Ganesh Tamadapu

In this work a mathematical model based on interface energy is proposed within the framework of surface continuum mechanics to study the dynamics of encapsulated bubbles. The interface model naturally induces a residual stress field into the bulk of the bubble, with possible expansion or shrinkage from a stress-free configuration to a natural equilibrium configuration. The significant influence of interface area strain and the coupled effect of stretch and curvature is observed in the numerical simulations based on constrained optimization. Due to the bending rigidity related to additional terms, the dynamic interface tension can become negative, but not due to the interface area strain. The coupled effect of interface strain and curvature term observed is new and plays a dominant role in the dominant compression behaviour of encapsulated bubbles observed in the experiments. The present model is validated by fitting the experimental data of m, m and m radii bubbles by calculating the optimized parameters. This work also highlights the role of interface parameters and natural configuration gas pressure in estimating the size-independent viscoelastic material properties of encapsulated bubbles with interesting future developments.

Gelatin hydrogels are a promising candidate in biomedical fields due to their mechanical and chemical characteristics. In the present work, the effect of variation of water content on the mechanical properties of gelatin-based hydrogels is investigated through mechanical characterization and mathematical modeling. The pure gelatin hydrogels and gelatin/polyvinyl alcohol-based composite hydrogels having 90%, 70%, and 50% water content are prepared using the solvent casting method. To characterize the mechanical behavior, these hydrogels are subjected to monotonic stretch, constant stretch, constant stress, multistep stretch, and cyclic stretch loading. On the basis of experimental observations, a phenomenological and micromechanics approach-based mathematical model is proposed to capture the hyperelastic and viscous behavior of the hydrogels. Further, the simulations based on the multistart optimization are performed to obtain the material parameters using the proposed model. The mechanical characterization and the modeling results indicate that the gelatin-based hydrogels show the significant viscoelastic behavior at lower water content (70% and 50%), and it reduced at higher water content (90%).

The present work introduces an interesting revamp to the recently proposed interface energy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022)] for gas-filled encapsulated bubbles (EBs) suspended in a viscous fluid. Here, the elastic and viscous parts of the viscoelastic shell material are described by the Gent hyperelastic material model and a polymer solute following upper-convected Maxwell (UCM) constitutive relations, respectively. Using the aforementioned framework, the integrodifferential type governing equation has been derived, and the physical features of the radial dynamics of the EB model are studied in detail using numerical simulations. The nonlinear behavior and the underlying implications of the newly introduced interface energy model for EBs are also investigated. It was observed that the interface parameters arising from the interface energy formulation and the Gent material model collectively introduce a stiffening effect into the EB model and the extension limit parameter at its lower values affects the radial dynamics of the bubble. Analysis has been carried out at different relaxation time scales, where the viscoelastic shell material resembles a fluid-like or solid-like behavior. The UCM-type viscous part of the viscoelastic shell material introduces strong nonlinear effects into the bubble model and significantly influences the EB's behavior. For the present model, a detailed study has been conducted to capture the dynamic behavior of the bubble through the time series curves, phase space analysis, and the nonlinear frequency response of the bubble.

This work mainly focuses on the free swelling and inflation mechanics of a hyperelastic homogeneous and isotropic gas-filled toroidal gel balloon of an initially circular cross-section. Two compressible hyperelastic material models, namely neo-Hookean and Gent, are considered with Flory–Huggins mixing energy. Mechanics of free swelling configurations are studied using equilibrium equations obtained for incompressible and compressible axisymmetric inflation. The two-point boundary value problem of the balloon was solved using the Nelder–Meads search technique by constructing an optimization problem. Non-uniform solvent concentration is resulted in the meridional direction for the equilibrium swelling and inflation. For the neo-Hookean material, the instant/delayed burst phenomenon is concluded for almost all the geometric and material parametric ranges due to the softening type nonlinearity. On the other hand, for the Gent material model, instant/delayed short burst phenomenon is found for a specific range of dimensionless material constants. The inflation pressure range for the burst phenomenon and equilibrium swelling is identified for particular material parametric ranges. The critical pressure for the delayed short burst is roughly estimated and found to be highly dependent on the nonlinear nature of the swollen toroidal gel balloon inflation pressure-stretch curve. Also, deswelling is observed at the larger inflation stretch values of the gel.

