Recent advances in technology, in particular soft robotics and micro-electronics, have renewed the interested in the impact of viscoelastic boundaries and active boundary modulation on hydrodynamic drag and boundary layer turbulence. Viscoelastic boundary materials, such as those found in dolphin skin, are known to have the potential to reduce boundary drag, by delaying the transition from laminar to turbulent flow in the boundary layer around the body and minimizing boundary layer turbulence. The possible mechanisms to reduce boundary layer turbulence include counteracting boundary layer coherent structures or impacting momentum transfer near the boundary. Actuating a deformable membrane in a channel flow allows the investigation of the impact of boundary actuation on boundary layer turbulence for a range of actuation parameters and flow channel speeds. We developed a deformable boundary and tested the system in channel flow, in direct contact with the water, actuating at various wave patterns and frequencies. The impact on boundary layer velocity was investigated with Particle Image Velocimetry, as well as numerical simulations (see companion paper). Boundary actuation is shown to impact the boundary layer velocity profile and near boundary momentum transfer. We characterize the parameter space most likely to reduce boundary layer turbulence in a natural environment, which could lead to more energy-efficient platforms and underwater vehicles.
With the advent of 3D printing and the increasing list of available materials, various functional devices can be printed for low-cost, rapid prototyping. In particular, 3D-printed strain gauges show promise in multiple applications such as robotics and structural health monitoring. However, characterization and compensation of the thermal dependence of such strain gauges have been limited in the literature. In this work the temperaturedependent resistive behavior is characterized for strain gauges printed with a commercially available filament, conductive PLA (Polylactic Acid), which has also shown other desirable uses such as stiffness-tuning for soft robots. The relationship between temperature and resistance is shown to be hysteretic. Several compensation methods (Temperature-based algebraic subtraction, Material-based algebraic subtraction, and a Wheatstone bridge-based method) are explored to mitigate the effect of temperature and show the material’s feasibility as a strain gauge. The compensation methods are quantitatively compared by calculating the mean squared error between the predicted and the ground truth strain values. It is shown that the Wheatstone bridge-based method provides the best compensation. This method achieves average errors of less than 10% and a maximum error less than 20% over a working range of approximately 15,000 microstrain (0.15% strain) over a range 30 to 40°C.
Ionic polymer-metal composites (IPMCs) have inherent sensing properties, one application of which is flow sensing. However, the transduction physics and mechanics of IPMC pose challenges in deciphering the sensor output for DC flows. In this work we propose a novel IPMC flow sensor that exploits self-generated von Kármán vortices to produce vibration of the sensor, the frequency and amplitude of which are correlated with the stream flow. The sensor consists of a 3D-printed soft cylindrical sheath housing an IPMC beam, and one end of the sheath takes the shape of a sphere. In the sensing configuration, the sheath is placed parallel to the stream flow direction, with the sphere end fixed. Experiments are conducted in a flow channel to measure the IPMC sensor output and free-end displacement of the sheath under different flow speeds. The results indicate that the proposed sensor structure can produce significant oscillatory signals for effectively decoding the flow speed.
The lateral line system is the flow-sensing organ of fishes, which consists of arrays of flow sensors, known as neuromasts, with hair cells embedded inside a gel-like structure called cupula. There are two types of neuromasts: the superficial ones, which extend from the skin and respond directly to the local velocity, and the canal ones, which are located in recessed canals under the skin and tend to respond to the flow pressure gradient. Inspired by the canal system of fish lateral lines, we propose a pressure gradient sensor integrating an ionic-polymer metal composite (IPMC) sensor with a 3D-printed canal filled with a viscous fluid. Unlike the biological counterpart that has open ends on the surface of the body, the proposed canal has two pores that are covered with a latex membrane, which prevents the canal fluid from mixing with the ambient fluid. Experimental results involving a dipole source show that the proposed sensor is able to capture the pressure difference across the two pores, and the viscosity of the canal fluid has a pronounced effect on the sensitivity of the device. Preliminary finite-element simulation results are also presented to provide insight into the experimental observations.
