The buckling characteristics of thin functionally graded (FG) nano-plates subjected to both thermal loads and biaxial linearly varying forces is investigated. Eringen’s nonlocal elasticity theory is employed to account for the nano-scale phenomena in the plates. Hamilton’s principle and the constitutive relations are used to derive the partial differential governing equations of motion for the thin plates that are modeled using Kirchhoff’s plate theory. The mechanical properties of the FG nano-plates are assumed to vary smoothly across the thickness of the plate following a power law. Three types of thermal loads are presented and the spectral collocation method is utilized to solve for the critical buckling loads. The accuracy of the numerical solution of the proposed model is verified by comparing the results with those available in the literature. A comprehensive parametric study is carried out, and the effects of the nonlocal scale parameter, power law index, aspect ratio, slopes of the axial loads, boundary conditions, assumed temperature distributions, and the difference between the ceramic-rich and metal-rich surfaces on the nonlocal critical buckling loads of the nano-plates are examined. The results reveal that these parameters have significant influence on the stability behavior of the FG nano-plates.

Bone is a highly adaptive biological structure. Following Wolff’s law, bone realigns and grows to adapt to its mechanical environment. This leads to structural heterogeneity of trabecular bone and orthotropic symmetry of the elastic properties. Determining the bone alignment and material properties for living patients is difficult and involves implantation of force and displacement sensors on the bone to determine the compliance and stiffness properties. Micro-computed tomography along with finite element modeling have been limited to the vertebrae of donor cadavers to evaluate trabecular architecture, material properties, and density. Here, an adaptive structure topology optimization algorithm is presented and used to predict trabecular architecture. The algorithm predicts the optimal structure by minimizing the global compliance. The lumbar 1 (L1) vertebra is used as an example. Loads common to L1 vertebrae are applied and bone volume fraction measurements that can be taken easily from living patients through bone mineral density scans are used as the only inputs. The mathematical model is an adaptation of “99 Line Topology Optimization Code Written in Matlab” developed by Sigmund (2001). Bone is locally assumed to be isotropic with an elastic modulus of 13 GPa and the Poisson ratio of 0.3 applied to each element. The resulting structural heterogeneity results in global orthotropic relations. The model uses bone volume fraction and the loading orientation as inputs and gives the corresponding ideal bone structure geometry as an output. The trabecular structure can be predicted solely from the results of a bone mineral density scan. Finite element analysis of the optimized structure is then conducted and the global material properties are determined. While this model is for two-dimensional examples representing planes within the vertebral bone, it is extended to three-dimensional modeling to develop the cortical bone geometry and define the total volume. Matlab is then used to run the topology optimization simulation. The ideal structure is defined by optimizing for a prescribed displacement field of the system following the implementation of a gradient descent optimization method. The results are compared to published values from a combined experimental and numerical procedure. The procedure on sectioned vertebrae reported average ratios between elastic moduli of E 1 / E 2 = 5.2, E 1 / E 3 = 8.8, and E 2 / E 3 = 1.4. Results between the models and the previously published data yield similar transversely isotropic symmetry in the elastic moduli of trabecular bone. However, the elastic moduli ratios are not quite in agreement. Improving the accuracy of the boundary conditions and loading of the finite element model may improve the correlation between the optimization models and published data.

This manuscript investigates one way sound propagation in Magnetorheological fluids (MRF) using spatio-temporal modulation of the applied magnetic field. One-way propagation of waves in a structure can have potential technological applications such as sound isolation, filtering and echo suppression. Several experimental works in the literature have shown that elastic properties of MRF’s (local speed of sound, in particular) are dependent on the applied magnetic field. Therefore, several fascinating possibilities regarding the manipulation of sound waves in MRF, by tailoring the applied magnetic field, exist. A effective medium approximation (previously used in literature) is used to analyze sound propagation in a MRF composed of hydrogen-reduced Iron particles suspended in pure glycerine. Floquet-Bloch theory is used to obtain a quadratic eigenvalue problem that gives the band structure as a function of the material and modulation parameters. When the applied magnetic field is allowed to vary only in space, regular bandgaps are obtained as a result of Bragg scattering. In contrast, the temporal variation of the magnetic field to induce a traveling wave like variation of the modulated parameters, breaks the symmetry of the Brilloouin zones and we obtain directional bandgaps. The theoretical band structure is validated by numerical band diagrams obtained using a Finite Element code. This research has important applications in active sound manipulation.

