Nonlinear Large Deformation Research Articles

Nonlinear elastic behavior induced by nano-scale α phase in β matrix of β-type Ti–25Nb–3Zr–2Sn–3Mo titanium alloy

Large scale nonlinear elastic deformation behavior is induced by moderate precipitation of nano-scale α phase for Ti–25Nb–3Zr–2Sn–3Mo alloy after a strategy of cold rolling and short-time aging. Quantitive relationships are established between volume fraction of α phase (Vα) and elastic modulus, strength as well as maximal recoverable strain (εmax-R), where the highest εmax-R of 2.25% with strength of 900MPa corresponds to Vα of 10%. With the Vα increasing, the elastic behavior transforms from “double yielding” to nonlinear elasticity and then normal linearity. It is considered that the nonlinear elasticity of the studied (α+β) microstructure is probably related to “mechanical” stabilization of the alloy, i.e. a blocking effect of α phase on the lattice shear from body-centered cubic β phase to orthorhombic-α″ martensite.

Nonlinear contact between inner walls of deep sea pipelines in buckling process

In order to study buckling propagation mechanism in deep sea pipelines, the contact between pipeline’s inner walls in buckling process was studied. A two-dimensional ring model was used to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between inner walls. Based on the elastoplastic constitutive relationship and the principle of virtual work theory, the coupling effect of pipeline’s nonlinear large deformation and wall contact was included in the theoretical analysis with the aid of MATLAB, and the application scope of the theoretical model was also discussed. The calculated results show that during the loading process, the change in external pressure is closely related to the distribution of section stress, and once the walls are contacting each other, the external pressure increases and then remains stable after it reaches a specific value. Without fracture, the pipeline section will stop showing deformation. The results of theoretical calculations agree well with those of numerical simulations. Finally, in order to ensure reliability and accuracy of the theoretical results, the collapse pressure and propagation pressure were both verified by numerical simulations and experiments. Therefore, the theoretical model can be used to analyze pipeline’s buckling deformation and contact between pipeline’s inner walls, which forms the basis for further research on three-dimensional buckling propagation.

大埋深高应力软岩巷道围岩支护技术研究

以深部软岩巷道为研究背景，对某矿西盘区底板措施巷巷道表面位移进行监测，监测结果表明巷道围岩出现非线性大变形、锚索破断及支架扭曲变形等现象。利用FLAC3D对巷道围岩进行数值模拟，得出软岩巷道围岩变形属于给定变形，巷道支护体不仅要提供足够的支护强度，还必须适应软岩巷道大变形，据此提出可接长锚杆协调支护技术，使稳定后顶板下沉量在200~250 mm之间，两帮相对移近量在200 mm上下，得到预期的支护效果。 In this study, the deep soft rock roadway was as the research background. The roadway of the mine’s west bottom panel measure’s lane surface displacement was monitored. Data show that the rock roadway deformation is nonlinear large deformation of surrounding rock deformation and widespread cable breakage and other support bracket distorted body damage phenomena. Using FLAC3D software to simulate on the rock roadway, we obtained that the deformation of soft rock roadway belonged to given deformation. Roadway body not only has to provide sufficient supporting strength, but also must adapt to large deformation of soft rock roadway. Hereby, proposing the coordinated supporting technology with docking bolt, making the roof sinkage between 200 and 250 mm when it is stable and the relative two sides moving quantity in 200 mm up and down, getting the expected supporting effect.

Finite element based tracking of deforming surfaces

We present an approach to robustly track the geometry of an object that deforms over time from a set of input point clouds captured from a single viewpoint. The deformations we consider are caused by applying forces to known locations on the object’s surface. Our method combines the use of prior information on the geometry of the object modeled by a smooth template and the use of a linear finite element method to predict the deformation. This allows the accurate reconstruction of both the observed and the unobserved sides of the object. We present tracking results for noisy low-quality point clouds acquired by either a stereo camera or a depth camera, and simulations with point clouds corrupted by different error terms. We show that our method is also applicable to large non-linear deformations.

