Nanocomposites made of a hosting polymer matrix integrated with carbon nanotubes as nanofillers exhibit an inherent hysteretic behavior arising from the CNT/matrix frictional sliding. Such stick-slip mechanism is responsible for the high damping capacity of CNT nanocomposites. A full 3D nonlinear constitutive model, framed in the context of the Eshelby-Mori-Tanaka theory, reduced to a 1D phenomenological model is shown to describe accurately the CNT/polymer stick-slip hysteresis. The nonlinear hysteretic response of CNT nanocomposite beams is experimentally characterized via displacement-driven tests in bending mode. The force-displacement cycles are identified via the phenomenological model featuring five independent constitutive parameters. A preliminary parametric study highlights the importance of some key parameters in determining the shape of the hysteresis loops. The parameter identification is performed via one of the variants of a genetic-type differential evolution algorithm. The nanocomposites hysteresis loops are identified with reasonably low mean square errors. Such outcome confirms that the 1D phenomenological model may serve as an effective tool to describe and predict the nanocomposite nonlinear hysteretic behavior towards unprecedented material optimization and design.

Piezoelectric voltage transformers (PTs) have many uses in electromechanical systems, including voltage transformation and galvanic isolation, and have been commercialized on the macro scale in electronics powering consumer laptop liquid crystal displays. The present work investigates PTs on smaller size scales, that are currently in the academic research sphere, with an eye towards applications including micro-robotics and other small-scale electronic and electromechanical systems. PTs and a competing technology, inductive electromagnetic voltage transformers, are compared on the basis of power and energy density, with PTs showing favorable trends for micro-system designers. Among PT topologies, bulk disc-type PTs, operating in radial extension modes, are a good candidate for microfabrication, and are considered here. Bulk disc-type PT analysis is based on constitutive equations of thin piezoelectric disc dynamics, and the standard piezoelectric radial mode disc dynamics equations are reviewed, followed by an alternate method of derivation, based on the Generalized Hamilton method. This alternate derivation shows the promise of the Hamilton method in potentially developing a full model of device behavior, including mechanical boundary conditions such as tethering, and predictions of device voltage gain, based on energy considerations. Additionally, experimental resonance frequencies of 4.00mm diameter, 0.13mm thick bulk disc PTs are compared with numeric and analytic results, showing good agreement.

The microstructural characteristics of materials processed via powder-based additive manufacturing (PAM) methods can be significantly different from those made by conventional manufacturing process using the same material. In an effort to link PAM process parameters with the functional performance of manufactured part, it is necessary to identify the effect of the special microstructural features generated by PAM on the final constitutive response of the relevant materials. In the present study, a microstructure-informed constitutive model is developed to describe the mechanical behavior of solidified material produced by PAM processes. The model is based on crystal plasticity and accounts for the effect of grain size and aspect ratio of the microstructure. The effect of these dominant features is captured by considering a core and mantle configuration for the grain volume, and by introducing a grain boundary influence region. The constitutive model’s ability to capture the grain size and shape effect is demonstrated by simulating the stress-strain behavior under uniaxial loading of a representative volume element (RVE) with columnar microstructure characterized by a range of grain sizes and aspect ratios.

For soft robots to be utilized in medical devices, locomotion, industrial automation, and a number of other fields, they require accurate and computationally efficient models that capture both the kinetic behavior and inherent non-linearity. Fiber reinforcement enables soft robots to create useful motions, such as rotation, but poses additional complexity in modeling. The purpose of this paper is to present a constitutive model that relates the kinematic behaviour of a pneumatic fiber-reinforced soft actuator with its torsional loading. This model has the advantage of requiring minimal experimental parameter determination, being inclusive of torsional loads, without requiring large-scale computing systems. Experimental data in multiple kinematic configurations shows agreement between the models moment prediction and the moments that the actuators generate.