Periodic structures are the repetition of unit cells in space, that provide a filtering behavior for wave propagation. In particular, it is possible to tailor the geometrical, physical and elastic properties of the unit cells, in order to attenuate certain frequency bands, called band-gaps or stop-bands. Having each element characterized with the same parameters, the filtering behavior of the system can be described through the wave propagation properties of the unit cell. This is technologically impossible to obtain, therefore the Lyapunov factor is used, in order to define the mean attenuation of a quasi-periodic structure. Tailoring Gaussian unit cell properties potentially allows to extend the stop-bands width in the frequency domain. A drawback is that some unexpected resonance peaks may lie in the neighborhood of the extended regions. However, the correspondent mode-shapes are localized in a particular region of the structure, and they partially decrease the global attenuating behavior. In this paper, the aperiodicity introduced in the otherwise perfect repetition is investigated, providing an explanation for the mode-localization problem and for the stop-bands extension. Then, the proposed approach is applied to a passive quasi-periodic beam, characterized from a localized peak within a designed band-gap. The geometrical properties of its aperiodic parts are changed in order to deterministically move the localization peak in the frequency response. Numerical and experimental results are compared.

Periodic structures provide filtering behavior for vibrations, as a result of the repetition in space of unit blocks, or unit cells. In general, they are characterized by an internal mechanical impedance mismatch, so that waves are reflected and transmitted every time a discontinuity is present. The global behavior given by waves superposition is their cancellation, only for specific frequency ranges, generally called stop-bands or band-gaps. The variation of non-dimensional parameters shows how these attenuation regions move in the frequency domain: the correspondent diagrams are the main tools for the design problem and are known as band-maps. The selection of the geometrical, physical and elastic properties of the unit cell is therefore dependent on the designer experience and nothing can be said about the optimality of the proposed solution. Numerical methods are used for the selection of the best cell geometry, in order to get optimal attenuation. Generally, this is a time consuming approach. In this paper, an new method is presented, based on how the waves are reflected and transmitted at cells interface. Both beam and rod case studies are investigated. The algorithm allows matching between band-gap central frequency and the desired value, while the designed attenuation is optimal there, under certain physical and geometrical constraints. Moreover, the design of the bandgap location has been decoupled from the design of the magnitude of attenuation. This approach is purely analytic, therefore the computational efforts required are minimum. In order to validate the analytical model, a passive periodic beam has been manufactured. Its real frequency response is therefore compared to the expected one.

This work is based on the original concept of coupling two resonant vibration modes to reproduce insect wing kinematics and generate lift. The key issue is designing the geometry and the elastic properties of the artificial wings to achieve quadrature coupling of the bending and twisting motions using only one actuator. Qualitatively, this implies bringing the frequency of the two resonant modes closer. In the light of this challenge, an optimal wing configuration was determined for a micromachined polymer prototype three centimeters wide and validated through experimental modal analyses to illustrate the proximity of the frequencies of the bending and twisting modes. Then, a dedicated lift force measurement bench was developed and used to demonstrate a lift force equivalent to 110% of the prototype weight. For the first time, high-speed camera measurements of the wing motion confirmed that maximum lift was obtained as expected for bending and twisting motions in phase quadrature with a fully resonant motion of the wings using a single actuator.

Foot drop usually happens due to neurological and muscular diseases. It limits individuals’ abilities in ankle and toe represented in dorsiflexion during swing phase, and plantar flexion during heel strike. A non-surgical solution to such weakness is the use of ankle foot orthoses (AFOs) which can assist in such abnormal ambulation. The purpose of this work is to develop a new ankle foot orthosis that helps patients to have more normal ankle joint behavior. The proposed AFO device takes advantage of the superelastic behavior of Ni-rich NiTi alloys. In order to evaluate the performance of the Ni-rich NiTi hinged ankle foot orthoses, several motion analysis tests for a normal walking of a healthy subject were conducted. Also, a finite element model were developed to evaluate the performance of superelastic versus stainless steel springs. A Ni-rich NiTi wire was wrapped around a designed rod and the two heads were fixed to the rod (to get the shape of a spring). Then a heat treatment process was performed in a furnace to shape set the NiTi wires and to provide them with the needed superelastic behavior. The produced springs were connected to a designed hinged ankle foot orthoses. Motion analysis was performed on a healthy subject during normal walking in the case of using conventional stainless steel springs, and with using the produced NiTi springs. Joint kinematics and kinetics data of left lower limb (which was equipped with the AFO brace) were collected and calculated to compare normal walking patterns to the resultant walking patterns with the proposed ankle foot orthosis. The CAD file of the AFO, hinge structure and the springs were developed. Each component was meshed and the convergence study were conducted. A finite element model was developed after assembling and introducing all the interactions between parts in Abaqus. The boundary conditions were applied to the system in a way simulating normal walking conditions. Different material properties (stainless steel and superelastic NiTi) were assigned to the springs in the model to evaluate the performance of the system under the aforementioned loading scenario. The results of the motion analysis on a healthy subject during walking indicate that the use of the superelastic NiTi springs causes more normal walk compare to the use of the conventional stainless steel springs, especially during swing phase and heel strike. Moreover, the ankle has closer stiffness profile to the normal walking in the case of using NiTi springs. The results of the finite element analysis show that the super elastic behavior of NiTi results in more hinge rotation while the stress concentration developed on the springs is within the safe levels and cannot cause failure of the NiTi springs. Motion analysis and finite element models were conducted for the proposed hinged AFO and the results were compared with conventional AFO. By taking advantage of the super elastic characteristic of NiTi, more normal walking behavior was observed in the case of using the proposed AFO with Ni-rich NiTi springs.

