Nonlinear Stress-strain Curves Research Articles

Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics

Fractal-inspired designs represent an emerging class of strategy for stretchable electronics, which have been demonstrated to be particularly useful for various applications, such as stretchable batteries and biointegrated electrophysiological electrodes. The fractal-inspired constructs usually undergo complicated, nonlinear deformations under mechanical loading, because of the highly complex and diverse microstructures inherent in high-order fractal patterns. The underlying relations between the nonlinear mechanical responses and microstructure geometry are essential in practical applications, which require a relevant mechanics theory to serve as the basis of a design approach. Here, a theoretical model inspired by the mechanism of ordered unraveling is developed to study the nonlinear stress–strain curves and elastic stretchability for a class of fractal-inspired horseshoe microstructures. Analytic solutions were obtained for some key mechanical quantities, such as the elastic modulus and the tangent modulus at the beginning of each deformation stage. Both the finite-element analyses (FEA) and experiments were carried out to validate the model. Systematic analyses of the microstructure–property relationship dictate how to leverage the various geometric parameters to tune the multistage, J-shaped stress–strain curves. Moreover, a demonstrative example shows the utility of the theoretical model in design optimization of fractal-inspired microstructures used as electrophysiological electrodes, aiming to achieve maximum elastic stretchability for prescribed filling ratios. The results indicate a substantial enhancement (e.g., >4 times) of elastic stretchability by using fractal designs, as compared to traditional horseshoe designs. This study can serve as design guidelines of fractal-inspired microstructures in different stretchable electronic systems.

Glycosaminoglycans contribute to extracellular matrix fiber recruitment and arterial wall mechanics.

Elastic and collagen fibers are well known to be the major load-bearing extracellular matrix (ECM) components of the arterial wall. Studies of the structural components and mechanics of arterial ECM generally focus on elastin and collagen fibers, and glycosaminoglycans (GAGs) are often neglected. Although GAGs represent only a small component of the vessel wall ECM, they are considerably important because of their diverse functionality and their role in pathological processes. The goal of this study was to study the mechanical and structural contributions of GAGs to the arterial wall. Biaxial tensile testing was paired with multiphoton microscopic imaging of elastic and collagen fibers in order to establish the structure-function relationships of porcine thoracic aorta before and after enzymatic GAG removal. Removal of GAGs results in an earlier transition point of the nonlinear stress-strain curves [Formula: see text]. However, stiffness was not significantly different after GAG removal treatment, indicating earlier but not absolute stiffening. Multiphoton microscopy showed that when GAGs are removed, the adventitial collagen fibers are straighter, and both elastin and collagen fibers are recruited at lower levels of strain, in agreement with the mechanical change. The amount of stress relaxation also decreased in GAG-depleted arteries [Formula: see text]. These findings suggest that the interaction between GAGs and other ECM constituents plays an important role in the mechanics of the arterial wall, and GAGs should be considered in addition to elastic and collagen fibers when studying arterial function.

ABAQUS를 이용한 강섬유보강 콘크리트 패널의 고속 충돌 거동 해석

Dept. of Architectural Engineering, Chungnam National University, Daejeon 34134, Rep. of KoreaABSTRACT This paper employed finite element method (FEM) to study the dynamic response of Steel Fiber-Reinforced Concrete(SFRC) panels subjected to impact loading by spherical projectiles. The material properties and non-linear stress-strain curves of SFRC were obtained by compression test and flexural test. Various parametric studies, such as the effect of fiber volume fraction and thickness of panels, are made and numerical analyses are compared with experiments conducted. It is shown that protective performance of concrete panels will be improved by adding steel fiber. Area loss rates and weight loss rates are dec reased with increasing fiber volume fraction. Also, penetration modes can be expected by FEM, showing well agreement with experiment. Results can be applied for designing the protection of military structures and other facilities against high-velocity projectil es.Keywords : SFRC, high velocity impact, fiber volume fraction, fracture, penetration, finite element method

Modified Method for Dynamic Stress-Strain Curve Determination of Closed-Cell Foams