Soft pressure sensors have a wide range of applications, such as aerodynamic control of cars and unmanned aerial vehicles, navigation of underwater vehicles, and wearable electronics. Existing soft pressure sensors are typically based on capacitive or resistive principles. However, these sensors, made of multiple layers of different materials, tend to delaminate under negative pressures and thus cause sensor failure. In this work, we present the fabrication method for soft capacitive pressure sensors that can reliably detect both positive and negative pressures. The pressure sensor is comprised of one layer of Ecoflex-0030 substrate with cavity channels embedded inside, and two layers of polydimethylsiloxane (PDMS), with two layers of patterned PEDOT:PSS films serving as the electrodes of the sensor. The PEDOT:PSS films are screen printed orthogonally on both sides of the Ecoflex-0030 substrate, and each side is encapsulated by another PDMS layer, which is much stiffer than the Ecoflex-0030 substrate. More importantly, the cavity channels in the Ecoflex-0030 substrate greatly enhance the substrate deformation, hence the capacitive sensor would exhibit remarkable relative change in capacitance when a pressure is applied. Secondly, the encapsulation of PDMS on the Ecoflex substrate protects the electrodes and effectively avoids the delamination problem under negative pressure. In particular, we report the detailed characterization of sensitivity and repeatability of the fabricated pressure sensor for positive and negative pressures of up to 50 kPa. Furthermore, a 12×12 pressure sensor array is fabricated to demonstrate the capability of mapping pressure distributions created by both compressive loads and vacuum suction.
Ionic polymer-metal composites (IPMCs) have inherent underwater sensing and actuation properties. They can be used as sensors to collect ﬂow information. Inspired by the hair-cell mediated receptor in the lateral line system of ﬁsh, the impact of a ﬂexible, cupula-like structure on the performance of IPMC ﬂow sensors is experimentally explored. The fabrication method to create a silicone-capped IPMC sensor is reported. Experiments are conducted to compare the sensing performance of the IPMC ﬂow sensor before and after the PDMS coating under the periodic ﬂow stimulus generated by a dipole source in still water and the laminar ﬂow stimulus generated in a ﬂow tank. Experimental results show that the performance of IPMC ﬂow sensors is signiﬁcantly improved under the stimulus of both periodic ﬂow and laminar ﬂow by the proposed silicone-capping.
Ionic polymer-metal composites (IPMCs) have intrinsic sensing and actuation properties. An IPMC sensor typically has the beam shape and responds to bending deﬂections only. Recently tubular IPMCs have been proposed for omnidirectional sensing of bending stimuli. In this paper we report, to our best knowledge, the ﬁrst study on torsion sensing with tubular IPMCs. In particular, a dynamic, physics-based model is presented for a tubular IPMC sensor under pure torsional stimulus. With the symmetric tubular structure and the pure torsion condition, the stress distribution inside the polymer only varies along the radial direction, resulting in a one-dimensional model. The dynamic model is derived by analytically solving the governing partial diﬀerential equation, accommodating the assumed boundary condition that the charge density is proportional to the mechanically induced stress. Experiments are further conducted to estimate the physical parameters of the proposed model.
Ionic polymer-metal composites (IPMCs) have inherent sensing and actuation properties. An IPMC sensor typically
consists of a thin ion-exchange membrane, chemically plated with electrodes on both surfaces. Such IPMC
sensors respond to deflections in the beam-bending directions only and thus are considered one-dimensional. In
this paper, a novel IPMC sensor capable of two-dimensional sensing is proposed by plating two pairs of electrodes
on orthogonal surfaces of a Nafion beam that has comparable thickness and width. The fabrication method is
reported along with the characterization of the fabricated sensor. Experimental results show that the proposed
IPMC sensor can be used for 2D flow sensing with promising applications in artificial lateral line systems. In
the fabrication process Nafion solution is first cast and solidified, and the resulting structure is then cut to form
beams with square cross-sections. In particular, the sample we fabricated has cross section of 1mm by 1mm and
length of 15mm. Platinum electrodes are then plated on four side surfaces of the Nafion beam, insulated from
each other. The fabricated IPMC sensor is shown to respond to 2D mechanical stimuli, and separate sensor
signals are collected from the two pairs of electrodes. The responses (short-circuit currents) of the fabricated
IPMC sensor are characterized both in air and in water, to verify the 2D sensing capability and examine the
correlation between the two sensor signals.
