A convenient formulation of Sadowsky's model for elastic ribbons

Elastic ribbons are elastic structures whose length-to-width and width-to-thickness aspect ratios are both large. Sadowsky proposed a one-dimensional model for ribbons featuring a nonlinear constitutive relation for bending and twisting: it brings in both rich behaviours and numerical difficulties. By discarding non-physical solutions to this constitutive relation, we show that it can be inverted; this simplifies the system of differential equations governing the equilibrium of ribbons. Based on the inverted form, we propose a natural regularization of the constitutive law that eases the treatment of singularities often encountered in ribbons. We illustrate the approach with the classical problem of the equilibrium of a Möbius ribbon, and compare our findings with the predictions of the Wunderlich model. Overall, our approach provides a simple method for simulating the statics and the dynamics of elastic ribbons.

Damping Energy Dissipation and Parameter Identification of the Bellows Structure Covered with Elastic-Porous Metal Rubber

In order to improve damping energy dissipation of a U-shaped bellows structure, elastic-porous metal rubber as a cover layer was adopted and the corresponding vibration parameters were identified. First, the evolution of energy dissipation characteristics with respect to the changes of amplitude and frequency was investigated through a dynamic experimental test in the bending direction of the covered bellows structure. Second, the conspicuous hysteresis loop characteristics were described while the nonlinear constitutive relation was analytically modelled based on the exact decomposition method. Third, the corresponding parameters on dynamic properties of the covered bellows structure were determined by generalized least-squares estimation. Finally, the prediction results were compared with the measured displacement-restoring force curves to verify the accuracy of the developed dynamic model. The results indicate that the proposed dynamic model associated with the nonlinear constitutive relation for the covered bellows structure can well describe the evolution of the restoring force in terms of amplitude and frequency.

Physics-Based Modeling for Lap-Type Joints Based on the Iwan Model

This study proposed a physics-based heuristic modeling for the nonlinear constitutive relation of bolted joints based on the Iwan model accompanying with the rough surface contact theory. The approach led to an Iwan distribution function which possesses the tribology-related features of the contact interface. In particular, the break-free force distribution function of the Jenkins elements could be expressed in terms of height distribution of surface asperities. The model considered the contribution of elastically, elasto-plastically as well as plastically deformed asperities to the total tangential loads. Following this, constitutive relations for lap-type bolted joints and the corresponding backbone curves, hysteresis loops, and energy dissipation per cycle were obtained. A model application was implemented and the results were compared with the published experimental results. The proposed model agrees very well with the experimental results when the contact parameters met the actual contact situation. The obtained results indicated that the model can be used to study the tangential behaviors of rough surfaces.

Vibration Control of a Rotating Cantilever Beam by Using the Giant Magnetostrictive Actuator

The dynamic model and control strategy of a rotating cantilever beam are investigated in the paper. The magnetostrictive layer is applied as the actuator and the nonlinear constitutive relation is analyzed. The kinetic energy and potential energy of the beam are obtained. The Hamilton method and Galerkin approach are adopted to obtain and disperse the dynamic equations, respectively. The negative feedback control methodology is used in the control system, which is performed by the solenoid coils. Numerical results show that the magnetostrictive control method is effective and plays the role of damping in the dynamic equations. The nonlinear constrictive characteristics of the magnetostrictive material can affect the control results deeply and should be paid enough attention. The magnetostrictive control performances are influenced by many parameters such as the bias magnetic field, control gain and pre-stress etc.

An Analog of Einstein’s General Relativity Emerging from Classical Finite Elasticity Theory: Analytical and Computational Issues

The “analogue gravity formalism”, an interdisciplinary theoretical scheme developed in the past for studying several non relativistic classical and quantum systems through effective relativistic curved space-times, is here applied to largely de-formable elastic bodies described by the nonlinear theory of solid mechanics. Assuming the simplest nonlinear constitutive relation for the elastic material given by a Kirchhoff-St Venant strain-energy density function, it is possible to write for the perturbations an effective space-time metric if the deformation is purely longitudinal and depends on one spatial coordinate only. Theoretical and numerical studies of the corresponding dynamics are performed in selected cases and physical implications of the results obtained are finally discussed.

Study on Mechanics Behavior of Human Ear Sound Transmission Based on Nonlinear Constitutive Relation

Based on the normal CT scan image of human right ear, numerical model has been established combined with self-compiling program. The nonlinear constitutive relation of real middle ear material has been included, and sound - solid and liquid - solid coupling method have been adopted to simulate the sound transmission process from external auditory canal to tympanic membrane, auditory ossicle chain, and eventually to the inner ear. Frequency response and sound transmission behavior has been obtained, and numerical calculation results have been verified by comparing the calculation results with the experimental data. The amplitude, vibration velocity, and stress distribution of middle ear have been analyzed by the model, and the most easy damage part of the tympanic membrane and ossicular chains owing to stress concentration have been obtained in sound transmission of middle ear, which exposes the inner relationship between mechanical behavior of middle ear and pathological changes.

The Hysteresis Model of Terfenol-D with Magneto-Stress Coupling

The output of Terfenol-D is nonlinear and hysteretic under the effect of magnetic field and prestress. The nonlinear constitutive relation between magnetostriction and magnetization with magneto-stress coupling was built in consideration of the magnetostriction saturation and the prestress correlation. Then, the hysteresis behavior of Terfenol-D was modeled based on the Jiles-Atherton model. The error of magnetostriction between simulations and experimental data is less than 6%. This result indicates that the model can adequately predict the nonlinear hysteresis and magneto-stress coupling character of Terfenol-D.