David Chuen Chun Lam

Couple stress based strain gradient theory for elasticity

The deformation behavior of materials in the micron scale has been experimentally shown to be size dependent. In the absence of stretch and dilatation gradients, the size dependence can be explained using classical couple stress theory in which the full curvature tensor is used as deformation measures in addition to the conventional strain measures. In the couple stress theory formulation, only conventional equilibrium relations of forces and moments of forces are used. The couples association with position is arbitrary. In this paper, an additional equilibrium relation is developed to govern the behavior of the couples. The relation constrained the couple stress tensor to be symmetric, and the symmetric curvature tensor became the only properly conjugated high order strain measures in the theory to have a real contribution to the total strain energy of the system. On the basis of this modification, a linear elastic model for isotropic materials is developed. The torsion of a cylindrical bar and the pure bending of a flat plate of infinite width are analyzed to illustrate the effect of the modification.

EXPERIMENTS AND THEORY IN STRAIN GRADIENT ELASTICITY

Abstract Conventional strain-based mechanics theory does not account for contributions from strain gradients. Failure to include strain gradient contributions can lead to underestimates of stresses and size-dependent behaviors in small-scale structures. In this paper, a new set of higher-order metrics is developed to characterize strain gradient behaviors. This set enables the application of the higher-order equilibrium conditions to strain gradient elasticity theory and reduces the number of independent elastic length scale parameters from five to three. On the basis of this new strain gradient theory, a strain gradient elastic bending theory for plane-strain beams is developed. Solutions for cantilever bending with a moment and line force applied at the free end are constructed based on the new higher-order bending theory. In classical bending theory, the normalized bending rigidity is independent of the length and thickness of the beam. In the solutions developed from the higher-order bending theory, the normalized higher-order bending rigidity has a new dependence on the thickness of the beam and on a higher-order bending parameter, bh. To determine the significance of the size dependence, we fabricated micron-sized beams and conducted bending tests using a nanoindenter. We found that the normalized beam rigidity exhibited an inverse squared dependence on the beams thickness as predicted by the strain gradient elastic bending theory, and that the higher-order bending parameter, bh, is on the micron-scale. Potential errors from the experiments, model and fabrication were estimated and determined to be small relative to the observed increase in beams bending rigidity. The present results indicate that the elastic strain gradient effect is significant in elastic deformation of small-scale structures.

Strain gradient plasticity effect in indentation hardness of polymers

Plasticity in material is typically described as a function of strain, but recent observations from torsion and indentation experiments in metals suggested that plasticity is also dependent on strain gradient. The effects of strain gradient on plastic deformation in thermosetting epoxy and polycarbonate thermoplastic were experimentally investigated by nanoindentation and atomic force microscopy in this study. Both thermosetting and thermoplastic polymers exhibited hardening as a result of imposed strain gradients. Strain gradient plasticity theory developed on the basis of a molecular kinking mechanism has predicted strain gradient hardening in polymers. Comparisons made between indentation data and theoretical predictions correlated well. This suggests that strain gradient plasticity in glassy polymers is determined by molecular kinking mechanisms.

Torsion and Bending of Micron-Scaled Structures

Typical microelectromechanical systems (MEMS) devices and packages are composed of micron-scaled structures. Experimental investigations on the effect of size on the deformation behavior of simple structures have shown that the deformation behavior of metals and polymers is size dependent. The size dependence in small structures is attributed to the contribution of nonnegligible strain gradients. In this work, torsion and bending of micron-sized rods and plates were analyzed by using a two-parameter model of strain-gradient plasticity. Microrod torsion and microplate bending experimental data were analyzed to determine the magnitude of the strain-gradient material parameters. The parametric analyses showed that conventional analysis is applicable only when the size of the structure is significantly larger than the material parameters, which are typically in the micron range. Strain-gradient analysis of micron-sized rod revealed that the presence of strain gradient increased the torque by three to nine times at the same twist. For MEMS structures with micron-sized features, conventional structural analysis without strain gradient is potentially inadequate, and strain-gradient analysis must be conducted to determine the elastoplastic behavior in the micron scale.