Ionic polymer-metal composites (IPMCs) have intrinsic actuation and sensing capabilities, and they need hydration
to operate. For an IPMC sensor operating in air, the water content in the polymer varies with the humidity
level of the ambient environment, which leads to its strong humidity-dependent sensing behavior. However, the
study of this behavior has been very limited. In this paper, the influence of environmental humidity on IPMC
sensors is characterized and modeled from a physical perspective. Specifically, a cantilevered IPMC beam is excited
mechanically at its base inside a custom-built humidity chamber, where the humidity is feedback-controlled
by activating/deactivating a humidifier or a dehumidifier properly. We first obtain the empirical frequency responses
of the sensor under different humidity levels, with the IPMC base displacement as input and the tip
displacement and short-circuit current as outputs. Based on physics-based model for a given humidity level, we
then curve-fit the measured frequency responses to identify the humidity-dependent physical parameters, including
Young’s modulus and strain-rate damping coefficient for the mechanical properties, and ionic diffusivity for
the mechanoelectrical dynamics. These parameters show a clear trend of change with the humidity. By fitting
the identified parameters at a set of test humidity levels, the humidity-dependence of the physical parameters
is captured with polynomial functions, which are then plugged into the physics-based model for IPMC sensors
to predict the sensing output under other humidity conditions. The latter humidity-dependent model is further
validated with experiments.
Motivated by the lateral line system of fish, arrays of flow sensors have been proposed as a new sensing modality
for underwater robots. Existing studies on such artificial lateral lines (ALLs) have been mostly focused on the
localization of a fixed underwater vibrating sphere (dipole source). In this paper we examine the problem of
tracking a moving dipole source using an ALL system. A nonlinear estimation problem is formulated based on an
analytical model for the moving dipole-generated flow field, which is subsequently solved with the Gauss-Newton
method. The effectiveness of the proposed approach is illustrated with simulation results.
In this paper a dynamic, physics-based model is studied analytically and experimentally for an ionic polymermetal
composite (IPMC) sensor that is excited at the base. This work is motivated by structural monitoring and
energy-harvesting applications of IPMCs. The model combines the vibration dynamics of a flexible beam under
base excitation and the ion transport dynamics within the IPMCs. The vibration dynamics of a base-excited IPMC beam is obtained from the Euler-Bernoulli beam equation incorporating damping and accommodating
suitable boundary conditions. The charge dynamics is derived by analytically solving the governing partial differential equation, which captures electrostatic interactions, ionic diffusion and ionic migration along the thickness direction. The derived model relating short-circuit sensing current to the base excitation is expressed
as an infinite-dimensional transfer function, in terms of physical and geometric parameters, and is thus scalable. The model is then reduced to a finite-dimensional one for real-time signal processing. In particular, we present an inversion scheme for reconstructing the mechanical stimuli given the sensor output. Experimental results show that the proposed model captures well both the beam dynamics and the overall sensing dynamics. Simulation results are also presented to illustrate the inversion algorithm.
As the primary flow sensing organ for fishes, the lateral line system plays a critical role in fish behavior. Analogous
to its biological counterpart, an artificial lateral line system, consisting of arrays of micro flow sensors, is
expected to be instrumental in the navigation and control of underwater robots. In this paper we investigate the
microfabrication of ionic polymer-metal composite (IPMC) cilia for the purpose of flow sensing. While existing
macro- and microfabrication methods for IPMCs have predominantly focused on planar structures, we propose
a device where micro IPMC beams stand upright on a substrate to effectively interact with the flow. Challenges
in the casting of 3D Nafion structure and selective formation of electrodes are discussed, and potential solutions
for addressing these challenges are presented together with preliminary microfabrication results.
Because of size and complexity concerns, implementing feedback control for ionic polymer-metal composite
(IPMC) actuators is often difficult or costly in many of their envisioned biomedical and robotic applications.
It is thus of interest to develop open-loop control strategies for these actuators. Such strategies, however, are
susceptible to change of IPMC dynamics under varying environmental conditions, a predominant example being
the temperature. In this paper we present a novel approach to open-loop control of IPMC actuators in the
presence of ambient temperature changes. First, a method is proposed for modeling the temperature-dependent
actuation dynamics. The empirical frequency response of an IPMC actuator, submerged in a water bath with
controlled temperature, is obtained for a set of temperatures. For each temperature, a transfer function of a
given structure is found to fit the measured data. A temperature-dependent transfer function model is then
derived by curve-fitting each zero or pole as a simple polynomial function of the temperature. Open-loop control
is then realized by inverting the model at a given temperature based on the auxiliary temperature measurement.
However, the obtained model for IPMC actuators is of non-minimum phase and cannot be inverted directly. A
stable but non-causal algorithm is adopted to implement the inversion. Furthermore, a finite-preview algorithm
is proposed to enable near real-time tracking of desired outputs. Experimental results show that the proposed
approach is effective in improving the tracking performance of IPMC actuators under varying temperatures.