The motion capability of a flexure hinge made of shape memory alloy (SMA) can be greatly improved because of the material’s superelasticity. In this paper, the nonlinear deformation characteristics of a superelastic flexure hinge are analyzed. The flexure hinge is considered as a non-prismatic cantilever beam subjected to a combined load at the free end. Superelastic behavior of the SMA is represented by Auricchio’s constitutive model. Govern equations of the large deformation superelastic flexure hinge are derived by using the Bernoulli-Euler beam theory and solved numerically. Based on the static deformation model, the rotation capacity, the stiffness characteristic and the rotation error of the flexure hinge are discussed respectively. Numerical examples compared with Finite Element analysis (FEA) show the accuracy of the proposed methodology.

Topology optimization (TO) aims to find a material distribution within a reference domain, which optimizes objective function(s) and satisfies certain constraints. Topology optimization has various potential applications in early phases of structural design, e.g., reducing structural weight or maximizing structural stiffness. However, most research on TO has focused on linear elastic materials, which has severely restricted applications of TO to hyperelastic structures made of, e.g., rubber or elastomer. While there is some work in literature on TO of nonlinear continua, to the best knowledge of the authors there is no work which investigates the different models of hyperelastic material. Furthermore, topology optimized designs often possess complex geometries and intermediate densities making it difficult to manufacture such designs using conventional methods. Additive Manufacturing (AM) is capable of handling such complexities. Continuing advances in AM will allow for usage of rubber-like materials, which are modeled by hyperelastic constitutive laws, in producing complex structures designed by TO. The contribution of this paper is an investigation of different models of hyperelastic materials taking account of both geometrical and material nonlinearities, and their influences on the resulting topologies. Topology optimization of nonlinear continua is the main topic of few papers. This paper considers different isotropic hyperelastic models including the Ogden, Arruda–Boyce and Yeoh model under finite deformations, which have not yet been implemented in the context of topology optimization of continua. This paper proposes to start with a reference domain having known boundary and loading conditions. Material parameters of different models that fill the domain are also known. Maximizing the stiffness of the structure subject to a volume constraint is used as the design objective. The domain is then meshed into a large number of finite elements, and each element is assigned a density between 0 and 1, which becomes design variable of the optimization problem. These densities are further penalized to make intermediate densities (i.e., not 0 or 1) less favorable. Optimized material distribution will be constructed from optimized values of design variables. Because of the penalization factors that make the problem nonlinear, the Method of Moving Asymptotes (MMA) is utilized to update it iteratively. At each iteration the nonlinear finite element problem is solved using the Finite Element Analysis Program (FEAP), which has been modified to accept penalized densities on element stiffness matrices and internal nodal forces, and a filtering scheme is applied on the sensitivities of objective function to guarantee the existence of solution. The proposed method is tested on several numerical examples. The first two examples are common benchmark models, which are a simply supported beam , and a beam fixed at two ends. Both models are subjected to a concentrated force at midpoints of their edges. The effects of linear and nonlinear material behaviors are compared with regards to resulting designs. The third example is a foremost attempt to reflect on TO in design of airless tire through a simple model, which demonstrates capability of the method in solving real-world design problems.

Continuum models of slender structures are effective in simulating the mechanics of nano-scale filaments. However, the accuracy of these simulations strictly depends on the knowledge of the constitutive laws that may in general be non-homogeneous. It necessitates an inverse problem framework that can leverage the data provided by physical experiments and molecular dynamics simulations to estimate the unknown parameters in the constitutive law. In this paper, we formulate a simple but representative inverse problem as a nonlinear least-squares optimization problem whose cost functional is the misfit between synthetic observations of a cantilever displacement field and model predictions. A Tikhonov regularization term is added to the cost functional to render the problem well-posed and account for observational error. We solve this optimization problem with an adjoint-based inexact Newton-conjugate gradient method. We show that the reconstruction of the Lamé parameter field converges to the exact coefficient as the observation error decreases.