Nickel Titanium (NiTi) shape memory alloys (SMAs) exhibit shape memory and/or superelastic properties, enabling them to demonstrate multifunctionality by engineering microstructural and compositional gradients at selected locations. This paper focuses on the design optimization of NiTi compliant mechanisms resulting in single-piece structures with functionally graded properties, based on user-defined target shape matching approach. The compositionally graded zones within the structures will exhibit an on demand superelastic effect (SE) response, exploiting the tailored mechanical behavior of the structure. The functional grading has been approximated by allowing the geometry and the superelastic properties of each zone to vary. The superelastic phenomenon has been taken into consideration using a standard nonlinear SMA material model, focusing only on 2 regions of interest: the linear region of higher Young’s modulus of elasticity and the superelastic region with significantly lower Young’s modulus of elasticity. Due to an outside load, the graded zones reach the critical stress at different stages based on their composition, position and geometry, allowing the structure morphing. This concept has been used to optimize the structures’ geometry and mechanical properties to match a user-defined target shape structure. A multi-objective evolutionary algorithm (NSGA II - Non-dominated Sorting Genetic Algorithm) for constrained optimization of the structure’s mechanical properties and geometry has been developed and implemented.

The present work deals with the design of a fiber-reinforced composite lamina with varying fiber-volume fraction (FVF) along its thickness direction. In the available elastic analyses of this kind of composite, the elastic properties are evaluated based on the assumptions like continuous variation of FVF and existence of decoupled representative volume element (RVE) at every point along the thickness direction. In order to predict the graded material properties without any of these assumptions at present, first a micro-structure of similar graded composite is designed for the variation of FVF according to a sigmoid function of thickness coordinate. Next, a continuum micro-mechanics finite element model of the corresponding representative volume (RV) is derived. The RV is basically composed of several micro-volumes of different FVFs and the classical homogenization treatment is implemented over these micro-volumes without decoupling them from the overall volume of RV. The importance of this coupled analysis is verified through a parallel decoupled analysis. The effect of the total number of micro-volumes within a specified thickness of lamina on its graded elastic properties is presented. The characteristics of graded elastic properties according to the sigmoid function are also discussed.

This paper analyses the Rolamite architecture exploiting shape memory alloys as power element to obtain a solid state actuator. The Rolamite mechanism was discovered in the late sixties, initially as precision and low friction linear bearing. The most common Rolamite configuration consists of a flexible thin metal strip and two rollers mounted between two fixed parallel guide surfaces. The system can roll back and forth without slipping guided by the plates along its so called sensing axis. The system presents another relevant advantage in addition to low friction coefficient, which is the possibility to provide force generation in a quite simple way. In the original literature works the force was provided thanks to cutouts of various shape in the strip, though this method does not allow the Rolamite to be considered a proper actuator, but only a force generator. In this paper we developed the idea of exploiting the shape memory alloy as Rolamite power element and therefore to use the shape memory effect to change the elastic properties of the strip and to provide the actuation force. The mechanical analyses and the equations where the martensite-austenite transition is modelled in a simplified way, show that this application is feasible, mainly thanks to the initial precurvature of the SMA strip. The discussion of the results highlights some important merits of this architecture such as long stroke, constant force and compactness.