The paper presents a modified method for the non-linear dynamic stress-strain curve determination with the use of cushion curves provided by the manufacturers of closed-cell foams. This method consists of two main stages: stage 1 – the cushion curves transformation to the coordinate system of dynamic stress-energy density, combined with the cubic b-spline curve approximation, and stage 2 – development of the dynamic stress-strain curve considering that the area under the curve is equal to the energy density of a collision. The stress-strain curves are one of the basic parameters of the foam material models used to describe the collision process, in the modelling environments of finite element method (FEM), e.g. LS-DYNA. Performed verification consisting in the reconstruction of cushion curves using LS-DYNA showed that the proposed method of the dynamic stress-strain curves determination is efficient and effective. Taking into account that access to the stress-strain curves is hindered (cushioning material manufacturers do not publish them), and the access to charts of cushion curves is easier, the proposed method for determining the stress-strain curves can relevantly shorten the process of preparing the input data, which are required during modelling of spatial structures using FEM. Copyright © 2016 John Wiley & Sons, Ltd.

Elastic Properties of Freeze-Cast La0.6Sr0.4Co0.2Fe0.8O3

Elastic parameters, namely Young’s, shear and bulk moduli and Poisson’s ratio, of freeze-cast La0.6Sr0.4Co0.2Fe0.8O3-δ (LSCF) envisaged as porous substrate for the application of dense LSCF oxygen transport layers were investigated at room temperature by a quasi-static hysteresis compression test. The nonlinear stress-strain behavior of LSCF results in continuously changing elastic parameters. The evolution of these elastic parameters was studied as a function of the longitudinal strain. The elastic parameters showed extrema due to ferroelastic domain switching. Young’s and shear moduli revealed minimum values while bulk modulus and Poisson’s ratio demonstrated maximum values, due to the transverse strain contributed by ferroelastic domain switching. Bulk modulus shows relatively constant values before and after the domain switching process. Young’s modulus shows similar values as in literature and the Young’s modulus from bending tests is close to the lowest values evaluated continuously from nonlinear stress-strain curves. The apparent fractures stress in a compressive mode along the pore direction is much higher than the bending strength of porous LSCF with isotropic pore structure. It appears to benefit from its large, long, oriented pore structure, which not only provides large porosity but also relatively high mechanical stability along the pore direction. Figure 1

Fracture of epoxy-based marine coatings as free films and substrated coatings under static tension

Factors controlling crack development in two formulations of heavily filled epoxy anti-corrosion coatings have been studied as free films and on steel substrates. Both coatings were nominally 300μm thick. Tensile strength, Young’s modulus, strain to failure and fracture toughness of coating free films were measured at 23°C. Tensile tests of both coatings on steel substrates were performed at 23°C and strains to development of first coating crack and crack development with increasing strain were measured using extensometry and Digital Image Correlation (DIC). Finite element models of free film and substrated samples, incorporating non-linear stress–strain curves, were used to calculate residual stresses in substrated samples and J values of coating cracks. It was found that strain to first crack in coatings on substrates could be predicted using fracture mechanics models of coating cracks together with data on defect size, residual stress and toughness. Channelling crack development and factors influencing the relative ductility of free film and substrated coatings are discussed.

Egg-boxパネルの圧潰特性評価と荷重の変動を抑えた設計

In this paper, the compressive response of an egg-box panel was investigated using a nonlinear FE analysis. The egg-box panel was based on spherical shells and frusta, and its compressive response was predicted by considering the theoretical compressive responses of the spherical shell and frusta individually. Given that the material’s strain-hardening characteristics enhance the compressive response of the egg-box panel, the compressive response would be underestimated by using the initial yield stress as a material parameter. Instead, the flow stress based on the initial yield stress, the strain-hardening exponent in the nonlinear stress-strain curve and the ultimate tensile strength were effective for estimating the compressive response of egg-box panel. Also, the compressive load continued to increase as the displacement increased. By adopting appropriate dimensions for the flat-shaped basement in the egg-box panel, a uniform load-displacement curve could be obtained.

