Elastic Limit Point Research Articles

Superelastic Conductive Fibers with Fractal Helices for Flexible Electronic Applications

AbstractThe widespread application of flexible electronic devices places higher demands for stretchable conductors as crucial components owing to their stable and consistently high conductivity and high stretchability. In this study, a superelastic conductive fractal helix fiber (FHF) consisting of a thermoplastic polyurethane fiber and Ag wire is developed, which exhibits excellent waterproofing ability. The maximum strain of the FHF can be improved to 8300% by increasing the helical index C and Ag wire winding density. A high conductivity of 6.3 × 107 S m−1 and ultra‐high Q value of 3.37 × 104 at a strain of 5600% are realized for the conductive fiber owing to its fractal helical structure. The elastic limit point A of the FHF can be obtained by the relative resistance change (0.166%) to ensure that elastic deformation only occurs when stress is applied. In the elastic strain range, FHF demonstrates high electrical reliability under repeated deformation (over 10 000 cycles of stretching with a strain of 5600%) with a negligible increase in resistance. Moreover, the FHF can be easily integrated with the fabrics as an interconnection for wearable electronics. The newly developed twined FHF can also be used as a capacitive strain sensor to monitor human activity.

DETAILED EVALUATION OF THE SKELTON CURVE OF BEAMS IN CRUCIFORM UNBONDED PRECAST PRESTRESSED CONCRETE FRAMES

Strength and deflection for beams in cruciform unbonded precast prestressed concrete frames are evaluated using a skeleton curve consisted of four characteristic points (flexural cracking point, tendon’s elastic limit point, ultimate flexural point, safety limit point), based on theoretical approach. The flexural cracking point is evaluated by elasticity theory, and other points are estimated by a macro-model, which well produces the seismic behavior of the target structure. Skeleton curves composed of four characteristic points correspond well to the load-deformation relationship of previous experimental results. Calculated strength and deflection, as well as the tendon strain, show good agreement with the experiments.

Molecular dynamics analysis on bending mechanical behavior of alumina nanowires at different loading rates

The molecular dynamics (MD) model of α-Al2O3 nanowires in bending is established by using LAMMPS to calculate the atomic stress and strain at different loading rates in order to study the effect of loading rate on the bending mechanical behaviors of the α-Al2O3 nanowires. Research results show that the maximum surface stress—rotation angle curves of α-Al2O3 nanowires at different loading rates are all divided into three stages of elastic deformation, plastic deformation and failure, where the elastic limit point can be determined by the curve symmetry during loading and unloading cycle. The loading rate has great influence on the plastic deformation but little on the elastic modulus of α-Al2O3 nanowires. When the loading rate is increased, the plastic deformation stage is shortened and the material is easier to fail in brittle fracture. Therefore, the elastic limit and the strength limit (determined by the direct and indirect MD simulation methods) are closer to each other. The MD simulation result of α-Al2O3 nanowires is verified to be valid by the good agreement with the improved loop test results. The direct MD method becomes an effective way to determine the elastic limit and the strength limit of nanoscale whiskers failed in brittle or ductile fracture at arbitrary loading rate.

Semi-mechanism-based hysteretic model for traditional heavy timber frames with forked column foot joints and various wood panel infill

Frames are essential lateral load-resisting elements in traditional Chinese timber structures. This paper presents a semi-mechanism-based hysteretic model for the lateral load-displacement relationship of traditional heavy timber frames with forked column foot joints and various wood panel infill. The backbone curve of the proposed model was determined based on the rocking and the racking mechanisms of the frames. Key points of the backbone curve, including the elastic limit point and the peak load point, and the corresponding tangent stiffness were expressed by the geometrical and physical parameters of the frames. Reloading and unloading paths were defined based on the elastic limit load and the elastic stiffness. Experimental results of typical frames were utilized to verify the proposed model regarding the backbone curve, hysteretic behavior and energy dissipation. Good agreement was achieved. Model-based parametric study was further conducted. The influence of infilled wood panels and vertical compression load was investigated. It is found that the lateral resistance contribution of the wood panels with a door opening is slightly greater than that of wood panels with a window opening, and the performance of frames under higher vertical compression load levels (without causing compression failure of the columns, which is rare) are superior to those under lower levels, e.g., a reduction of 50% in the vertical load can lead to a drop in the peak load and the cumulative dissipated energy of the frame of 13% and 30%, respectively.

Generalization of the Ramberg–Osgood Model for Elastoplastic Materials

The paper dwells upon two plastic material models: the “inverse” and the modified Ramberg–Osgood laws. What makes the modified law different is that it postulates the existence of a strictly linear nonzero portion on a deformation curve, limited by the elastic limit point. The plastic strain portion begins beyond this point and ends with the ultimate stress point, which is another characteristic point of the strain curve. Strain curves corresponding to the inverse law and to the modified law have ben plotted on a sample consisting of 30 experimental Russian 20HGR-steel (Grade 900M SAE/USA) strain curve points. Standard error for the inverse law is sinvers = 0.45, while that for the modified law is an order of magnitude lower: smodif = 0.02. It is proven that the inverse law is a strict limit case of the modified law, where the elastic limit point converges to the origin and contracts the linear strain portion to a point, while the entire strain curve becomes a plastic strain curve.