INDENTATION MODEL AND STRAIN GRADIENT PLASTICITY LAW FOR GLASSY POLYMERS

Plastic deformation of metals is generally a function of the strain. Recently, both phenomenological and dislocation-based strain gradient plasticity laws were proposed after strain gradients were experimentally found to affect the plastic deformation of the metal. A strain gradient plasticity law is developed on the basis of molecular theory of yield for glassy polymers. A strain gradient plasticity modulus with temperature and molecular dependence is proposed and related to indentation hardness. The physics of the strain gradient plasticity in glassy polymer is then discussed in relation to the modulus.

Effect of cross-link density on strain gradient plasticity in epoxy

The variation of specific strain gradient plasticity modulus in epoxy has been examined as a function of cross-link density in epoxy. Cross-link density is controlled by varying the hardener content in the epoxy and the moduli are determined from nanoindentation data. Nanoindentation revealed that hardness increased with decreased indent depth. Specific strain gradient plasticity moduli and the characteristic lengths were found to increase with cross-link density in the epoxy. Data analysis revealed that the characteristic length is inversely proportional to the square root of the kink density. Consequently, material that has a higher cross-link density will have a higher specific strain gradient modulus and a lower kink density at yield.

Model and experiments on strain gradient hardening in metallic glass

Hardnesses of polycrystalline metals at shallow indent depth have been observed to increase because of strain gradients. Dislocation-based strain gradient plasticity models were proposed and good agreements were obtained. Metallic glasses have been observed to exhibit shear localization behaviour similar to metals. Nanoindentation have been conducted on Vitreloy metallic glasses in this study to determine the hardness variation as a function of the indent depth. Hardnesses at shallow indent depth were observed to increase significantly and comparison of the dislocation-based strain gradient indentation model indicated disagreement. An alternate strain gradient plasticity indentation model based on cluster theory of yield for glassy metal was developed and good agreement with data was obtained. The implication of the results and analysis on strain gradient behaviour is discussed.

Performance of Printed Polymer-Based RFID Antenna on Curvilinear Surface

The performance of flexible printed RFID tags affixed onto cylindrical containers is dependent on the inductive behavior of the bent antenna on the tag. Conductive polymeric coil antennas were screen printed onto flexible substrates, and the coil resistances, the inductances, and the S-parameters of the antenna coils were measured and analyzed. The RFID dies were mounted onto the antenna coils and the read ranges were characterized as a function of curvature. The results show that the coil inductance decreased slowly with increasing curvature, and the maximum read range of the tags was markedly reduced with the curvature. The decrease in the coil inductance and the maximum read range were hypothesized to vary with the projected bent coil area instead of the geometric coil area. Experimental results confirmed that the maximum read range of an RFID tag affixed on a curvilinear surface can be predicted by the classical inductive coupling model with the bent projected coil area. On the basis of the experimental and analytical results, a reading reliability factor of two is proposed as a design parameter for flexible RFID tags.

Soft wearable contact lens sensor for continuous intraocular pressure monitoring.

Intraocular pressure (IOP) is a primary indicator of glaucoma, but measurements from a single visit to the clinic miss the peak IOP that may occur at night during sleep. A soft chipless contact lens sensor that allows the IOP to be monitored throughout the day and at night is developed in this study. A resonance circuit composed of a thin film capacitor coupled with a sensing coil that can sense corneal curvature deformation is designed, fabricated and embedded into a soft contact lens. The resonance frequency of the sensor is designed to vary with the lens curvature as it changes with the IOP. The frequency responses and the ability of the sensor to track IOP cycles were tested using a silicone rubber model eye. The results showed that the sensor has excellent linearity with a frequency response of ∼8 kHz/mmHg, and the sensor can accurately track fluctuating IOP. These results showed that the chipless contact lens sensor can potentially be used to monitor IOP to improve diagnosis accuracy and treatment of glaucoma.

Characterization of corneal tangent modulus in vivo

Purpose:  Intraocular pressure (IOP) measured using Goldmann Applanation Tonometry (GAT) changes with individual’s corneal properties, but the method to measure the in vivo corneal material properties to account for individual variation in GAT IOP is not available. In this study, a new method to measure the IOP‐dependent corneal tangent modulus in vivo is developed to address this research gap.