Design,Manufacture, and Quasi-Static Testing of Metallic Negative Stiffness Structures within a Polymer Matrix

A composite material system comprised of a monostable negative stiffness (NS) structure within a polymer matrix was designed, fabricated, and experimentally evaluated. The monostable negative stiffness (NS) structure was designed using a combination of analytical and numerical models and manufactured in stainless steel. The NS structure was arranged in parallel with different polymer matrices to experimentally evaluate the effects of the matrix properties on the overall stiffness and energy dissipation of the composite NS-matrix system when loaded in uniaxial compression. A strong influence of the matrix properties on the stiffness and energy absorption capacity of the composite system was observed. Unlike conventional composites for which there is a natural tradeoff between stiffness and energy absorption capacity, the composite NS-matrix system enhanced stiffness while simultaneously improving energy absorption relative to a neat matrix, but only when the stiffness of the matrix was carefully matched to the stiffness of the NS structure.     

Investigation of the Effects of Environmental Fatigue on the Mechanical Properties of GFRP Composite Constituents Using Nanoindentation

Background

Fatigue failure criteria for fibre reinforced polymer composites used in the design of marine structures are based on the micromechanical behaviour (e.g. stiffness properties) of their constituents. In the literature, there is a lack of information regarding the stiffness degradation of fibres, polymer matrix and fibre/matrix interface regions affected by environmental fatigue.

Objective

The aim of present study is to characterize the stiffness properties of composite constituents using the nanoindentation technique when fatigue failure of composites is due to the combined effect of sea water exposure and cyclic mechanical loads.

Methods

In the present study, the nanoindentation technique was used to characterize the stiffness properties of composite constituents where the effects of neighbouring phases, material pile up and viscoplasticity properties of the polymer matrix are corrected by finite element simulation.

Results

The use of finite element simulation in conjunction with nanoindentation test data, results in more accurate estimation of projected indented area which is required for measuring the properties of composite constituents. In addition, finite element simulation provides a greater understanding of the stress transfer between composite constituents during the nanoindentation process.

Conclusions

Results of nanoindentation testing on the composite microstructure of environmentally fatigue failed composite test coupons establish a strong link to the stiffness degradation of the fiber/matrix interface regions, verifying the degradation of composite constituents identified by scanning electron microscopy (SEM) and energy dispersive X-ray spectroscopy (EDX) analysis.

     

Direct Stiffness Analysis of Lateral Buckling

Abstract

A direct stiffness method of analyzing the elastic ftexural-torsional buckling of rigid-jointed plane frames composed of l-section members and subjected to in-plane loads is presented. The in-plane stiffness matrix and the fixed-end resultants are obtained from the member stiffness matrices derived from the in-plane differential equations. These member stiffness matrices are assembled and solved, and their solutions are used to linearize the flexural-torsional buckling equations. The out-of-plane member stiffness matrices are then obtained numerically from the buckling equations by the method of finite integrals. The out-of-plane frame -stiffness matrix is assembled, and the critical loads are obtained when its determinant is zero. A computer program is developed which carries out either a first- or second-order in-plane analysis, and then determines the flexural-torsional buckling loads. The effects of in-plane deformations prior to buckling can be included. Very good agreement is obtained between the results computed by this program and known solutions, and its ability to analyze large complex frames is demonstrated.     

Arterial Wall Stiffening in Caveolin-1 Deficiency-Induced Pulmonary Artery Hypertension in Mice

Background

Pulmonary artery hypertension (PAH) is a complex disorder that can lead to right heart failure. The generation of caveolin-1 deficient mice (CAV-1^?/?) has provided an alternative genetic model to study the mechanisms of pulmonary hypertension. However, the vascular adaptations in these mice have not been characterized.

Objective

To determine the histological and functional changes in the pulmonary and carotid arteries in CAV-1^?/? induced PAH.

