Large Deformation Conditions Research Articles

Revisit to three-dimensional percolation theory: Accurate analysis for highly stretchable conductive composite materials.

A percolation theory based on variation of conductive filler fraction has been widely used to explain the behavior of conductive composite materials under both small and large deformation conditions. However, it typically fails in properly analyzing the materials under the large deformation since the assumption may not be valid in such a case. Therefore, we proposed a new three-dimensional percolation theory by considering three key factors: nonlinear elasticity, precisely measured strain-dependent Poisson’s ratio, and strain-dependent percolation threshold. Digital image correlation (DIC) method was used to determine actual Poisson’s ratios at various strain levels, which were used to accurately estimate variation of conductive filler volume fraction under deformation. We also adopted strain-dependent percolation threshold caused by the filler re-location with deformation. When three key factors were considered, electrical performance change was accurately analyzed for composite materials with both isotropic and anisotropic mechanical properties.

Polycrystal plasticity modeling of nickel-based superalloy IN 617 subjected to cyclic loading at high temperature

A crystal plasticity finite element (CPFE) model considering isothermal, large deformation and cyclic loading conditions has been formulated and employed to investigate the mechanical response of a nickel-based alloy at high temperature. The investigations focus on fatigue and creep-fatigue hysteresis response of IN 617 subjected to fatigue and creep-fatigue cycles. A new slip resistance evolution equation is proposed to account for cyclic transient features induced by solute drag creep that occur in IN 617 at 950 °C. The crystal plasticity model parameters are calibrated against the experimental fatigue and creep-fatigue data based on an optimization procedure that relies on a surrogate modeling (i.e. Gaussian process) technique to accelerate multi-parameter optimizations. The model predictions are validated against experimental data, which demonstrates the capability of the proposed model in capturing the hysteresis behavior for various hold times and strain ranges in the context of fatigue and creep-fatigue loading.

Influence of Shear on Permeability of Clayey Soil

AbstractThe variation of stress–strain state induces changes in the permeability of clayey soil and then affects the properties of seepage and consolidation. In previous studies, variations of the permeability of soil in shear process were mainly neglected, and there were no reasonable descriptions of the permeability in such a condition. To study the variation of the hydraulic conductivity of clayey soil in shear process, new triaxial seepage equipment was designed by changing the conventional triaxial apparatus. Based on a series of tests under different confining pressures carried out by this equipment, the influences of the stress–strain state of clayey soil on hydraulic conductivity were investigated. Furthermore, a mathematical model for the hydraulic conductivity of clayey soil under the condition of large shear deformation was proposed. The comparison between the seepage test results and the calculated values of the proposed model indicates that the mathematical model can calibrate the effects of ...

Applicability of the Hertz Contact Theory to Rolling Rubber Cylinders Model

Hertz contact theory (HCT) is a study of contact stress and deformation which is widely used in many engineering fields. However, there are many limiting conditions for the applications of the HCT, in this paper, the contact model between a plastic cylinder and a rubber cylinder does not fit two limiting conditions: Small deformation and no rigid body motion. By applying three-dimensional finite element models, the deformation and the maximum contact stress of two rotating cylinders have been analyzed. Comparing the simulation results and the theoretical results, the applicability of Hertz contact theory to this model has been discussed. The results show that: In the condition of large deformation, the theoretical results of maximum contact stress fit the actual situation, but the half-width of the contact area does not fit. Under the rolling condition, the theoretical maximum contact stress has a large deviation to simulation result.

True stress and shakedown analysis of pressure vessel under repeated internal pressure

This study aims to investigate the true stress and the plastic shakedown behavior of a cyclically loaded pressure vessel. To serve this study, an experimental platform has been built up, which comprised of a self-made thin-wall cylinder pressure vessel, a water pressure loading system to simulate the actual working loading condition, and strain gauge sets for strain measurement. A number of experiments have been done by cyclically loading and unloading the vessel at different strain levels of plastic deformation to shakedown state in different experiments respectively. The relationship between plastic strain and shakedown range has therefore been obtained. The true stress-strain constitutive model of the vessel under large deformation condition has also been derived. The experiments lead to three observations: (1) the strain hardening technology can effectively reduce the residual stress of stainless steel pressure vessel. (2) The shakedown range is less than 2000 μe for a total strain under 4%, and yet the shakedown range increases fast to more than 3000 μe for a total strain higher than 6%. (3) It is also found that the true stress-strain constitutive model given in this paper describes the multi-axial stress-strain state of pressure vessels, and validates the engineering practicability of conventional uniaxial tensile shakedown constitutive curve.