Electrospun polyurethane and hydrogel composite scaffolds as biomechanical mimics for aortic valve tissue engineering

Electrospun polyurethane and hydrogel composite scaffolds as biomechanical mimics for aortic valve tissue engineering

Nonlinear material behaviour and failure of closed-cell polymer foams

Classical strength criteria, like the von Mises criterion, are used to postulate the failure of ductile materials like steel or brass. It is known that for the application of foams in modern lightweight structures extended criteria are required, since foams are sensitive to hydrostatic stress. This observation on the macroscale can be explained by the deformation mechanisms of one single foam cell. Under hydrostatic stress, the deformation of the cell causes a non-uniform stress state of the cell walls. To understand the mechanism on the microlevel, a finite element model on the basis of a tetrakaidecahedron as unit cell was implemented. Utilising a strain energy-based homogenisation concept, the effective properties of the foam can be obtained. To adapt the geometric properties of the model to the real microstructure of the foam, results of a computer tomography image analysis were used by considering several imperfections in the cell geometry. For the analysis of the stress state on the microlevel, different load cases were applied to the unit cell. By means of these simulations, the geometrically nonlinear stress–strain curves on the macrolevel were deduced. Furthermore, the analysis of the finite element model provides an insight into the deformation mechanism on the microscale and allows the prediction of failure as well. Finally, the predicted failure points are represented in the Burzynski plane and compared with experimental results. The current paper focuses on the hard foam ROHACELL\({^{\circledR}}\) IG-series (industrial grade), which is a closed-cell PMI foam produced by Evonik Industries AG, Germany.

Application of the Virtual Fields Method to the uniaxial behavior of rubbers at medium strain rates

The Virtual Fields Method (VFM) is used to explore strain-rate dependent mechanical properties of a hyperelastic material. In this method, the principle of virtual work is constructed to inversely obtain the Young’s modulus and Poisson’s ratio of a given material from optical measurements of displacement obtained during a dynamic loading event. The virtual displacement field is designed so that acceleration fields, and thereby inertial forces, are used to calculate the material properties, and the traction force term in the principle of virtual work can be eliminated. Experimentally, this means that no force measurements are required during dynamic loading. Prior to the experimental investigations, a simple analytical calculation and finite element model were used in order to simulate the method; the output from the VFM showed good agreement with the given material coefficients. For the experimental work, pure silicone rubber was chosen as a model material. This rubber was tested in tension using a drop-weight apparatus at a medium strain rate (c.a. 160s−1), using high speed photography and Digital Image Correlation to provide strain and acceleration data which were subsequently analyzed by use of the VFM. By using static pre-stretching prior to the dynamic load, the hyperelastic behavior can be investigated up to large strains, even though the dynamic loading itself only has a small strain amplitude. By optimizing the differential one-term Ogden model to modulus estimations at each of the pre-stretching locations, the nonlinear stress–strain curves were reconstructed. The initial modulus change between these dynamic experiments and quasi-static tests was compared to the storage modulus increment obtained from DMA tests on the same material.

Energy analysis of the critical force of slender RC columns

A semi-analytical procedure for the determination of the critical force of a pin-ended column loaded by axial force and bending moment is proposed. It is based on the principle of minimum potential energy of internal and external forces. The equations for strain energy have been derived for the first- and the second-order displacements per section, including compressed and tensile concrete and reinforcement. The energy of the external forces with axial and flexural displacement effects has been derived on the assumed sinusoidal deflection curve. The trapezoid rule is applied to integrate the segment internal energy. The proposed method uses a non-linear stress–strain curve for concrete; bilinear elastic–plastic relationship for reinforcement; equilibrium conditions at a sectional level to generate the strain energies along the member. The effects of shear deformations are neglected. The effect of lateral confining by the stirrups to strength is also analysed. The results obtained with the proposed model have been verified and compared with experimental results from the literature.

3点曲げ試験から非線形応力－ひずみ関係を推定する逆解析手法の提案

An inverse analysis method was proposed for estimating nonlinear stress-strain curve with plastic deformation from load-deflection curve of three-point bending test of simply supported beam with rectangular cross section. This method was based on a small deformation theory under a few assumptions. Curvature was derived from the relation of load-deflection by applying the moment area method and geometrical relation, and bending strain was derived from the relation of strain-curvature. Then bending stress was derived from the relation of moment-curvature. Finite element analysis was conducted for verifying that these equations could estimate stress-strain curve. The estimated stress-strain curve showed good agreement with the actual one, verifying the usefulness of the proposed method for estimating stress-strain relation from the load-deflection curve of three-point bending test.

