Observations on the nonlinear unloading behavior of advanced high strength steels

The unloading behavior was compared for three different steel grades: a dual-phase steel, a transformation-induced plasticity steel, and a twinning-induced plasticity steel. Steels that harden by phase transformation or deformation twinning exhibited a smaller component of microplastic strain during unloading and a smaller reduction in the chord modulus compared to the conventional hardening steel. As a result, unloading is closer to pure elastic unloading when the TRIP effect or TWIP effect is active.

Nonlinear dielectric behavior in three-component ferroelectric superlattices

Three-component ferroelectric superlattices consisting of alternating layers of SrTiO3, BaTiO3, and CaTiO3 (SBC) with variable interlayer thickness were fabricated on Pt(111)/TiO2/SiO2/Si (100) substrates by pulsed laser deposition. The presence of satellite reflections in x-ray-diffraction analysis and a periodic concentration of Sr, Ba, and Ca throughout the film in depth profile of secondary ion mass spectrometry analysis confirm the fabrication of superlattice structures. The Pr (remnant polarization) and Ps (saturation polarization) of SBC superlattice with 16.4-nm individual layer thickness (SBC16.4) were found to be around 4.96 and 34 μC/cm2, respectively. The dependence of polarization on individual layer thickness and lattice strain were studied in order to investigate the size dependence of the dielectric properties. The dielectric constant of these superlattices was found to be much higher than the individual component layers present in the superlattice configuration. The relatively higher tunability ( ∼ 55%) obtained around 300 K indicates that the superlattice is a potential electrically tunable material for microwave applications at room temperature. The enhanced dielectric properties were thus discussed in terms of the interfacial strain driven polar region due to high lattice mismatch and electrostatic coupling due to polarization mismatch between individual layers.

Nonlinear Constitutive Behavior Of Ferroelectric Materials

The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism, a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction of domain switching for each element. By using the hardening relation between the driving force of domain switching and the volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated by using the same method mentioned above. The interaction between different elements is taken into account in the finite element simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably with the experimental results.

Dynamic analysis of arrest of buckle propagation on a beam on a nonlinear elastic foundation by FEM

Based on the dynamic governing equation of propagating buckle on a beam on a nonlinear elastic foundation, this paper deals with an important problem of buckle arrest by combining the FEM with a time integration technique. A new conclusion completely different from that by the quasi-static analysis about the buckle arrestor design is drawn. This shows that the inertia of the beam cannot be ignored in the analysis under consideration, especially when the buckle propagation is suddenly stopped by the arrestors.

On the velocity of buckle propagation in a beam on a nonlinear elastic-foundation

The paper revisits a simple beam model used by Chater et al. (1983, Proc. IUTAM Symp. Collapse, Cambridge University Press) to examine the dynamics of propagating buckles on it. It was found that, if a buckle is initiated at a constant pressure higher than the propagation pressure of the model (P-p), the buckle accelerates and gradually reaches a constant velocity which depends upon the pressure, while if it is initiated at P-p, the buckle propagates at a velocity which depends upon the initial imperfection. The causes for the difference are also investigated.

Nonlinear elastic waves in a monatomic chain with nonlinear interaction

Nonlinear wave equation for a one-dimensional anharmonic crystal lattice in terms of its microscopic parameters is obtained by means of a continuum approximation. Using a small time scale transformation, the nonlinear wave equation is reduced to a combined KdV equation and its single soliton solution yields the supersonic kink form of nonlinear elastic waves for the system.

Dependence of the nonlinear electrical behavior of SnO2-based varistors on Cr2O3 addition

Tin dioxide varistors doped with Coo, ZnO, Ta2O5 and Cr2O3 were prepared by the mixed oxide method. Temperature dependent impedance spectroscopy revealed two different activation energies, one at low frequencies and the other at high frequencies. These activation energies were associated with the adsorption and reaction of O-2 species at the grain boundary interface. We show that Cr2O3 improves the varistor properties, generating sites for the adsorption of O' and O at the grain boundary region. The O' and O defects are truly responsible for the barrier formation at the grain boundary interface. (c) 2005 Elsevier Ltd and Techna Group S.r.l. All rights reserved.

On nonlinear dynamics behavior and control of a new model of a magnetically levitated vibrating system, excited by an unbalanced DC motor of limited power supply

We analyze new results on a magnetically levitated body (a block including a magnet whose bottom pole is set in such a way as to repel the upper pole of a magnetic base) excited by a non-ideal energy source (an unbalanced electric motor of limited power supply). These new results are related to the jump phenomena and increase of power required of such sources near resonance are manifestations of a non-ideal system and they are referred as the Sommerfeld effect, which emulates an energy sink. In this work, we also discuss control strategies to be applied to this system, in resonance conditions, in order to decrease its vibration amplitude and avoiding this apparent energy sink.

Nonlinear interface behavior between glass and liquid crystal

As has been shown in the literature, an interface between two dielectric materials, one of which has an intensity-dependent refractive index is capable of exhibing a wide range of complex and potentially useful optical phenomena.

Prediction of Effective Moduli of Carbon Nanotube-Reinforced Composites with Waviness and Debonding

Carbon nanotubes (CNTs) have been regarded as ideal reinforcements of high-performance composites with enormous applications. However, the waviness of the CNTs and the interfacial bonding condition between them and the matrix are two key factors that influence the reinforcing efficiency. In this paper, the effects of the waviness of the CNTs and the interfacial debonding between them and the matrix on the effective moduli of CNT-reinforced composites are studied. A simple analytical model is presented to investigate the influence of the waviness on the effective moduli. Then, two methods are proposed to examine the influence of the debonding. It is shown that both the waviness and debonding can significantly reduce the stiffening effect of the CNTs. The effective moduli are very sensitive to the waviness when the latter is small, and this sensitivity decreases with the increase of the waviness. (C) 2008 Elsevier Ltd. All rights reserved.

A coordination-based approach to elasticity of floppy and stiff random networks

We study the role of connectivity on the linear and nonlinear elastic behavior of amorphous systems using a two-dimensional random network of harmonic springs as a model system. A natural characterization of these systems arises in terms of the network coordination relative to that of an isostatic network $\delta z$; a floppy network has $\delta z<0$, while a stiff network has $\delta z>0$. Under the influence of an externally applied load we observe that the response of both floppy and rigid network are controlled by the same critical point, corresponding to the onset of rigidity. We use numerical simulations to compute the exponents which characterize the shear modulus, the amplitude of non-affine displacements, and the network stiffening as a function of $\delta z$, derive these theoretically and make predictions for the mechanical response of glasses and fibrous networks.

Towards the stabilization of the low density elements in topology optimization with large deformation

This work addresses the treatment of lower density regions of structures undergoing large deformations during the design process by the topology optimization method (TOM) based on the finite element method. During the design process the nonlinear elastic behavior of the structure is based on exact kinematics. The material model applied in the TOM is based on the solid isotropic microstructure with penalization approach. No void elements are deleted and all internal forces of the nodes surrounding the void elements are considered during the nonlinear equilibrium solution. The distribution of design variables is solved through the method of moving asymptotes, in which the sensitivity of the objective function is obtained directly. In addition, a continuation function and a nonlinear projection function are invoked to obtain a checkerboard free and mesh independent design. 2D examples with both plane strain and plane stress conditions hypothesis are presented and compared. The problem of instability is overcome by adopting a polyconvex constitutive model in conjunction with a suggested relaxation function to stabilize the excessive distorted elements. The exact tangent stiffness matrix is used. The optimal topology results are compared to the results obtained by using the classical Saint Venant–Kirchhoff constitutive law, and strong differences are found.