Light-activated shape memory polymers (LaSMPs) exhibit stiffness variations when exposed to ultraviolet (UV) lights. Thus, LaSMP could manipulate structural natural frequencies with UV light exposures when laminated on structures. This study aims to experimentally demonstrate the effectiveness of LaSMP frequency control of a flexible beam. The natural frequency of a three-layered Euler-Bernoulli beam composed of LaSMP, adhesive tape and the flexible beam is analyzed and its frequency formulation exhibits the LaSMP stiffness influence. As the LaSMP adopted in this study is a new spiropyran based composition, a generic Young’s modulus model is proposed and then simplified to model the present LaSMP composition. To make sure the experiment is carried out in a homogenous light field, the light intensities of the UV surface light source at different positions are tested. The temperature change of the LaSMP sample under UV exposures is also measured. The time constant of the reverse reaction and the threshold intensity of the reverse reaction are measured. LaSMP Young’s modulus variation is tested with a uniaxial tension experiment. The constitutive model of LaSMP’s Young’s modulus is validated by experimental data. With these preparations, the LaSMP laminated flexible beam model is exposed to the UV lights and its natural frequencies are identified with a data acquisition and analysis system. The maximum natural frequency variation ratio achieves 5.67%. Comparing both theoretical and experimental data of natural frequency control, this study also validates the LaSMP Young’s modulus constitutive model.

This paper presents an efficient finite element method for the discretization of wire ropes in multibody models of reeving systems. The method is based on line-parametrized Absolute Nodal Coordinate Formulation (ANCF) finite elements defined in the framework of an Arbitrary Lagrangian–Eulerian (ALE) description. In the ALE description the finite element nodes have variable material coordinates thus allowing the finite element to change its position within the flexible body. This property is very convenient to model wire ropes rolled in sheaves that have variable-length free spans, as usually occurs in hoisting machines. Following a previous publication by the author about the general method to model reeving systems, this paper presents a new 3D ALE-ANCF finite element that is able to describe the axial-torsional coupling behaviour of wire ropes. The constitutive model of these new elements is able to reproduce accurately experimental axial-torsion tests of non-rotating wire ropes. The new finite element method is applied to the modelling of the reeving system of a large crane and to investigate the tendency of the load to rotate around a vertical axis.

Relative to the free surface stereolithography (SLA) process, the bottom-up process has several advantages that include better vertical resolution, higher material filling rate, less production time, and less waste of photopolymer materials. However, one of the major concerns of the bottom-up SLA process is that the built-up part may break due to the resultant force generated during the pulling up process. This resultant force may become significant if the adhesive mechanism between the two contact surfaces (i.e., newly cured layer and the bottom of the resin vat) produces a strong bonding characteristic. In this work, the traction force is monitored using FlexiForce ® force sensors. The experimental data are analyzed in order to obtain the initial guess for the fracture properties of the separation process. Then the separation process has been modelled based on the concept of Cohesive Zone Model (CZM) in order to study crack propagation behavior in the field of fracture mechanics. The classic bi-linear traction-separation law is adopted in the present work as the nominal constitutive law that relates the resultant traction stress and the separation distance between the two contact surfaces. The results from simulation are compared with experimental data, a good agreement for maximum traction force is found, and the discrepancy is discussed.

Several of the authors, and others, have explored the use of modal-like models for structures having nonlinearities associated with compressive joints (such as bolted connections.) In these models, the deformations are treated as consisting of modal expansions, but with the modal coordinates that evolving nonlinearly over time. There have been several theoretical treatments of this strategy and the authors report here on an early effort to confirm the approach through experiment. For this purpose simple structures consisting of pairs of plates were assembled using four bolted connections. The structures were excited by modal hammer at various locations and the modes identified by scanning laser vibrometer. In each case, multiple modes were excited and the evolution of modal coordinates was achieved by band-pass filtering at the relevant frequencies. Making some simple kinematic assumptions about relative deformations of the component plates and exploiting symmetries permits the mapping from ring-down of each mode to constitutive behavior of each joint. If the strategy of using joint-like modal models for bolted structures is valid, the joint constitutive models deduced from any mode should be adequate to predict the apparent, but nonlinear modal behavior at other resonances. Multiple test specimens were manufactured to assess this predictive capability in the context of part-to-part variability intrinsic to the dynamics of such structures.