Creep behavior of porous La0.6Sr0.4Co0.2Fe0.8O3−δ oxygen transport membrane supports

Advanced oxygen transport membrane designs rely upon a thin functional layer supported by a porous substrate material that carries the mechanical loads. The creep deformation behavior needs to be assessed in order to warrant a long-term reliable operation at elevated temperatures. The current study reports the creep behavior of porous La0.6Sr0.4Co0.2Fe0.8O3−δ in air for a temperature range of 750–950°C. Stress exponents and activation energies are derived from the deformation data. A comparison with the creep rates of dense material revealed a progressively increasing creep rate with increasing temperature that might be related to surface diffusional effects. Additional tests at room temperature revealed non-linear stress–strain curves and an apparent ferroelastic creep due to domain switching in the rhombohedral phase that is stable at lower temperature.

Linear Analysis of the Constitutive Relation of Concrete Elastoplastic Disturbance

A linearization method of the uniaxial non-fitting nonlinear stress-strain curve given by the author of the paper is presented. The evolution equation between disturbances variable and plastic strain is derived based on Theory of Duality Disturbance. A simple method for concrete structures preforming elastoplastic analysis is presented (including softening analysis).

Nonlinear Deformation Properties of Composites with Transversely Isotropic Components

The deformation model of composite materials with physically nonlinear components is generalized to materials reinforced with unidirectional spheroidal inclusions. It is assumed that the matrix is isotropic and described by a nonlinear stress–strain curve and the inclusions are transversely isotropic and linear elastic. The stochastic differential equations of the physically nonlinear theory of elasticity are reduced to integral equations, which are then reduced by the method of conditional moments to a system of algebraic equations solved by the simple iteration method. The proposed approach underlies algorithms developed to evaluate the effective elastic properties of composites with transversely isotropic components when nonlinearity is due to the nonlinear deformation of the matrix. The dependence of Poisson’s ratios on macrostrains and the macrostress–macrostrain curves for different volume fractions of components and different shapes of inclusions are analyzed

The importance of the material properties on the burst speed of turbine disks for aeronautical applications

Abstract The computation of the burst of turbine disks for aeronautical engines is a current problem of great practical interest. Turbine disks are stressed by severe loads, for this reason the knowledge of the burst angular velocity is of primary importance for the whole safety of the aircraft during ordinary missions or extra-ordinary conditions that engines may encounter during service. In this work, a numerical method to predict the burst speed is presented, introducing the physical phenomenon at the base of the burst: the inertial instability. The method is based on Finite Element simulations taking into account the spin-softening effect which leads to instability and therefore to the burst of the disk. Two analytical solutions of rotating structures are used for a preliminary validation of the numerical results that simulate the inertial instability: in both cases the calculated burst speed agrees with the analytical results. The correlation between the nonlinear stress–strain curve and the inertial instability is then addressed by means of simulations that are performed in the end on a real disk subjected to typical loads acting on it. In conclusion, a comparison between the semi-empirical method of Robinson [14] , which is at the base of standard disks certifications, and the FE approach is presented in terms of burst speed prediction to show that FE calculation is more accurate to predict the limit speed.

Analysis of nonlinear shear stress–strain response of unidirectional GF/EP composite

Reasons for nonlinear stress–strain curves in shear of unidirectional glass fibre composite are analysed. Laminate with stacking sequence [45/−45]s is used in tensile quasi-static as well as in tensile creep and strain recovery tests to study the development of viscoelastic and viscoplastic shear strains in local coordinates of the ply. It is shown that Zapa’s integral representation of viscoplasticity is applicable for this material and methodology for parameter determination is given. Schapery’s nonlinear viscoelastic material model was used for shear response characterisation and the nonlinearity parameters’ dependence on the shear stress was determined and described by fitting functions. Microdamage development is quantified by measuring axial modulus and Poisson’s ratio of the laminate. The obtained nonlinear viscoelastic, viscoplastic model with included effect of microdamage was successfully used to predict the nonlinear shear stress–strain curve in strain controlled tensile loading.