A coarse-grained model for the mechanical behavior of multi-layer graphene

Graphene is the strongest and highest weight-to-surface ratio material known, rendering it an excellent building block for nanocomposites. Multi-layer graphene (MLG) assemblies have intriguing mechanical properties distinct from the monolayer that remain poorly understood due to spatiotemporal limitations of experimental observations and atomistic modeling. To address this issue, here we establish a coarse-grained molecular dynamics (CG-MD) model of graphene using a strain energy conservation approach. The model is able to quantitatively reproduce graphene’s mechanical response in the elastic and fracture regimes. The hexagonal symmetry of graphene’s honeycomb lattice is conserved, and therefore the anisotropy in the non-linear large-deformation regime between the zigzag and armchair directions is preserved. The superlubricity effect, namely the strong orientational dependence of the shear rigidity between graphene layers, is also captured. We demonstrate the applicability of the model by reproducing recent experimental nanoindentation results in silico. Our model overcomes the limitations of current CG-MD approaches, in accurately predicting the fracture properties, the interlayer shear response, and the intrinsic anisotropy of MLG. Additionally, our fast, transferable force-field can be straightforwardly combined with existing coarse-grained models of polymers and proteins to predict the meso-scale behavior of hybrid carbon nanomaterials.

FEM Simulation on Uniaxial Tension of Hyperelastic Elastomers

Modeling large nonlinear elastic deformation of elastomers is an important issue for developing new materials. Particularly, this is very promising for design and performance analysis of dielectric elastomers (DEs). These “smart materials” are capable of responding to an external electric field by displaying significant change in shape and size. In this paper, finite element method (FEM) was used to simulate the mechanical behavior of soft elastomers on uniaxial tension. Experimental data from uniaxial tensile tests were used in order to calibrate hyperelastic constitutive models of the material behavior. The constitutive model parameters were evaluated in ABAQUS/CAE. The 3D-model simulation results of a dumbbell shaped specimen at uniaxial tension shows very good correspondence with experimental data.

Development of Hyperelastic Model for Natural Rubber Containing Weldlines

Several constitutive models of non-linear large elastic deformation based on strain-energy-density functions have been developed for hyperelastic materials. These models, coupled with the Finite Element Method (FEM), can effectively utilized by design engineers to analyze and design elastomeric products operating under the deformation states. However, due to the complexities of the mathematical formulation which can only obtained at the moderate strain and the assumption of material used for the analysis. Therefore it is formidable task for design engineer to make use of these constitutive relationships. In the present work, the strain-energy-density function of natural rubber part containing a weldline was constructed by using the Neural Network (NN) model. The analytical results were compared to those obtained by Neo-Hookean, Mooney-Rivlin, Ogden models. Good agreement between developed NN model and the existing experimental data was found, especially at very low strain and at very high strain.

Modeling of the mechanical degradation induced by moisture absorption in short natural fiber reinforced composites

Abstract This paper develops a constitutive model of short natural fiber reinforced composites (SNFRCs), with the consideration of nonlinear constitutive relation and large deformation induced by moisture absorption. This model accounts for the processes of moisture absorption and mechanical degradation in SNFRCs by a single internal variable, since these two thermodynamic processes are found correlated with each other. This internal variable is introduced to modify the Neo-Hookean model, from which the evolution equations of these two processes are derived by specifying a suitable energy dissipation function. Both the moisture absorption and the mechanical degradation are shown sensitive to the fiber content and could be enlarged with exposure time in a humid environment. Theoretical predictions of the evolution of the internal variable are compared with experimental results of short sisal fiber reinforced polypropylene and it is shown a good agreement between them. Moreover, this model is used to give a reasonable prediction of the degraded Young’s modulus of SNFRCs.

Suppression of nonlinear phonon relaxation in Yb:YAG thin disk via zero phonon line pumping.