Constitutive model of cold roll-beating forming of 40Cr

An impact experiment was conducted under high-speed cold roll-beating conditions, appropriate for the deformation mechanism of the metal material, including the effects of the deformation temperature, strain rate and dislocation density on the rheological stress in the deformation was studied in order to reveal the forming mechanism that occurs during the high-speed cold roll-beating of 40Cr. Based on the Zener–Hollomon constitutive relation, the experimental data with the parameters of the 40Cr obtained under the high-speed and large-deformation conditions, which is a material evolution model established to determine the initial stress and peak stress. Furthermore, the relationship between the macroscopic deformation and forming factors was revealed, which provided a macroscopic theoretical foundation for explaining the cold roll-beating process.

Analysis and modelling of a rotary forming process for cast aluminium alloy A356

Spinning of a common aluminium automotive casting alloy A356 (Al–7Si–0.3Mg) at elevated temperatures has been investigated experimentally with a novel industrial-scale apparatus. This has permitted the implementation of a fully coupled thermomechanical finite element model aimed at quantifying the processing history (stress, strain, strain-rate and temperature) and predicting the final geometry. The geometric predictions of this model have been compared directly to the geometry of the workpieces obtained experimentally. This study is novel in regards to both the size and shape of the component as well as the constitutive material representation employed. The model predictions are in reasonable agreement with experimental results for small deformations, but errors increase for large deformation conditions. The model has also enabled the characterization of the mechanical state which leads to a common spinning defect. Suggestions for improving the accuracy and robustness of the model to provide a predictive tool for industry are discussed.

Rheology and microstructure characterisation of small intestinal digesta from pigs fed a red meat-containing Western-style diet

A method to characterise rheological and microstructure features of whole digesta collected from pigs fed meat-containing western style diets is described. Digesta are shown to contain suspensions of meat fibre particles up to 300 μm in size which exhibit weak gel behaviour, have a dynamic viscosity higher than steady shear viscosity indicative of structural breakdown at the initiation of flow, and shear thinning behaviour under steady shear. The power law index approach is useful for capturing the overall features of rheological behaviour under both small (n*<0.3) and large deformation (typically 0.2 < n < 0.5) conditions. Values obtained for rheological parameters represent a balance between the digestion of structural components (meat particles and starch granules in this case) with the absorption of water along the small intestine, and result in the absence of any systematic pattern as a function of small intestinal site. Both primary rheological data (G′, G″, η, η*) and power law index parameters show a high level of variability between animals fed identical diets. This study provides a baseline from which to investigate the in vivo effects of hydrocolloids on the rheology of porcine digesta from diets representative of human meals.

Modeling of Steel Bolted T-Stub Connection under Large Deformation Condition

Based on the component method of EuroCode3, a new component model to evaluate properties of T-stub connections under large deformation condition has been proposed in this paper. Firstly, the T-stub connection was breakdown into several components. And then those components was equivalent to bilinear springs. Finally the multi-spring model of T-stub connection was set up to describe its load deformation behaviour. With the purpose of verifying and calibrating the proposed model, a series of case studies were carried out and corresponding finite element models has also been set up. Results of FEM and multi-spring model fit well each other. And the applicability of the proposed model can be testified by the parametric study. The method of this paper can describe the behaviour of T-stub connections under large deformation condition, which can be a useful improvement to conventional design codes.

An upper bound solution for twist extrusion process

Twist extrusion, a promising severe plastic deformation technique for grain refinement down to ultrafine/nanocrystalline microstructures, was introduced as an attempt to provide large plastic deformation conditions similar to those in high pressure torsion while allowing large workpiece dimensions for industrial applications. As a relatively new severe plastic deformation technique, twist extrusion requires in-depth investigation of its plastic deformation characteristics. In this study, the twist extrusion process with a square shape die cavity has been analyzed using an upper bound solution to estimate the required power, deformation pattern, and optimum process condition. The analysis has been performed based on two kinematically admissible velocity fields while the effects of friction condition, die geometry, and mean equivalent strain have been considered. The results indicate that the die geometry and process parameters can dramatically change the deformation pattern and extrusion power.

Synthesis of ultrahard fullerite with a catalytic 3D polymerization reaction of C60

3D polymerization of C60 realizes under conditions of large plastic deformation at pressure 6–7GPa and room temperature in the presence of CS2. The phase of 3D-polymerized C60 is identical to ultrahard fullerite synthesized from pure C60 at 18GPa pressure: in both cases, the samples plough diamond during the rotation of the sample in a shear diamond anvil cell, bulk module is 585GPa, and a sequence of phase transitions preceding to ultrahard phase is also the same in both cases (in the presence of CS2, the phase transitions take place at lower pressures than in pure C60). Raman and transmission microscope studies confirm the structure equivalence of samples of both types. The absence of sulfur in the structure of ultrahard fullerite synthesized in the presence of CS2 proves the catalysis role of CS2 in the 3D polymerization of C60.