Methods

Pulmonary and carotid arteries of young (4–6 months old) and mature (9–12 months old) CAV-1^?/? mice were tested and compared to normal wild type mice.

Results

Artery stiffness increases in CAV-1^?/? mice, especially the circumferential stiffness of the pulmonary arteries. Increases in stiffness were quantified by a decrease in circumferential stretch and transition strain, increases in elastic moduli, and an increase in total strain energy at physiologic strains. Changes in mechanical properties for the pulmonary artery correlated with increased collagen content while changes in the carotid artery correlated with decreased elastin content.

Conclusions

We demonstrated that an increase in artery stiffness is associated with CAV-1 deficiency-induced pulmonary hypertension. These results improve our understanding of arterial remodeling in PAH.

     

Optimal Design of Thin-Walled Cylinders of Variable Wall-Thickness Subject to Flexural and Torsional Stiffness Constraints

ABSTRACT

This paper considers the problem of determining center-line shape and wall-thickness distribution of a thin-walled cylinder of given center-line length that uses the minimum possible amount of material to achieve prescribed minimum stiffnesses in torsion and bending in a given plane. Necessary optimality conditions are derived and the solution is found partly in closed form and partly by numerical methods. Optimal solutions are presented for various stiffness ratios and compared with other admissible designs.     

Design Sensitivity Analysis of Truss Structures with Elastoplastic Material*

ABSTRACT

A continuum-based design sensitivity analysis (DSA) method is presented for configuration (or layout) design of nonlinear structural systems with rate-independent elastoplastic material. Configuration design variables are characterized by shape and orientation changes of the structural component. A continuum-based shape DSA method that utilizes the material derivative of continuum mechanics is extended to account for effects of shape and orientation variations. The incremental analysis method, with updated Lagrangian formulation, is used to derive the design sensitivity for the nonlinear structural system.

To derive the design sensitivity, incremental energy and load forms are utilized. The first variations of energy and load forms and the static response with respect to configuration design variables are described using the material derivative. Direct differentiation is utilized to obtain the first variation of the performance measure explicitly in terms of variations of configuration design variables. With the consistent tangent stiffness matrix employed at the end of each load step to compute the design sensitivity, it is found that no iterations are necessary to compute design sensitivity. In addition, the linear design velocity is used to account for configuration design changes, with the velocity field being updated at each load step of the incremental analysis.     

Transverse Stiffness of a Sinusoidally Corrugated Plate∗

Abstract

An analytical model for the initial transverse stiffness of a sinusoidally corrugated plate is derived, incorporating deformations due to extension, shear, and bending. A nondimensional plot is developed for determining transverse stiffness based on thickness and corrugation for a range of plate geometries. This model shows that for most corrugated plates the transverse stiffness is dramatically decreased from that of an uncomigated plate of the same thickness. For thin plates, a simple approximate polynomial expression for initial transverse stiffness is obtained. For thick plates with a small degree of corrugation, transverse stiffness is not negligible relative to longitudinal stiffness. The exact model is verified using a linear-elastic two-dimensional finite element model.     

Analytical Model and Experimental Verification of the Interfacial Peeling Strength of Electrodes

Background

The interfacial peeling strength of lithium-ion battery electrodes is a very important mechanical property that significantly affects the electrochemical performance of battery cells.

Objective

To characterize the interfacial peeling strength of an electrode, an analytical model based on the energy balance principle is established by considering the state of charge (SOC), the energy release rate, the tensile stiffness, and the peeling angle.

Methods

Uniaxial tensile tests and 180-degree peeling tests are conducted to determine the Young’s modulus and the interfacial peeling strengths of electrodes at different SOCs, respectively. The experimental data serve as a validation of the accuracy of the analytical model.

Results

The interfacial peeling strength of the electrode shows a strong reliance on many factors. Specifically, the interfacial peeling strength increases with the SOC and the energy release, and decreases with the peeling angle. When the tensile stiffness of the active layer equals that of the current collector, the interfacial peeling strength has a maximum value.