Twisting and bending dynamics of biological filaments such as DNA play a central role in their biological activity including gene expression. The elastic rod model is an efficient tool to simulate such deformations. However, the accuracy of elastic rod predictions depend strongly on the constitutive law, which follows from the atomistic structure of the DNA molecule and is known to be nonlinear and to vary along the length according to the base pair sequence of the DNA. Unfortunately, it is impractical to derive the constitutive law analytically from the atomistic structure. Identification of the nonlinear sequence-dependent constitutive law from experimental data and feasible molecular dynamics simulations remains a significant challenge. In this paper, we extend earlier work by employing techniques based on input reconstruction and state estimation filters to estimate the constitutive law using molecular dynamics data of deformations in bio-filaments.

In this paper, a physically motivated micromechanical model for connective soft tissues like tendon and ligament is presented. A representative volume element (RVE) is introduced based on the crimped pattern of collagen fiber in the tissue. In order to investigate the macroscopic behavior of tissue, numerical homogenization and appropriate periodic boundary conditions are used. Neglecting the effects of nano scale structures and properties on tissues macroscopic behavior leads to linear transversely isotropic model for collagen fibers. Comparison of obtained result with available experimental one, shows that this assumption leads to inaccurate results. Including the effects of nano scale structures into the presented model leads to a nonlinear transversely isotropic constitutive model for collagen fibers which leads to results that are in good agreement with experimental results.

There are several biological filaments that play vital role in cellular processes via twisting and bending deformations. From the double-stranded DNA molecule containing genetic information to the cytoskeletal fibers that provide shape to the cell, biological filaments undergo conformational changes as they perform their biological tasks. Therefore the ability of a filament to deform, which depends on their atomistic structure, is a characteristic property that governs its biological functions. Since there is no direct analytic method to derive the deformability or constitutive law of such filaments from their atomistic structure, the constitutive law has to be identified from their actual deformations. An inverse approach based on a continuum rod model was developed recently that uses deformations in static equilibrium to estimate the constitutive law in bending and torsion. We extend the inverse method to use dynamic states of deformations, and consequently expand its scope to leverage a wide variety of choices in molecular dynamics simulations for identifying the constitutive law. This paper presents and validates the technique applying it to filaments with artificial atomistic structure.

The objective of this investigation is to present a new flexible multibody system (MBS) approach for modeling textile roll-drafting sets used in chemical textile industry. The proposed approach can be used in the analysis of textile materials which have un-common material properties best described by specialized continuum mechanics constitutive models, for instance, the lubricated polyester filament bundles (PFB) presented in this paper. In this investigation, PFB is modeled as a hyper-elastic transversely isotropic material using absolute nodal coordinate formulation (ANCF). The PFB strain energy density function is decomposed into a fully isotropic component and an orthotropic, transversely isotropic component expressed in terms of five invariants of the right Cauchy-Green deformation tensor. Using this energy decomposition, the second Piola-Kirchhoff stress and the elasticity tensors can also be split into isotropic and transversely isotropic parts. Constitutive equations are used to evaluate the generalized material forces associated with the coordinates of three-dimensional fully-parameterized ANCF finite elements. The proposed model allows for modeling the dynamic interaction between the rollers and PFB and allows for using spline functions to specify the PFB forward velocity. The paper demonstrates that the textile material constitutive equations and the MBS algorithms can be used effectively to obtain numerical solutions that define the state of strain of the textile material and the relative slip between rollers and PFB and therefore provide a good method to study the roll-drafting process in the chemical textile industry.

It is often necessary to consider material dissipation effects in structural dynamics analysis. A novel three-dimensional viscoelastic beam formulation is proposed. A systematic procedure is proposed to incorporate existing viscoelastic material models into beam theories. The generalized Maxwell model is used to demonstrate the procedure. Starting from a three-dimensional beam theory, classical material viscoelastic constitutive laws are used to develop viscoelastic beam models for flexible multibody dynamics. In contrast with classical beam theories, the proposed beam formulation captures three-dimensional stress and strains distributions based on a novel dimensional reduction method, and models dissipative phenomena at the same time. All cross-sectional deformation modes are considered in the formulation. With the generalized Maxwell model, the formulation is valid for a broad range of frequencies. Because it is based on a three-dimensional formulation, the proposed approach uses a decomposition of the strain tensor into bulk and deviatoric components, thereby eliminating Poisson locking effects. This is particularly important because many highly dissipative materials are also nearly incompressible. Numerical examples are presented to illustrate these characteristics. Because the formulation developed is a beam model, it is computationally efficient and can be used for the simulation of flexible multibody dynamics systems.