A quantitative comparison of conventional absorption line (940 nm) pumping and zero phonon line (ZPL) (969 nm) pumping of a Yb:YAG thin disk laser is reported. Characteristics of an output beam profile, surface temperature, and deformation of a thin disk under the different pump wavelengths are evaluated. We found that a nonlinear phonon relaxation (NPR) of the excited state in Yb:YAG, which induces nonlinear temperature rise and large aspheric deformation, did not appear in the case of a ZPL pumped Yb:YAG thin disk. This means that the advantage of ZPL pumping is not only the reduction of quantum defect but also the suppression of NPR. The latter effect is more important for high power lasers.

Exploring the Geometry of the Space of Shells

AbstractWe prove both in the smooth and discrete setting that the Hessian of an elastic deformation energy results in a proper Riemannian metric on the space of shells (modulo rigid body motions). Based on this foundation we develop a time‐ and space‐discrete geodesic calculus. In particular we show how to shoot geodesics with prescribed initial data, and we give a construction for parallel transport in shell space. This enables, for example, natural extrapolation of paths in shell space and transfer of large nonlinear deformations from one shell to another with applications in animation, geometric, and physical modeling. Finally, we examine some aspects of curvature on shell space.

Stability Analysis for Extendable Leg of Pump Truck

There are mainly two areas of the lap part for the force transmission on the extension type retractable outriggers of the concrete pump truck, especially the bottom plate. If the side vertical plate at opening area isn’t designed properly, it may cause instability, which is really hard to be solved by analytical method. During structural checking of the leg with front-stretching type by ANSYS, the vertical plate at the area overlapped with the base is found to be out of convergence when load reaches a certain magnitude. Then the geometric nonlinear analysis is done by ANSYS and LS-DYNA respectively, and the results of them both verify the above conclusion. And the results of them are compared and analyzed. Finally the structure is improved to avoid buckling, and the improved structure meets the design requirements after the re-calculation. It also shows that the geometric nonlinear large deformation analysis is effective in solving the problem of buckling stability of complex structures.

Biaxial mechanical properties of the human thoracic and abdominal aorta, common carotid, subclavian, renal and common iliac arteries

The biomechanics of large- and medium-sized arteries influence the pathophysiology of arterial disease and the response to therapeutic interventions. However, a comprehensive comparative analysis of human arterial biaxial mechanical properties has not yet been reported. Planar biaxial extension was used to establish the passive mechanical properties of human thoracic (TA, [Formula: see text]) and abdominal (AA, [Formula: see text]) aorta, common carotid (CCA, [Formula: see text]), subclavian (SA, [Formula: see text]), renal (RA, [Formula: see text]) and common iliac (CIA, [Formula: see text]) arteries from 11 deceased subjects ([Formula: see text]years old). Histological evaluation determined the structure of each specimen. Experimental data were used to determine constitutive parameters for a structurally motivated nonlinear anisotropic constitutive model. All arteries demonstrated appreciable anisotropy and large nonlinear deformations. Most CCA, SA, TA, AA and CIA specimens were stiffer longitudinally, while most RAs were stiffer circumferentially. A switch in anisotropy was occasionally demonstrated for all arteries. The CCA was the most compliant, least anisotropic and least frequently diseased of all arteries, while the CIA and AA were the stiffest and the most diseased. The severity of atherosclerosis correlated with age, but was not affected by laterality. Elastin fibers in the aorta, SA and CCA were uniformly and mostly circumferentially distributed throughout the media, while in the RA and CIA, elastin was primarily axially aligned and concentrated in the external elastic lamina. Constitutive modeling provided good fits to the experimental data for most arteries. Biomechanical and architectural features of major arteries differ depending on location and functional environment. A better understanding of localized arterial mechanical properties may support the development of site-specific treatment modalities for arterial disease.