In this study, the primary response of an Euler-Bernoulli beam resting on nonlinear elastic foundation is investigated. The beam is subjected to thermal and magnetic axial loads. The nonlocal Eringen’s elasticity theory is used to derive the mathematical model to account for the scale effect of the beam. A simply supported beam is considered in the analysis, and the multi-mode approach is used to obtain the reduced nonlinear temporal equations of motion that contain quadratic and cubic nonlinear terms. The method of multiple-scales is applied to obtain approximate analytical solutions for the nonlinear natural frequencies in addition to the primary resonance response curves. Moreover, the effective nonlinearity is obtained as a function of the natural frequencies and the coefficients of the elastic foundation. The results reveal that the scale parameter has a significant effect on the frequencies and amplitudes of the beam. The obtained results are presented over a selected range of physical parameters such as the scale effect parameter, foundation parameters, thermal and magnetic loads, and the excitation level. Time responses, phase planes and Poincaré maps are generated for the beam under consideration.

Designing devices made from epoxy-based shape memory polymers is difficult because few material behavior parameters are available for these materials in the rubbery/shape changing region. This work examines the rubbery state, greater than 20° C above the glass transition temperature (Tg), as an elastomeric regime suited to characterization with simple tension and planar tension experiments. Differential scanning calorimetry (DSC) results show a 70° C Tg, which agrees with prior research. Simple tension experiments at 100° C exhibited nonlinear elastic behavior, and finite element analysis (FEA) agreed with the constitutive behavior exhibited in the experiments. Planar tension experiments exhibited novel results. The stress/strain response was sigmoidal with a significant plateau in stress followed by rising stress to failure. The typical 10:1 gage width/gage length ratio seemed to over constrain the material. The strain to failure is small, and suggests the material behavior is a hybrid of elastic and hyperelastic behavior.

Fluidic flexible matrix composite (F 2 MC) tubes are fiber-reinforced tubes that have been designed to change structural characteristics (e.g., shape, stiffness, damping, actuation force, etc.) based on the control of fluid flow and pressure inside the tubes. In the current investigation, miniature F 2 MC tubes (2 mm diameter) are designed and evaluated. The tubes are made with fine steel wire and a flexible polyurethane matrix. Tubes with reinforcement angles of ±40 and ±24 degrees relative to the longitudinal axis were evaluated in terms of blocked force and free strain versus internal pressure and axial modulus of elasticity. Sheets of multiple, unidirectionally aligned tubes positioned side by side and potted into a surrounding compliant matrix material were evaluated as well. Encouraging agreement with elasticity solutions based on infinitely long multi-layer tubes with internal pressurization was observed. Over the long term, this line of research is aimed at the development of thin skins for structures that can change shape and stiffness differently as a function of direction.

In this article we present the feasibility of using the shape memory alloy (SMA) wires, namely Nitinol, as an actuator for a steerable surgical cannula. A 3D finite element (FE) model of the actuated steerable cannula was then developed in ANSYS to show deflection of the surgical cannula under the actuation force. The behavior of SMAs was simulated by defining the isothermal stress-strain curves using the multi-elasticity capability of ANSYS. The transformation temperatures of the Nitinol wire at different levels of stress were gathered to form the transformation diagram. Using the one-dimensional Brinson model, the isothermal stress-strain response of the wire was obtained. The thermomechanical characteristics of SMAs were also studied completely by a series of experiments performed on the wires. Birth and death method was used in the solution procedure to have the prestrain condition on Nitinol wire prior to the actuation step. A prototype of the actuated steerable cannula was also developed to validate the numerical simulation. Finally a study was done on design parameters affecting the deflection such as Young’s modulus of cannula, SMA diameter and its offset from the neutral axis of the cannula which can be useful in design optimization.

Dielectric Elastomers (DEs) are incompressible rubber-like solids whose electrical and structural responses are highly nonlinear and strongly coupled. Thanks to their coupled electro-mechanical response, intrinsic lightness, easy-manufacturability and low-cost, DEs are perfectly suited for the development of novel solid-state polymeric energy conversion units with capacitive nature and high-voltage operation, which are more resilient, lightweight, integrated, economic and disposable than traditional generators based on conventional electromagnetic technology. Inflated Circular Diaphragm DE Generators (ICD-DEGs) are a special embodiment of polymeric transducer which can be used to convert pneumatic energy into usable electricity. Potential application of ICD-DEGs is as Power Take-Off (PTO) system for wave energy converters based on the Oscillating Water Column (OWC) principle. This paper presents a reduced, yet accurate, dynamic model for ICD-DEGs which features one degree of freedom and which accounts for DE visco-elasticity. The model is computationally simple and can be easily integrated into existing wave-to-wire models of OWCs to be used for fast analysis and real-time applications. For demonstration purposes, integration of the considered ICD-DEG model with a lumped-parameter hydrodynamic model of a realistic OWC is also presented along with a simulation case study.