The lateral line system, consisting of arrays of neuromasts functioning as flow sensors, is an important sensory
organ for fish that enables them to detect predators, locate preys, perform rheotaxis, and coordinate schooling.
Creating artificial lateral line systems is of significant interest since it will provide a new sensing mechanism for
control and coordination of underwater robots and vehicles. In this paper we propose recursive algorithms for
localizing a vibrating sphere, also known as a dipole source, based on measurements from an array of flow sensors.
A dipole source is frequently used in the study of biological lateral lines, as a surrogate for underwater motion
sources such as a flapping fish fin. We first formulate a nonlinear estimation problem based on an analytical
model for the dipole-generated flow field. Two algorithms are presented to estimate both the source location and
the vibration amplitude, one based on the least squares method and the other based on the Newton-Raphson
method. Simulation results show that both methods deliver comparable performance in source localization. A
prototype of artificial lateral line system comprising four ionic polymer-metal composite (IPMC) sensors is built,
and experimental results are further presented to demonstrate the effectiveness of IPMC lateral line systems and
the proposed estimation algorithms.
Ionic polymer-metal composites (IPMC) are soft actuation materials with promising applications in robotics
and biomedical devices. In this paper, a MEMS-based approach is presented for monolithic, batch fabrication of
IPMC pectoral fin actuators that are capable of complex deformation. Such an actuator consists of multiple, individually
controlled IPMC regions that are mechanically coupled through compliant, passive regions. Prototypes
of artificial pectoral fins have been fabricated with the proposed method, and sophisticated deformation modes,
including bending, twisting, and cupping, have been demonstrated, which shows the promise of the pectoral fin
in robotic fish applications.
In this paper, a model is proposed for a biomimetic robotic fish propelled by an ionic polymer metal composite
(IPMC) actuator with a rigid passive fin at the end. The model incorporates both IPMC actuation dynamics
and the hydrodynamics, and predicts the steady-state speed of the robot under a periodic actuation voltage.
Experimental results have shown that the proposed model can predict the fish motion for different tail dimensions.
Since its parameters are expressed in terms of physical properties and geometric dimensions, the model is expected
to be instrumental in optimal design of the robotic fish.
Conjugated polymer actuators provide delicate solutions in biomimetic robotics and bio/micromanipulation. For these
applications, it is highly desirable to have large deformation. Because linear elasticity theory is only valid when the
strain is small, this poses significant challenges in the electromechanical modeling. In this paper, we use a nonlinear
strain energy function to capture the stored elastic energy under actuation-induced swelling, which further allows us to
compute the induced stress. Numerical method is used to obtain the deformation variables by solving the force and
bending moment balance equations simultaneously. Experimental results for a trilayer conjugated polymer beam can be
predicted by the proposed model better than the linear model. This proposed framework can also be applied to the analysis
of large deformations of other electroactive polymers.
Ionic polymer-metal composites (IPMCs) form an important category of electroactive polymers. In this paper,
a nonlinear, physics-based model is proposed for IPMC actuators. A key component in the proposed model
is the nonlinear capacitance of IPMC, demonstrated by the nonlinear relationship between an applied step
voltage and the induced charge. A nonlinear partial differential equation (PDE) is fully considered in analytical
derivation of the capacitance of IPMC. The nonlinear capacitance is incorporated into a circuit model, which
includes additionally the pseudo capacitance, the ion diffusion resistance, and the nonlinear DC resistance of the
polymer. The model is verified in experiments.
The reduction-oxidation (redox) level of a conjugated polymer has significant impact on its electro-chemo-mechanical
properties, such as conductivity, impedance, and Young's modulus. A redox level-dependent impedance model is developed
in this paper by including the dynamics of ion diffusion, ion migration, and redox reactions. The model, in the form
of a transfer function, is derived through perturbation analysis around a given redox level. Experimental measurements
conducted under different redox conditions correlate well with the model prediction and thus validate the proposed model.
This work, for the first time, incorporates the effect of redox level into the dynamics of conjugated polymers, and facilitates
the future use of nonlinear control methods for the effective control of these materials.