This paper develops an experimentally validated model of a piezoelectric energy harvester under combined aeroelastic-galloping and base excitations. To that end, an energy harvester consisting of a thin piezoelectric cantilever beam subjected to vibratory base excitation is considered. To permit galloping excitation, a bluff body is rigidly attached at the free end such that a net aerodynamic lift is generated as the incoming airflow separates on both sides of the body giving rise to limit cycle oscillations when the flow velocity exceeds a critical value. A nonlinear electromechanical distributed-parameter model of the harvester under the combined excitation is derived using the energy approach and by adopting the nonlinear Euler-Bernoulli beam theory, linear constitutive relations for the piezoelectric transduction, and the quasi-steady assumption for the aerodynamic loading. The partial differential equations of the system are discretized and a reduced-order-model is obtained. The mathematical model is validated by conducting a series of experiments with different loading conditions represented by wind speed, base excitation amplitude, and excitation frequency around the primary resonance.

In this investigation, a bi-linear shear deformable shell element is developed using the absolute nodal coordinate formulation for the large deformation analysis of multibody shell structures. The element consists of four nodes, each of which has the global position coordinates and the gradient coordinates along the thickness introduced for describing the orientation and deformation of the cross section of the shell element. The global position field on the mid-plane and the position vector gradient at a material point in the element are interpolated by bi-linear polynomials. The continuum mechanics approach is used to formulate the generalized elastic forces, allowing for the consideration of nonlinear constitutive models in a straightforward manner. The element locking exhibited in this type of element can be eliminated using the assumed natural strain (ANS) and enhanced assumed strain (EAS) approaches. In particular, the combined ANS and EAS approach is introduced to alleviate the thickness locking arising from the erroneous transverse normal strain distribution. Several numerical examples are presented in order to demonstrate the accuracy and the rate of convergence of numerical solutions obtained by the bi-linear shear deformable ANCF shell element proposed in this investigation.

This work is concerned with the problem of nonlinear dynamical motion of a non-ideal autoparametric system with two active elements — shape memory alloys (SMA) spring and the magnetorheological (MR) pin joint dampers in the neighbourhood internal and external resonance. A polynomial constitutive model was assumed to describe the behaviour of SMA’s spring and there was observed the pseudoelastic effects associated with martensitic phase transformations. The simplified resistance moment generated by the MR pin joint can be approximated using the hyperbolic tangent function. The influence of damping forces in MR dampers on the phenomenon of energy transfer and pseudoelastic effects associated with the martensitic phase transformation was studied. It was shown that in this type system one mode of vibrations might excite or damp another mode, and that except different kinds of periodic vibrations there may also appear chaotic vibrations. For the identification of the responses of the system various techniques, including chaos techniques such as bifurcation diagrams and time histories, power spectral densities (FFT), Poincarè maps and exponents of Lyapunov may be used. The SMA spring and MR damper can be used to change the dynamic behaviour of the autoparametric system giving reliable semiactive control possibilities.

Refined theories are employed to study nonlinear vibrations of elastic rings in the mth flexural mode away from autoparametric resonances involving other flexural modes. A top-down modeling approach is followed to describe the rings undergoing all deformation modes in space by the Special Cosserat theory of curved rods. The specialization to extensional-flexural-shearing, then to extensional-flexural, and finally to purely flexural planar motions is illustrated. Free undamped extensional-flexural nonlinear motions involving the mth mode and its companion mode are investigated via a direct asymptotic approach based on the method of multiple scales applied to the geometrically exact equations of motion and it is shown that these motions are softening for linearly elastic rings while there are thresholds in the constitutive laws separating softening from hardening behaviors.