Opto-mechanical analysis of nonlinear elastomer membrane deformation under hydraulic pressure for variable-focus liquid-filled microlenses

Nonlinear large deformation of a transparent elastomer membrane under hydraulic pressure was analyzed to investigate its optical performance for a variable-focus liquid-filled membrane microlens. In most membrane microlenses, actuators control the hydraulic pressure of optical fluid so that the elastomer membrane together with the internal optical fluid changes its shape, which alters the light path of the microlens to adapt its optical power. A fluid-structure interaction simulation was performed to estimate the transient behavior of the microlens under the operation of electroactive polymer actuators, demonstrating that the viscosity of the optical fluid successfully stabilizes the fluctuations within a fairly short period of time during dynamic operations. Axisymmetric nonlinear plate theory was used to calculate the deformation profile of the membrane under hydrostatic pressure, with which optical characteristics of the membrane microlens were estimated. The effects of gravitation and viscoelastic behavior of the elastomer membrane on the optical performance of the membrane microlens were also evaluated with finite element analysis.

Numerical solutions for nonlinear large deformation behaviour of deepwater steel lazy-wave riser

To meet the increasing challenges of simple steel catenary riser on large hang-off tension and fatigue damage of the touchdown point (TDP) in deepwater or ultra deepwater applications, the steel lazy-wave risers (SLWR) have gained a viable solution. This paper is focused on the static equilibrium of SLWR which is of great importance to the basic configuration design of the riser. A more accurate model based on nonlinear large deformation beam theory is proposed to simulate the suspended part of SLWR, having evident advantage over previously applied small deformation beam or catenary theory which ignores the riser's bending stiffness and is hard to simulate the rapid change of the inclination angle. The model also deals with the pipe–soil interaction for simulating the TDP. The finite difference method is applied to obtain the numerical solutions. The results are comparatively in agreement with OrcaFlex. As an application, parametric analysis of the SLWR is carried out to investigate the influences of arc length of buoyancy section, arc length of upper section and soil stiffness on the static performance. The proposed model can be a basic reference for the dynamic analysis of the deepwater SLWR.

Passive biaxial mechanical properties and in vivo axial pre-stretch of the diseased human femoropopliteal and tibial arteries

Surgical and interventional therapies for atherosclerotic lesions of the infrainguinal arteries are notorious for high rates of failure. Frequently, this leads to expensive reinterventions, return of disabling symptoms or limb loss. Interaction between the artery and repair material likely plays an important role in reconstruction failure, but data describing the mechanical properties and functional characteristics of human femoropopliteal and tibial arteries are currently not available. Diseased superficial femoral (SFA, n=10), popliteal (PA, n=8) and tibial arteries (TA, n=3) from 10 patients with critical limb ischemia were tested to determine passive mechanical properties using planar biaxial extension. All specimens exhibited large nonlinear deformations and anisotropy. Under equibiaxial loading, all arteries were stiffer in the circumferential direction than in the longitudinal direction. Anisotropy and longitudinal compliance decreased distally, but circumferential compliance increased, possibly to maintain a homeostatic multiaxial stress state. Constitutive parameters for a four-fiber family invariant-based model were determined for all tissues to calculate in vivo axial pre-stretch that allows the artery to function in the most energy efficient manner while also preventing buckling during extremity flexion. Calculated axial pre-stretch was found to decrease with age, disease severity and more distal arterial location. Histological analysis of the femoropopliteal artery demonstrated a distinct sub-adventitial layer of longitudinal elastin fibers that appeared thicker in healthier arteries. The femoropopliteal artery characteristics and properties determined in this study may assist in devising better diagnostic and treatment modalities for patients with peripheral arterial disease.

Development of the distinct lattice spring model for large deformation analyses

SUMMARYThis study develops the distinct lattice spring model (DLSM) for geometrically nonlinear large deformation problems. The formulation of a spring bond deformation under a large deformation is derived under the Lagrange framework using polar decomposition. The results reveal that the DLSM's stiffness matrix under small deformations is the tangent stiffness matrix of the DLSM under large deformations. The formulation of the spring bond internal force under a given configuration is also presented and can be used to calculate the unbalanced force. Using these formulations, three nonlinear solving methods (the Euler method, modified Euler method, and Newton method) are developed for the DLSM with which to tackle large deformation problems. To investigate the performance of the developed model, three numerical examples involving large deformations are presented, the results of which are also in good agreement with the analytical and finite element method solutions. Copyright © 2013 John Wiley & Sons, Ltd.