Ionic polymer-metal composites (IPMCs) have built-in sensing and actuation capabilities which make them attractive in
many biomedical and biological applications. In this paper a physics-based but control-oriented dynamic model is proposed
for IPMC actuators. The modeling work starts from the governing partial differential equation (PDE) that describes the
charge redistribution dynamics under external electrical field, electrostatic interactions, ionic diffusion, and ionic migration
along the thickness direction. It is further extended by incorporating the effect of distributed surface resistance. The
electrical impedance model is obtained by deriving the exact solution to the governing PDE in the Laplace domain. By
assuming a linear electromechanical coupling, an actuation model which relates bending displacement to voltage input
is derived. The model is represented as an infinite-dimensional transfer function, which is amenable to model reduction
and real-time control design while capturing fundamental physics. It thus bridges the traditional gap between the physics-based
perspective and the system-theoretic perspective on modeling of IPMC materials. The model is expressed in terms
of fundamental material parameters and dimensions of the IPMC, and is therefore geometrically scalable. The latter has
been further confirmed in experiments.
In this paper the behavior of conjugated polymers as mechanical sensors is experimentally characterized and modeled. A
trilayer conjugated polymer sensor is considered, where two polypyrrole (PPy) layers sandwich an amorphous polyvinylidene
fluoride (PVDF) layer, with the latter serving as an electrolyte tank. A theory for the sensing mechanism is proposed
by postulating that, through its influence on the pore structure, mechanical deformation correlates directly to the concentration
of ions at the PPy/PVDF interface. This provides a key boundary condition for the partial differential equation (PDE)
governing the ion diffusion and migration dynamics. By ignoring the migration term in the PDE, an analytical model is
obtained in the form of a transfer function that relates the open-circuit sensing voltage to the mechanical input. The model
is validated in experiments using dynamic mechanical stimuli up to 50 Hz.
Compact sensing schemes are desirable for feedback control of ionic polymer-metal composite (IPMC) actuators
in their targeted bio, micro, and nano applications. In this paper, a novel integrated sensory actuator with both
position and force feedback is designed by combining IPMC with polyvinylidene fluoride (PVDF) films. The
design adopts differential configurations for both the sensor-actuator structure and the sensing circuit, and thus
eliminates capacitive coupling between IPMC and PVDF, minimizes the internal stress at bonding interfaces,
and enables excellent immunity to thermal and electromagnetic noises. Closed-loop position control of the IPMC
output is demonstrated together with simultaneous tip force measurement, based upon the integrated PVDF
position and force sensors.
Conjugated polymers are promising actuation materials for bio and micromanipulation systems, biomimetic
robots, and biomedical devices. Sophisticated electrochemomechanical dynamics in these materials, however,
poses significant challenges in ensuring their consistent, robust performance in applications. In this paper an
effective adaptive control strategy is proposed for conjugated polymer actuators. A self-tuning regulator is
designed based on a simple actuator model, which is obtained through reduction of an infinite-dimensional
physical model and captures the essential actuation dynamics. The control scheme is made robust against
unmodeled dynamics and measurement noises with parameter projection, which forces the parameter estimates to
stay within physically-meaningful regions. The robust adaptive control method is applied to a trilayer polypyrrole
actuator that demonstrates significant time-varying actuation behavior in air due to the solvent evaporation.
Experimental results show that, during four-hour continuous operation, the proposed scheme delivers consistent
tracking performance with the normalized tracking error decreasing from 11% to 7%, while the error increases
from 7% to 28% and to 50% under a PID controller and a fixed model-following controller, respectively. In the
mean time the control effort under the robust adaptive control scheme is much less than that under PID, which
is important for prolonging the lifetime of the actuator.
Electroactive polymers (EAPs) are receiving increasing interest from researchers due to their unique capabilities
and numerous potential applications in biomimetic robots, smart structures, biomedical devices, and micro/nanomanipulation. Since these materials are relatively new, it is imperative to educate students and the
general public to raise their awareness of EAP potentials and produce the talent pool needed for continuing, rapid
advances in the field of EAPs. In this paper we describe our concerted effort in teaching EAP to undergraduates,
grade school students, and the general public, through hands-on research and learning on EAP-based biomimetic
robots. Two integrated activities are highlighted: A senior Capstone design program on EAP robots, and the
subsequent programs that use these developed robots to reach out to pre-college students. A robotic fish and a
sociable robot enabled by ionic polymer-metal composite materials are used as examples throughout the paper.
Conjugated polymers have promising applications as actuators in biomimetic robotics and bio/micromanipulation.
For these applications, it is highly desirable to have predictive models available for feasibility study and design
optimization. In this paper a geometrically-scalable model is presented for trilayer conjugated polymer actuators
based on the diffusive-elastic-metal model. The proposed model characterizes actuation behaviors in terms of
intrinsic material parameters and actuator dimensions. Experiments are conducted on polypyrrole actuators of
different dimensions to validate the developed scaling laws for the quasi-static force and displacement output,
the electrical admittance, and the dynamic displacement response.