Polymer materials have been proposed to be good candidates for the development of new actuators. Due to their tunable mechanical and electrical properties, they can be used as electro-active devices. In this contribution, we focus on dielectric elastomers based actuators, and word toward establishing innovative and alternative integration/miniaturization processes inspired from microelectronics and MEMS technology. Dielectric elastomer actuators are made of an elastomer dielectric layer sandwiched between two conductive electrodes. Upon voltage application attraction forces between the electrodes generates a mechanical displacement correlated with the elastomer Young modulus and permittivity. Here, we propose to use the polydimethylesiloxane (PDMS) due to its high elasticity and its permittivity made adjustable by addition of ceramic nanoparticles. An original process for structuring PDMS layers is developed to overcome the technological challenges encountered during the integration of such materials in a micro-actuator. In this paper, we present several results of characterization that allowed us to better understand the physicochemical mechanisms involved at different technological steps for both the material alone or mixed with Titanate of Barium (TiO 3 Ba) nanoparticles. We also measured the permittivity and the elasticity modulus of these materials at the end of the manufacturing process thereby verifying the conservation and the enhancement of the initial properties that set our choice. These results are very promising for increasing the electrostatic pressure or to lower the actuation voltage. To make a prediction of permittivity by a mixing rule, we inspect some theories in this aim. Finally, we demonstrate that the actuation response of charged elastomer with TiO 3 Ba nanoparticles follows a hyperelastic behavior. This result is particularly helpful for the design of a micro-actuator in a given application.

In this paper, strain gradient thermo-elasticity formulation for Functionally Graded (FG) thick-walled cylinders is presented. Elastic strain energy density function is considered to be a function of gradient of strain tensor in addition to the strain tensor. The material properties are assumed to vary according to power law in radial direction. Using the constitutive equations and equation of equilibrium in the cylindrical coordinates, fourth order non-homogenous governing equation for thermo-elastic analysis of thick-walled FG cylinders subjected to thermal and mechanical loadings is obtained and solved numerically. Results show that the intrinsic length parameter affects the stress distribution in FG thick-walled cylinders greatly and increasing the intrinsic length parameter reduces the maximum radial and hoop stresses. Also, the effect of FG power indices on the radial and hoop stresses are studied.

In this paper, an attempt is made to extend the deformation model of a communication device embedded in a viscoelastic thermoset composite polymer commonly known as Sheet Moulding Compound (SMC). The original model takes into account time dependent heat transfer from the mould surface into the SMC charge and the consequent time dependent viscosity propagation during the initial stage of the mould closing and subsequent filling. The required model parameters for viscosity and elasticity have been determined from rheological testing. The extended model will examine the effects of a number of process parameters such as mould closing speed, mould temperature and initial charge temperature. The effect of these parameters on the deformation of the communication device is discussed and is compared to experimental findings.

Applications of topology optimization to design compliant cellular mechanisms with and without a contact mechanism are presented in this paper. A two-step procedure is developed. For cellular structures without contact, the inverse homogenization method is employed using ‘Solid Isotropic Material with Penalization’ approach. The compliant mechanism is optimized to yield prescribed elasticity coefficients. The structure is also required to undergo a large overall strain without exceeding the allowable local strain. Results including a honeycomb similar structure and a negative Poisson’s ratio structure are presented. To implement a contact mechanism in the second step, the continuum model of a non-contact structure is converted into a frame model. Such a model is investigated for a contact pair which would reduce the maximum local strain. The scheme demonstrates that stress relief can be obtained.

This paper presents a novel Tuned Vibration Absorber (TVA) using Fluidic Flexible Matrix Composites (F 2 MC). Fiber reinforcement of the F 2 MC tube kinematically links the internal volume with axial strain. Coupling of a fluid-filled F 2 MC tube through a fluid port to a pressurized air accumulator can suppress primary mass forced vibration at the tuned absorber frequency. 3-D elasticity model for the tube and a lumped fluid mass develops a 4 th -order model of an F 2 MC-mass system. The model provides a closed form isolation frequency that depends mainly on the port inertance, orifice flow coefficient, and the tube parameters. A small amount of viscous damping in the orifice increases the isolation bandwidth. With a fully closed orifice, the zero disappears and the system has a single resonant peak. Variations in the primary mass do not change the isolation frequency, making the F 2 MC TVA robust to mass variations. Experimental results validate the theoretical predictions in showing a tunable isolation frequency that is insensitive to primary mass variations, and a 94% reduction in forced vibration response relative to the closed-valve case.