of isolating the low-frequency seismic wave using a small-size isolation barrier.However,in previous studies,the energy absorption properties of locally resonant seismic metamaterials remain one of the least understood aspects of isolation.Benefit from the fascinating energy absorption characteristic of negative Poisson ratio(NPR)metamaterial,we creatively design a new seismic metamaterial structure by assembling the locally resonant seismic metamaterial and NPR metamaterial,to isolate seismic waves.The sound cone technique combining the transmission spectrum is employed to identify the surface wave from the hybrid waves.The generation mechanism of frequency bandgap and the isolation effectiveness of the proposed seismic metamaterial are discussed in detail.The results indicate that the generation of ultra-low and ultra-wide frequency bandgap with the range of 0.65 Hz–18.9 Hz is attributed to the locally resonant and energy absorption of the proposed seismic metamaterial structure and the excellent isolation effect is achieved by transforming the surface wave into the bulk wave.The frequency bandgap narrows as the distance increases between each resonator.In addition,the mechanical properties of the NPR bearing,such as the Poisson ratio,mass density,and elastic modulus,have remarkable impact on the frequency bandgap,especially on the upper bound frequency.In practical engineering,the NPR bearing with a low Poisson ratio,small mass density,and high elastic modulus is suggested for the design of the NPR locally resonant seismic metamaterial structures.Time domain analysis for the practical seismic wave verifies that the proposed seismic metamaterial has a promising application in isolating ultra-low and ultra-wide seismic waves,with the isolation effectiveness larger than 70%.This work contributes a new locally resonance seismic metamaterial design idea for isolating and adjusting the low-frequency seismic wave.

Implementation of the Integrated Green’s Function Method for 3D Poisson’s Equation in a Large Aspect Ratio Computational Domain

The solution of Poisson’s Equation plays an important role in many areas, including modeling high-intensity and high-brightness beams in particle accelerators. For the computational domain with a large aspect ratio, the integrated Green’s function method has been adopted to solve the 3D Poisson equation subject to open boundary conditions. In this paper, we report on the efficient implementation of this method, which can save more than a factor of 50 computing time compared with the direct brute force implementation and its improvement under certain extreme conditions.

Support characteristics of flexible negative Poisson’s ratio anchor cable response to blasting impacts

With the gradual decrease and exhaustion of shallow mineral resources,underground mining has progressed to greater depths.Here,the geological environment is significantly more complex and nonlinear,and large deformations of rock masses have great potential to occur.Many geotechnical engineering disasters have occurred even while using Poisson’s ratio(PR)anchor cable supports.To efficiently deal with these issues,a new support material called negative Poisson’s ratio(NPR)anchor cable is proposed;this material can withstand large deformations and provide high constant resistance.In this study,the support characteristics of macro-NPR anchor cable under blasting impact were mainly studied.The support effects of PR anchor cable and macro-NPR anchor cable were compared and analyzed with the help of field experiments and numerical simulations.The results indicate that field experiments and discontinuous deformation analysis accurately reflect the failure state of the selected roadway,as well as the tension and deformation of the anchor cables.The road-way supported by PR anchor cables cannot resist rock bursts under ordinary circumstances.However,the NPR anchor cable-supported roadway resisted a rock burst caused by the impact equivalent to a mine earthquake magnitude above 3;it meets the requirements of roadway stability.