Design of rectangular industrial duct plates subjected to out-of-plane pressure considering nonlinear large deformations

Large industrial steel ducts are often rectangular and are built-up of stiffened plates. The plates along with stiffeners act to resist the pressure loads and transfer these loads to the supports. Parallel wide flange steel profiles, usually beams, are used as transverse stiffeners that are spaced perpendicular to the longitudinal axis of duct. The design process involves determining the load carrying capacity and deflection of the plate based on the plate thickness and the spacing between stiffeners. The current analysis and design method for industrial ducts is based on the elastic large deflection plate theory using standard tables.A nonlinear finite element parametric study was conducted on dimensionless parameters to investigate the behavior of laterally loaded long plates. Through-thickness yielding of the plate and formation of partial plastic hinges at the ends is allowed. The results are presented in terms of a proposed dimensionless Normalized Load Factor (NLF) representing the applied pressure, the Normalized Deflection Factor (NDF) representing the out-of-plane deflection and the Normalized Maximum Stress Factor (NMSF) representing the maximum stresses induced in the plates. Design equations for deflection and stresses of plates are established with the aid of Bezier curves. A simple design procedure allowing for large deflection and partial yielding of edges is proposed. A limiting value for pressure has been found where it becomes irrelevant to check deflection. Results show that the proposed design procedure is simple and can lead to economic plate thicknesses and spacing of stiffeners in industrial ducts in ambient temperatures.

Reliability of in vivo human Achilles tendon stiffness assessed using acoustoelastography

Introduction: Current ultrasound-based sonoelastography methods, such as shear-wave elastography, are constrained to assessing tissue properties under minimal deformation (∼1%). Human tendons, such as the Achilles tendon, undergo relative large deformation (∼8%) during physiological loading, such as with running and jumping. A new post-processing method, acoustoelastography (AE), uses a tissue's acoustic properties to estimate stiffness under forces resulting in large nonlinear deformation. AE may be particularly well-suited for estimating in vivo tendon biomechanics in humans due to its comparative ease of use (requires only ultrasound) and potential for examining tendon mechanical behavior under high-load conditions.

Distribution of Underground Pressure Law and Fracture Zone Prediction Research of Overburden in Steep and Multiple Coal Seams Mining

Use Taiping coal mines second horizontal (+1100m~+900 m level ) 1#, 3# and 5# coal seam in Panzhihua Baoding as the research object, apply the problem solving nonlinear large deformation finite difference method (FLAC), to research the steep multi-seam mining of pressure distribution and characteristics of fracture zone. The results show that: (1)During the course of three coal mining extraction, the stress of goaf surrounding rocks will be changed. (2)When the nearby coal is mining, the coal pillar come into being stress concentration near the area. when the mining work continues, the goaf will have an effect on the protection pillar, which is similar to the "liberate". the effect of coal pillar and stress concentration nearby will be eased; (3)After the coal mining, plastic failure has occurred over the protection pillar, forming a water guide channel. Research results can be as a reference for similar steep seam mining.

Study on the Response of Surrounding Rock for Gob-Side Entry Retaining under the Mining

A coal mine in Chongqing +590m south four district 2443 working face as the research object, using the finite difference method (FLAC) which can solve the nonlinear large deformation problem, setting up the mechanical analysis model of the gob-side entry retaining, analyzing the structure characteristics of surrounding rock, and studying on the stability of surrounding rock of the gob-side entry retaining under the mining. the results showed that:(1) After the coal mining, the maximum displacement of roof has occurred on the edge of the roadway upper side near the filling body. The floor heave at the beginning mining, the floor has a downward displacement after the mining;(2)After the coal mining, the surrounding rock of the gob-side entry retaining has a larger range of shear failure, a strong tensile damage was occurred in filling body, big horizontal displacement was happened in the middle of filling body. Research results can provide reference for similar coal mining..