Numerical study of anisotropic failure in wood under large deformation

Brittle fracture mechanisms, characterizing wood behavior, are investigated numerically with the help of the smeared-crack approach combined with a multi-surface plasticity model. Numerical instabilities, accompanying the significant strain-softening behavior, are treated by using both a localization limiter and viscous regularization. In addition, extension of the model to large deformation conditions is proposed based on an objective stress rate using the rotation of wood fibers. Computations are carried out to predict the load carrying capacity and the post-cracking behavior of wood members under compression, bending and buckling, respectively. Competition between the multiple fracture processes is also analyzed from the simulation results.

Robust 3D–2D image registration: application to spine interventions and vertebral labeling in the presence of anatomical deformation

We present a framework for robustly estimating registration between a 3D volume image and a 2D projection image and evaluate its precision and robustness in spine interventions for vertebral localization in the presence of anatomical deformation. The framework employs a normalized gradient information similarity metric and multi-start covariance matrix adaptation evolution strategy optimization with local-restarts, which provided improved robustness against deformation and content mismatch. The parallelized implementation allowed orders-of-magnitude acceleration in computation time and improved the robustness of registration via multi-start global optimization. Experiments involved a cadaver specimen and two CT datasets (supine and prone) and 36 C-arm fluoroscopy images acquired with the specimen in four positions (supine, prone, supine with lordosis, prone with kyphosis), three regions (thoracic, abdominal, and lumbar), and three levels of geometric magnification (1.7, 2.0, 2.4). Registration accuracy was evaluated in terms of projection distance error (PDE) between the estimated and true target points in the projection image, including 14 400 random trials (200 trials on the 72 registration scenarios) with initialization error up to ±200 mm and ±10°. The resulting median PDE was better than 0.1 mm in all cases, depending somewhat on the resolution of input CT and fluoroscopy images. The cadaver experiments illustrated the tradeoff between robustness and computation time, yielding a success rate of 99.993% in vertebral labeling (with ‘success’ defined as PDE <5 mm) using 1,718 664 ± 96 582 function evaluations computed in 54.0 ± 3.5 s on a mid-range GPU (nVidia, GeForce GTX690). Parameters yielding a faster search (e.g., fewer multi-starts) reduced robustness under conditions of large deformation and poor initialization (99.535% success for the same data registered in 13.1 s), but given good initialization (e.g., ±5 mm, assuming a robust initial run) the same registration could be solved with 99 993% success in 6.3 s. The ability to register CT to fluoroscopy in a manner robust to patient deformation could be valuable in applications such as radiation therapy, interventional radiology, and an assistant to target localization (e.g., vertebral labeling) in image-guided spine surgery.

A thermomechanically coupled viscoelastic cohesive zone model at large deformation

A new viscoelastic cohesive zone model is formulated for large deformation conditions and within a fully coupled thermomechanical framework. The model is suitable for the simulation of a wide range of problems especially for polymeric materials. It can capture viscoelastic crack propagation as well as energy dissipation due to this process. Starting from the principles of thermodynamics, a 3D finite element formulation is derived for a fully coupled simultaneous solution of the thermal field and the deformation field. The viscoelastic model is constructed by extending an elastic exponential traction separation law using a simple rheology. The viscous part of the tractions is postulated to have the same characteristic length as the elastic part and that they are related by a single material parameter. A Newtonian dashpot is used to describe the evolution of the viscous separation. Furthermore, thermal effects are accounted for using temperature expressions in both the traction laws and the viscosity of the dashpot, and using a heat conduction law across the interface. The model is implemented within an implicit finite element code and the internal variable is calculated using an internal iteration. Different numerical examples are used to verify the model and a comparison with experimental data shows a satisfactory agreement.

Study on the Simulation of Anti-Flood Spiral Pile-Driven Process

Pile-driven operation is the essential means of flood control and river harnessing. Anti-flood Spiral Pile is an innovative flood fighting and rescue equipment. Based on the experiment, established the spiral pile finite element model in FEM method and constructed the soil model with SPH smooth particles, set the keywords and parameters by using LS-DYNA softwares own processor, and then, the large deformation (soil extrusion and shearing status, etc.) and stress conditions be simulated truthfully. With reference to the experiment, the simulation results of SPH method with ALE method was contrasted, which could provide a reliable reference and scientific basis for the subsequent analysis and design of the spiral pile.