Compact sensing methods are desirable for ionic polymer-metal composite (IPMC) actuators in microrobotic and biomedical applications. In this paper a novel sensing scheme for IPMC actuators is proposed by integrating an IPMC with a PVDF (polyvinylidene fluoride) thin film. The problem of feedthrough coupling from the actuation signal to the sensing signal, arising from the proximity of IPMC and PVDF, presents a significant challenge in real-time implementation. To reduce the coupling while minimizing the stiffening effect, the thickness of the insulating layer is properly chosen based on the Young's modulus measurement of the IPMC/PVDF structures. Furthermore, a nonlinear circuit model is proposed to capture the dynamics of the still significant coupling effect, and its parameters are identified through a nonlinear fitting process. A compensation scheme based on this model is then implemented to extract the correct sensing signal. Experimental results show that the developed IPMC/PVDF structure, together with the compensation algorithm, can perform effective, simultaneous actuation and sensing. As a first application, the sensori-actuator has been successfully used for the open-loop micro-injection of living Drosophila embryos.
Hysteresis in smart materials hinders the wider applicability of such materials in actuators. In this paper, a systematic approach for coping with hysteresis is presented. The method is illustrated through the example of controlling a commercially available magnetostrictive actuator. We utilize the low-dimensional model for the magnetostrictive actuator that was developed in earlier work. For low frequency inputs, the model approximates to a rate-independent hysteresis operator, with current as its input and magnetization as its output. Magnetostrictive strain is proportional to the square of the magnetization. In this paper, we use a classical Preisach operator for the rate-independent hysteresis operator. In this paper, we present the results of experiments conducted on a commercial magnetostrictive actuator, the purpose of which was the control of the displacement/strain output. A constrained least-squares algorithm is employed to identify a discrete approximation to the Preisach measure. We then discuss a nonlinear inversion algorithm for the resulting Preisach operator, based on the theory of strictly-increasing operators. This algorithm yields a control input signal to produce a desired magnetostrictive response. The effectiveness of the inversion scheme is demonstrated via an open-loop trajectory tracking experiment.
Computational micromagnetics in three dimensions is of increasing interest with the development of magnetostrictive sensors and actuators. In solving the Landau-Lifshitz-Gilbert (LLG) equation, the governing equation of magnetic dynamics for ferromagnetic materials, we need to evaluate the effective field. The effective field consists of several terms, among which the demagnetizing field is of long-range nature. Evaluating the demagnetizing field directly requires work of O(N2) for a grid of N cells and thus it is the bottleneck in computational micromagnetics. A fast hierarchical algorithm using multipole approximation is developed to evaluate the demagnetizing field. We first construct a mesh hierarchy and divide the grid into boxes of different levels. The lowest level box is the whole grid while the highest level boxes are just cells. The approximate field contribution from the cells contained in a box is characterized by the box attributes, which are obtained via multipole approximation. The algorithm computes field contributions from remote cells using attributes of appropriate boxes containing those cells, and it computes contributions from adjacent cells directly. Numerical results have shown that the algorithm requires work of O(NlogN) and at the same time it achieves high accuracy. It makes micromagnetic simulation in three dimensions feasible.
Computational micromagnetics plays an important role in design and control of magnetostrictive actuators. A systematic approach to calculate magnetic dynamics and magnetostriction is presented. A finite difference method is developed to solve the coupled Landau-Lifshitz-Gilbert (LLG) equation for dynamics of magnetization and a one dimensional elastic motion equation. The effective field in the LLG equation consists of the external field, the demagnetizing field, the exchange field, and the anisotropy field. A hierarchical algorithm using multipole approximation speeds up to the evaluation of the demagnetizing field, reducing computational cost from O(N2) to O(NlogN). A hybrid 3D/1D rod model is adopted to compute the magnetostriction: a 3D model is used in solving the LLG equation for the dynamics of magnetization; then assuming that the rod is along z-direction, we take all cells with same z-coordinate as a new cell. The values of the magnetization and the effective field of the new cell are obtained from averaging those of the original cells that the new cell contains. Each new cell is represented as a mass- spring in solving the motion equation. Numerical results include: (1) domain wall dynamics, including domain wall formation and motion; (2) effects of physical parameters, grid geometry, grid refinement and field step on H - M hysteresis curves; (3) magnetostriction curve.