Conclusions

By comparing with experimental data of the 180-degree peeling test, the model prediction shows excellent agreement at different SOCs, and the analytical model established in this paper can be used to guide and assess the interfacial properties of electrodes for industry.

     

A FENE-P k–ε turbulence model for low and intermediate regimes of polymer-induced drag reduction

A new low-Reynolds-number k–ε turbulence model is developed for flows of viscoelastic fluids described by the finitely extensible nonlinear elastic rheological constitutive equation with Peterlin approximation (FENE-P model). The model is validated against direct numerical simulations in the low and intermediate drag reduction (DR) regimes (DR up to 50%). The results obtained represent an improvement over the low DR model of Pinho et al. (2008) [A low Reynolds number k–ε turbulence model for FENE-P viscoelastic fluids, Journal of Non-Newtonian Fluid Mechanics, 154, 89–108]. In extending the range of application to higher values of drag reduction, three main improvements were incorporated: a modified eddy viscosity closure, the inclusion of direct viscoelastic contributions into the transport equations for turbulent kinetic energy (k) and its dissipation rate, and a new closure for the cross-correlations between the fluctuating components of the polymer conformation and rate of strain tensors (NLT_ij). The NLT_ij appears in the Reynolds-averaged evolution equation for the conformation tensor (RACE), which is required to calculate the average polymer stress, and in the viscoelastic stress work in the transport equation of k. It is shown that the predictions of mean velocity, turbulent kinetic energy, its rate of dissipation by the Newtonian solvent, conformation tensor and polymer and Reynolds shear stresses are improved compared to those obtained from the earlier model.     

The role of dissipation and defect energy in variational formulations of problems in strain-gradient plasticity. Part 1: polycrystalline plasticity

A general set of flow laws and associated variational formulations are constructed for small-deformation rate-independent problems in strain-gradient plasticity. The framework is based on the thermodynamically consistent theory due to Gurtin and Anand (J Mech Phys Solids 53:1624–1649, 2005), and includes as variables a set of microstresses which have both energetic and dissipative components. The flow law is of associative type. It is expressed as a normality law with respect to a convex but otherwise arbitrary yield function, or equivalently in terms of the corresponding dissipation function. Two cases studied are, first, an extension of the classical Hill-Mises or J ₂ flow law and second, a form written as a linear sum of the magnitudes of the plastic strain and strain gradient. This latter form is motivated by work of Evans and Hutchinson (Acta Mater 57:1675–1688, 2009) and Nix and Gao (J Mech Phys Solids 46:411–425, 1998), who show that it leads to superior correspondence with experimental results, at least for particular classes of problems. The corresponding yield function is obtained by a duality argument. The variational problem is based on the flow rule expressed in terms of the dissipation function, and the problem is formulated as a variational inequality in the displacement, plastic strain, and hardening parameter. Dissipative components of the microstresses, which are indeterminate, are absent from the formulation. Existence and uniqueness of solutions are investigated for the generalized Hill-Mises and linear-sum dissipation functions, and for various combinations of defect energy. The conditions for well-posedness of the problem depend critically on the choice of dissipation function, and on the presence or otherwise of a defect energy in the plastic strain or plastic strain gradient, and of internal-variable hardening.     

Adaptive Rotated Gaussian Weighted Digital Image Correlation (RGW-DIC) for Heterogeneous Deformation Measurement

Background

Digital image correlation (DIC) has advanced to become a flexible, reliable and fast optical method for the measurement of non-contact and full-field surface deformation. However, the accuracy of existing methods in measuring heterogeneous deformation fields—especially for the high gradient strain field – can be improved.

Objective

In state-of-art local DIC applications, several methods have been put forward to adapt a subset to unknown deformation. Although improvements in performance using these methods are obtained, results are still ungratified for severely heterogeneous deformation such as the Star 2 and Star 5 images from DIC Challenge 2.0.