Dynamic response of towed line array

Three-dimensional motion equations with consideration of the bending and torsional effects of a marine towed cable system under large elastic deformation conditions are formulated using the lumped parameter model. The lumped mass model is used to simulate a circular maneuver of a towed horizontal array that was first presented by Ablow. The results of this paper are in a good agreement with those obtained by finite difference schemes, and the minimum depth is closer to the experimental result. Although the calculations take more computation time, the lumped mass model is a good method, which can also be used to solve problems of towed line array, especially multi-branched towed line array, because of its flexibility.

Three-Dimensional Fully Parameterized Triangular Plate Element Based on the Absolute Nodal Coordinate Formulation

In this work, a new three-dimensional fully parameterized triangular plate element based on the absolute nodal coordinate formulation (ANCF) is introduced. This plate element has 12 coordinates per node; therefore, it can be used in thick plate applications. The proposed 12 shape functions are obtained by adding three shape functions to the nine shape functions that were previously used with the ANCF thin triangular plate element. Unlike the existing ANCF thin triangular plate element, which allows only the use of classical Kirchoff's plate theory, the fully parameterized ANCF triangular plate element proposed in this work allows for the use of a general continuum mechanics approach and also allows for a straight forward implementation of general nonlinear constitutive equations. Moreover, all deformation modes including thickness deformation can be captured using the fully parameterized ANCF triangular plate element proposed in this paper. The numerical results obtained in this investigation show that in case of negligible deformation, the fully parameterized ANCF triangular plate element behaves like a rigid body. Moreover, it is found that there is a good agreement between the solutions obtained using the proposed fully parameterized ANCF triangular plate element and the theoretical model in the case of small deformations. Furthermore, it is shown that the results of the proposed element agree well with the results obtained using the existing fully parameterized ANCF rectangular plate element when large deformation conditions are applied. The twist behavior of the proposed element is verified by comparison with the results obtained using a conventional nonlinear rectangular plate element.

A polynomial analytical model of rubber bearings based on series of tests

Rubber bearings are among the most frequently applied devices in seismic isolation. Although the behavior of rubber bearings under strong earthquakes is nonlinear, it is often interpreted through the bilinear constitutive law. The investigations presented in this paper represent a successful attempt to simulate nonlinear force–displacement relationships. The first part of the paper covers production and testing of rubber bearings and results obtained. The second part deals with development of a simple nonlinear mathematical model of a rubber bearing involving a polynomial function and eight additional parameters obtained from biaxial tests. The polynomial model can simulate the behavior of natural rubber bearings in case of small and large deformations. The model is capable of covering the strengthening of the rubber in conditions of large deformations, including the loading history effect. Based on comparison between the analytical and experimental results, it is concluded that the proposed polynomial model is capable enough to simulate the force–displacement relationship of rubber bearings.

Basis for viscoelastic modelling of polyethylene terephthalate (PET) near Tg with parameter identification from multi-axial elongation experiments

The mechanical response of Polyethylene Terephthalate (PET) in elongation is strongly dependent on temperature, strain and strain rate. Near the glass transition temperature Tg, the stress vs strain curves present a strain hardening effect vs strain under conditions of large deformations. At a given strain value, the strain rate has also an increasing influence on the stress value. The main goal of this work is to propose a visco-elastic model to predict the PET behaviour when subjected to large deformations and to determine the material properties from the experimental data. The visco-elastic model is written in a Leonov like way and the variational formulation is carried out for the numerical simulation using this model. To represent the non–linear effects, an elastic part depending on the elastic equivalent strain and a non-Newtonian viscous part depending on both viscous equivalent strain rate and cumulated viscous strain are tested. The model parameters can then be accurately obtained through the comparison with the experimental uniaxial and biaxial tests.

A numerical method for second order strain gradient theory

In classical mechanics, based on the generalized Hook’s law, stress is only a function of strain. However, in the strain gradient theory, stress is not only a function of strain, but also a function of high-order gradients of strain. This relationship between stress and strain and its new boundary conditions is derived using the principle of minimum total potential energy. Meanwhile, a new stress tensor called total stress tensor is introduced, which can be used as the total stress tensor in the momentum equation. Also, a length scale parameter is introduced, which appears in nonlinear equations and large deformation conditions. In this article, total stress has been calculated using the high-order gradients of strain. To calculate the high-order gradient of strain tensor through numerical methods, first, each strain tensor element is estimated based on a quadratic function. Then, the high-order strain tensor gradient is calculated by the least square numerical method, and the total stress of each element is obtained by inserting these tensors in the total stress-strain equation. The results of the numerical solution are compared with those of the analytical solution. The proposed innovative method is very efficient despite its simplicity. Key words: Strain gradient theory, principle of minimum total potential energy, total stress tensor, length scale parameter, least square method.