GBT-based elastic–plastic post-buckling analysis of stainless steel thin-walled members

When compared with carbon steel, stainless steel exhibits a more pronounced non-linearity and no well-defined yield plateau, as well as appealing features such as aesthetics, higher corrosion resistance and lower life cycle cost. Due to its considerably high ductility/strength and cost, stainless steel structural solutions tend to be adopted mostly for slender/light structures, thus rendering the assessment of their structural behaviour rather complex, chiefly because of the high susceptibility to instability phenomena. The first objective of this paper is to present the main concepts and procedures involved in the development of a geometrically and materially non-linear Generalised Beam Theory (GBT) formulation and numerical implementation (code), intended to analyse the behaviour and collapse of thin-walled members made of materials with a highly non-linear stress–strain curve (e.g., stainless steel or aluminium). The second objective is to validate and illustrate the application of the proposed GBT formulation, by comparing its results (equilibrium paths, ultimate loads, deformed configurations, displacement profiles and stress distributions) with those provided by shell finite element analyses of two lean duplex square hollow section (SHS) columns previously investigated, both experimentally and numerically, by Theofanous and Gardner (Eng Struct 2009; 31(12): 3047–3058.). The stainless steel material behaviour is modelled as non-linear isotropic and the GBT analysis includes initial geometrical imperfections, but neglects corner strength enhancements and membrane residual stresses. It is shown that the GBT unique modal nature makes it possible to acquire in-depth knowledge concerning the mechanics of the column behaviour, by providing “structural x-rays” of the (elastic or elastic–plastic) equilibrium configurations: modal participation diagrams showing the quantitative contributions of the global, local, warping shear and transverse extension deformation modes - moreover, this feature makes it possible to exclude, from future similar GBT analyses, those deformation modes found to play a negligible role in the mechanics of the behaviour under scrutiny, thus further reducing the number of degrees of freedom involved in a GBT analysis, i.e., increasing its computational efficiency.

Mechanical properties and details of composite laminates for the test cases used in the third world-wide failure exercise

This paper gives details of the input data and a full description of a set of 13 test cases provided to the participants of the third world-wide failure exercise for use in their theoretical models. World-wide failure exercise is aimed at benchmarking leading methods, capable of predicting initiation and progression matrix cracking and damage and failure in composites. The originators of leading theories were requested to use the exact input data provided here in their blind predictions of the test cases. The input data include all of the elastic constants, ultimate strains and strengths and the nonlinear stress–strain curves for the unidirectional laminae and their constituents. Various types of laminates, chosen for the analysis, are described together with the lay-up, layer thicknesses, stacking sequences and the loading conditions. Detailed instructions, issued to the contributors, are also presented at the end of this paper.

Quasi-static tensile behavior and damage of carbon/epoxy composite reinforced with 3D non-crimp orthogonal woven fabric

This paper presents a comprehensive experimental study and detailed mechanistic interpretations of the tensile behavior of one representative 3D non-crimp orthogonal woven (3DNCOW) carbon/epoxy composite. The composite is tested under uniaxial in-plane tensile loading in the warp, fill and ±45° bias directions. An “S-shape” nonlinearity observed in the stress–strain curves is explained by the concurrent contributions of inherent carbon fiber stiffening (“non-Hookean behavior”), fiber straightening, and gradual damage accumulation. Several approaches to the determination of a single-value Young’s modulus from a significantly nonlinear stress–strain curve are discussed and the best approach recommended. Also, issues related to the experimental determination of effective Poisson’s ratios for this class of composites are discussed, and their possible resolution suggested. The observed experimental values of the warp- and fill-directional tensile strengths are much higher than those typically obtained for 3D interlock weave carbon/epoxy composites while the nonlinear material behavior observed for the ±45°-directional tensile loading is in a qualitative agreement with the earlier results for other textile composites. Results of the damage initiation and progression, monitoried by means of acoustic emission, full-field strain optical measurements, X-rays and optical microscopy, are illustrated and discussed in detail. The damage modes at different stages of the increasing tensile loading are analyzed, and the principal progressive damage mechanisms identified, including the characteristic crack patterns developed at each damage stage. It is concluded that significant damage initiation of the present material occurs in the same strain range as in traditional cross-ply laminates, while respective strain range for other previously studied carbon/epoxy textile composites is significantly lower. Overall the revealed advantages in stiffness, strength and progressive damage behavior of the studied composite are mainly attributed to the absence of crimp and only minimal fiber waviness in the reinforcing 3DNCOW preform.