Methods

In this paper, a rotated Gaussian weighted zero-mean normalized sum of squared difference (RGW-ZNSSD) criterion function is proposed as the basis for RGW-DIC subset size adaptation. RGW-DIC can automatically determine the optimum weight distribution, hence self-adaptivity in subset size and orientation are achieved simultaneously.

Results

The effectiveness of the proposed RGW-DIC is verified using DIC-challenge 2.0 images and simulated sinusoidal deformation images. Results reveal that the adaptively determined subset weight distribution can significantly improve the accuracy of heterogeneous deformation measurement compared with traditional DIC and DIC with isotropic Gaussian weight functions.

Conclusions

The proposed RGW-DIC can be applied to unknown severely heterogeneous deformation measurement.

     

New Methodologies for Fracture Detection of Automotive Steels in Tight Radius Bending: Application to the VDA 238–100 V-Bend Test

Background

The VDA 238–100 tight radius V-bend test can be used to efficiently characterize the bendability and fracture limits of sheet metals in severe plane strain bending. Material performance in plane strain bending is critical for the selection of advanced high strength steels for energy absorbing structural components.

Objective

The detection of failure based upon a reduction in the punch force can lead to erroneous predictions of failure for ductile or thin gage alloys in the VDA 238–100 test. New failure criteria were proposed and evaluated across a range of automotive steels.

Methods

Four detection methods in the V-bend test were evaluated based upon the load drop, bending moment, novel stress metric and the strain rate for seven steels with strength levels from 270 to 1500 MPa. The appropriate failure threshold was identified from visual inspection of the surface during bending.

Results

The vertical punch force will decrease as a consequence of the mechanics in the V-bend test at intermediate bend angles even without fracture. The novel stress-based metric accounts for sheet thinning and could successfully identify “false positives” and punch lift-off when considering the strain-rate evolution.

Conclusions

Failure detection using the VDA load threshold method may significantly under-report the bend performance of alloys with intermediate-to-high bendability or thin gauges. The proposed stress-based metric can reliably detect fracture for bend angles in excess of 160° and be readily calculated using the existing data. The VDA load threshold for failure can work well for materials that exhibit significant cracking.

     

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Background

Image-based global correlation involves a class of ill-posed inverse problems associated with speckle quality and deformation gradients on specimen surfaces. However, the method used to simultaneously integrate the prior information related to images and deformations and effectively regularize these inverse problems still faces severe challenges, especially when complex heterogeneous deformation gradients exist over sample surfaces with locally degraded speckle patterns.

Objective

We propose a novel self-adaptive meshing-based regularization for global image correlation to determine spatially complex heterogeneous deformations.

Methods

A virtual truss system with a linearly elastic constitutive relationship is employed to self-adaptively implement surface meshing by numerically balancing the exerted virtual forces under the constraints of the local speckle image quality and deformation gradients. The 2-norm-based condition number of the local stiffness matrix is introduced to ensure numerical stability during meshing.

Results

The algorithms can behave as a smart regularization procedure integrating all the prior information during numerical calculations, consequently achieving an accurate, precise and robust characterization of heterogeneous deformations, as demonstrated by virtual simulations and actual experiments.

Conclusions

The regularization strategy coupled to image-based correlation is also promising for automatic quantification of complex heterogeneous deformations, particularly from images with locally degraded speckle patterns.

     

Novel Crash Sled with a Translating Support Mass

Background

A novel crash sled has been developed with a translating support incorporating transducers that allow multiple methods of measuring energy absorption to fully characterize the dynamic crush response of composite components.

Objective

The main goal of the current investigation was to demonstrate functionality, repeatability, and accuracy of crush testing using a crash sled with a translating support mass.