Instabilities in the axisymmetric magnetoelastic deformation of a cylindrical membrane

We study the inflation of a weakly magnetizable isotropic incompressible cylindrical membrane and the effects of an external magnetic field generated by a current carrying wire placed along the axis of cylinder. A variational formulation based on magnetization is used and the computational results obtained by using four elastic constitutive models (neo-Hookean, Mooney–Rivlin, Ogden, and Arruda–Boyce) are studied and compared. Cylinders of various aspect ratios are studied in each case. Our study shows that the external magnetic field alters the elastic limit point, does not lead to equilibrium solutions below certain value of internal pressure, and can give rise to multiple equilibrium states for a given value of pressure. Presence of magnetic limit point, a phenomenon recently reported in the literature is reconfirmed. Magnetic limit point is a state where a further strengthening of the applied magnetic field at a given pressure does not yield any static equilibrium state. In this case it is detected when the cylindrical membrane deflates into the volume enclosed by itself. We also observe a quadratic relation between the defined magnetic energy parameter and the internal pressure at the magnetic limit point. Relaxed form of the strain energy density is used to account for wrinkling in this case of inward inflation. A finite difference method coupled with an arc-length technique is used for the computations and the stability of the solution is determined from the second variation.

Limit points in the free inflation of a magnetoelastic toroidal membrane

One common phenomenon native to inflation of membranes is the elastic limit-point instability—a bifurcation point at which the membrane begins to deform enormously at the slightest increase of pressure. In the case of magnetoelastic materials, there is another possible phenomenon which we call magnetic limit-point instability, a state referring to the non-existence of an equilibrium state – either stable or unstable. In this work, we are concerned with such instabilities in an incompressible isotropic magnetoelastic toroidal membrane with an initial circular cross-section. A non-uniform magnetic field is generated using a circular current carrying loop placed inside the membrane in addition to inflation by a uniform hydrostatic pressure. An energy formulation based on magnetization is used to model the magneto-mechanical coupling along with a Mooney–Rivlin constitutive model for the elastic strain energy density. Computations show that the magnetic field strongly influences the location of elastic limit points and in some cases can cause them to vanish. Multiple equilibrium states are obtained as solutions of the governing equations and a criterion based on second variation is employed to determine their stability. Existence and dependence of magnetic limit point on the magnetic field is demonstrated. While the quantitative results obtained here are specific to the toroidal geometry, the deformation behaviour can be generalized to any magnetoelastic membrane.

Multi-linear stress–strain and closed-form moment curvature response of epoxy resin materials

A simplified multi-linear stress–strain approach has been used to obtain the closed form nonlinear moment curvature response for epoxy resin materials. The model consists of constant plastic flow in tension and compression. The multi-linear stress–strain model is described by two main parameters in addition to four non-dimensional tensile and six non-dimensional compressive parameters. The main parameters are modulus of elasticity in tension and strain at the proportional elastic limit point in tension. The ten non-dimensional parameters are strain at the ultimate tensile stress, maximum strain, post elastic proportionality stiffness, and post peak strength in the tension model and strain at the proportionality elastic limit, strain at yield strength point, maximum strain, initial elastic stiffness, post elastic proportionality stiffness, and post peak strength in the compression model. Explicit expressions are derived for the stress–strain behavior of the epoxy resins. Closed form equations for moment curvature relationship are presented. The results of tension, compression, and bending tests using digital image correlation technique are presented. Load deflection response of flexural three point bending (3PB) samples could be predicted using the moment curvature equations, crack localization rules, and fundamental static equations. The simulations and experiments reveal that the direct use of uniaxial tensile and compressive stress–strain curves underestimates the flexural response. This model gives an upper bound estimate for flexural over-strength factor.

Analytical Solution for Flexural Response of Epoxy Resin Materials

AbstractA piecewise linear parametric uniaxial stress-strain approach has been used to obtain the closed form nonlinear moment curvature response on the basis of strain compatibility in bending for epoxy resin materials. The stress-strain curves, consisting of a bilinear ascending curve followed by strain softening and constant plastic flow in tension and compression, are described by two main parameters, with an additional five nondimensional tensile and seven nondimensional compressive parameters. The main parameters are the modulus of elasticity and strain at the proportional elastic limit point in tension. Parametric studies show that ultimate tensile stress and compressive yield stresses and tension and compression flow stresses have the highest effects on flexural load carrying capacity. Moment curvature equations, in conjunction with softening localization and static equilibrium conditions, were used to simulate the flexural load-deflection response of a beam under three-point bending (3PB) conditi...

Instability and collapse of flexibly-connected gabled frames

A nonlinear elasto-plastic instability analysis of flexibly connected and supported gabled frames with uniform and nonuniform geometry is presented. The analysis incorporates stability and strength. The procedure is based on nonlinear kinematic relations and linearly elastic material behavior except at the plastic regions (concentrated plasticity). The nonlinear flexible connections are represented by polynomial models. Thus, various types of response can be predicted. Through the chosen examples, the following types of response have been observed: elastic bifurcation instability, elastic limit point instability, elasto-plastic limit point instability and plastic collapse. The effect of several parameters is assessed in order to enhance our understanding of frame behavior. These include the effects of nonuniform geometry, of rotational restraints at the supports, of rise to span ratio, of beam to column stiffness ratio, of load eccentricity and of joint flexible connections.

The effect of interaction of loadings and geometry imperfection on the buckling state of frames

In this paper the effect of the interaction of two loadings, and of the deviation from right angle on the buckling mechanism of a rectangular two-bar frame is discussed. Using a nonlinear stability analysis it is found that there is a critical value of the ratio of the two loadings, as well as of the deviation from right angle, for which the physical equilibrium path and the physically unacceptable complementary path meet each other at an asymmetric bifurcation point. At this point, the response of the frame changes from an elastic limit point instability to a stable equilibrium path associated with inelastic buckling. The analysis is supplemented by a variety of numerical results obtained by an efficient and reliable simplified nonlinear stability analysis applied for the first time to a non-rectangular frame.