Methods

A semi-automated algorithm for data reduction was developed based on impact mechanics principles. A preliminary set of tests was initially conducted using aluminum honeycomb specimens with a specified stable crushing force to quantify the accuracy and repeatability of the crush data. Following the success of these tests, triaxially-braided fiber-reinforced polymer (FRP) specimens were evaluated.

Results

Crush tests with the aluminum honeycomb specimens showed excellent outcomes for all three specimens. These data provided close agreement with cumulative energy absorption between individual instruments and stable crushing forces at expected values. For the FRP specimens, specific energy absorption (SEA) and force-displacement curves were successfully measured; however, data from the translating support mass accelerometer were excluded from the dataset due to clipping. The SEA of the corrugated specimens was greater than the SEA for the C-channel specimens at both test speeds.

Conclusions

The crash sled functionality was verified, the specimen geometry was found to contribute more to SEA than the impact speed in the speed range tested, and the support mass accelerometer will be upgraded to prevent clipping in future tests.

     

Dynamic Tensile Response of a Microwave Damaged Granitic Rock

Background

Understanding the dynamic tensile response of microwave damaged rock is of great significance to promote the development of microwave-assisted hard rock breakage technology. However, most of the current research on this issue is limited to static loading conditions, which is inconsistent with the dynamic stress circumstances encountered in real rock-breaking operations.

Objective

The objective of this work is to investigate the effects of microwave irradiation on the dynamic tensile strength, full-field displacement distribution and average fracture energy of a granitic rock.

Methods

The split Hopkinson pressure bar (SHPB) system combined with digital image correlation (DIC) technique is adopted to conduct the experiments. The overload phenomenon, which refers to the strength over-estimation phenomenon in the Brazilian test, is validated using the conventional strain gauge method. Based on the DIC analysis, a new approach for calculating the average fracture energy is proposed.

Results

Experimental results show that both the apparent and true tensile strengths increase with the loading rate while decreasing with the increase of the irradiation duration; and the true tensile strength after overload correction is lower than the apparent strength. Besides, the overload ratio and fracture energy also show the loading rate and irradiation duration dependency.

Conclusions

Our findings prove clearly that microwave irradiation significantly weakens the dynamic tensile properties of granitic rock.

     

考虑应变率效应的混凝土随机损伤本构模型研究

混凝土材料组分复杂且具有随机分布的特点, 其受力力学行为不可避免地存在非线性和随机性. 同时, 在动力荷载作用下, 混凝土材料具有不可忽视的率敏感性. 为了综合反映混凝土受力力学行为中的非线性、随机性与率敏感性, 本文从对材料的纳-微观裂纹扩展分析入手, 引入速率过程理论描述纳观裂纹的扩展速率, 并研究了对应的能量耗散过程. 在此基础上通过裂纹层级模型将纳观分析推演到微观尺度, 建立了微观能量耗散的基本表达式. 进而与微-细观随机断裂模型相结合, 形成了混凝土纳-微-细观随机损伤本构模型. 同时, 基于速率相关势垒的分析, 揭示了动力强度的提高源自加载速率和原子键断裂速率的竞争机制. 据此, 假定微裂纹间相互作用与应变率比值的相关关系以建立微弹簧能量耗散速率与应变率的联系, 实现了从静力本构模型向动力本构模型的扩展. 数值算例表明, 建议模型能够同时反映混凝土材料力学行为中的非线性、随机性和率敏感性. 最后通过与相关试验结果的对比, 验证了建议模型的正确性.      

On the correlation between enstrophy and energy dissipation rate in a turbulent wake

All three components of the vorticity fluctuation have been measured simultaneously in a turbulent wake using a new eight-sensor vorticity probe. The vorticity fluctuation spectra agree reasonably well with those from a direct numerical simulation of a turbulent channel flow at high wavenumbers. The similarity between the instantaneous energy dissipation rate ε and the instantaneous enstrophy ω² is examined using spectra and probability density functions. The correlation between ω² and ε is evaluated in some detail. The homogeneous value of ε is strongly correlated with ω². The full value of ε and, more especially its isotropic value, are less well correlated with the enstrophy. Conditional averaging indicates that high enstrophy regions are associated with high energy dissipation rate regions.     

The Image-Based Inertial Release (IBIR) Test: A New High Strain Rate Test for Stiffness Strain-Rate Sensitivity Identification

A key limitation of current moderate and high strain rate test methods is the need for external force measurement. For high loading rate hydraulic machines, ringing in the load cell corrupts the force measurement. Similarly, the analysis of split-Hopkinson bar tests requires the assumption that the specimen is in a state of quasi-static equilibrium. Recently, image-based inertial test methods have shown that external force measurement is not required if full-field measurements are available and inertial effects are significant enough. In this case the load information is provided by the acceleration fields which are derived from full-field displacement measurements. This article describes a new image-based inertial test method that can be used for simultaneous quasi-static and high strain rate stiffness identification on the same test sample. An experimental validation of the new test method is provided using PMMA samples. A major advantage of this new test method is that it utilises a standard tensile test machine and the only specialist equipment that is required is an ultra-high speed camera.

     

A New Technique for Curved Rod Bending Tests Based on Digital Image Correlation

Background

The study of the deformation of curved rods subjected to bending and its associated stress state is a complex task that has not been treated in depth in the literature, which makes difficult to obtain constitutive models or Finite Element Models (FEM) in which it is necessary to know all the components of the stress and strain tensors.

Objectives

This study focuses on a new calculation methodology to obtain stress and strain tensors of curved rods under bending.

Methods

The stress and strain tensors have been determined based on the theory of continuum mechanics and differential geometry of curves (moving bases), in a general methodology and valid for large strains, curved geometries and variable cross-sections along the specimen. This has been applied to the human rib and, in addition, a new experimental method for bending of curved specimens based on Digital Image Correlation (DIC) is presented.

Results

Both the test method and the proposed calculations applied to the human rib show results according to expectations, allowing to know the rib curvature changes along the test, the stresses and strains along the rib and the components of both stress and strain in all directions, in order to build the stress and strain tensors. In addition, the results of stress, strain and young’s modulus correspond to those of previous literature in tensile testing of human rib cortical bone.

Conclusions

The proposed calculations allow the construction of the strain and stress tensors of a curved specimen subjected to bending, which is of great importance for the development of constitutive models. Moreover, since with this method it is possible to calculate both tensors along the entire length of the specimen and in all directions, it is possible to apply this method in finite element models. Finally, the new test methodology allows to know the stress and strain in curved specimens such as the human rib, from bending tests.

     

Stretching Graphene to 3.3% Strain Using Formvar-Reinforced Flexible Substrate

Background

As a one-atom-thick material, the mechanical loading of graphene in large scale remains a challenge, and the maximum tensile strain that can be realized is through a flexible substrate, but only with a value of 1.8% due to the weak interfacial stress transfer.

Objective

Aims to illustrate the interface reinforcement brought by formvar resins as a buffering layer between graphene and substrates.

Methods

Single crystal graphene transferred to different substrates, applied with uniaxial stretching to compare the interface strength, and finite element analysis was performed to simulate tensile process for studying the influence of Poisson’s ratio of the buffering layer for interface reinforcement.

Results

In this work we use formvar resins as a buffering layer to achieve a maximum uniaxial tensile strain of 3.3% in graphene, close to the theoretical limit (3.7%) that graphene can achieve by flexible substrate stretching. The interface reinforcement by formvar is significantly higher than that by other polymers, which is attributed to the liquid–solid phase transition of formvar for more conformal interfacial contact and its suitable Poisson’s ratio with graphene to avoid its buckling along the transverse direction.

Conclusions

We believe that these results can provide guidance for the design of substrates and interfaces for graphene loading, as well as the support for mechanics analysis of graphene-based flexible electronic devices.