Gelatin-based magnetic hydrogels are composed of gelatin polymer, water, and magnetic nanoparticles. The properties of embedded nano-particles, such as coercivity and remanent magnetization, play an essential role while designing hydrogels for specific applications such as soft robotic tentacles, which can be used in minimally invasive surgery (e.g., catheters and endoscopes). The effective properties of the magnetic hydrogels can be tuned by combining various soft and hard magnetic nanoparticles. In the present work, carbonyl iron and strontium hexaferrite are used to prepare the hybrid hydrogels. The magnetization response (m-h curve) of the hydrogels is experimentally obtained, and the results confirm that the hydrogels’ effective properties are dependent on the embedded particles. Furthermore, experimental compression tests confirm that the stiffness of the hybrid hydrogels (75 kPa) is higher than the pure hydrogels (16.5 kPa). Subsequently, the strain developed in the hydrogels under the magnetic field is measured using the digital image correlation (DIC) method. Thus, the present study provides useful insights into synthesizing soft and hard magnetic hydrogels with customized magnetic and mechanical properties.

Workspace, the set of all possible positions reached by the end effector, must be large for a continuum robot for safe steerability. Magnetically actuated soft robots have high workspace due to their millimetre-scale size and large flexibility, enabling them to navigate constrained environments. When subjected to an external magnetic field, they undergo large deflections by interacting with magnetic particles. This work develops closed-form (assuming 2D planar) and numerical solutions to rotation and deflection for uniformly magnetised elastica at an angle using Cosserat rod theory. They are derived in terms of the elliptic function and shooting method, respectively, and are in good agreement with the experimental results provided in the literature. Deflection and rotation plots are presented for various input conditions. The analytical solutions show pitchfork bifurcation when the external field is antiparallel to the magnetic direction with a peak normalised half workspace of 0.103. In contrast, perturbed pitchfork bifurcation is observed for the other angles; increasing the workspace to 0.416 is not yet studied in the existing literature.

A unique approach to synthesize novel hard magnetic soft hydrogels with higher water content is proposed. The hard magnetic soft hydrogel contains cross-linked macromolecules of gelatin and water with embedded strontium hexaferrite (SFO) particles. First, SFO nanoparticles are synthesized using the auto-combustion method. Subsequently, the particles prepared are added to the hydrogels with three different weight fractions. The hydrogels are subjected to mechanical and magnetic loadings to investigate the mechanical, and actuation behavior, respectively. In addition, the hydrogels are also subjected to cyclic magnetic loading in transverse and antiparallel directions. Based on the experiments, it is observed that the deflections of the hydrogels can be controlled remotely by varying magnetic fields. Moreover, this study can be utilized to design a hydrogel beam with variable particle concentrations that can form complex shapes.

Spherical instability in acoustically driven encapsulated microbubbles (EBs) suspended in a fluid can trigger nonspherical oscillations within them. We apply the interface energy model [N. Dash and G. Tamadapu, J. Fluid Mech. 932, A26 (2022b)] to investigate nonspherical oscillations of smaller radius microbubbles encapsulated with a viscoelastic shell membrane under acoustic field. Using the Lagrangian energy formulation, coupled governing equations for spherical and nonspherical modes are derived, incorporating interface energy effects, shell elasticity, and viscosity. Numerical simulations of governing equations revealed that the parametrically forced even mode excites even modes, while the odd modes excite both even and odd modes. The model demonstrates that finite amplitude nonspherical oscillations are identifiable in smaller radius EBs only when the interface parameters are introduced into the model; otherwise, they are not. Realizing that nonlinear mode coupling is responsible for saturation of instability resulting in stable nonspherical oscillations, we perform a steady-state and stability analysis using the slow-time equations obtained from Krylov-Bogoliubov perturbation method. Analytical expressions for modal amplitudes and stability thresholds are derived in terms of interface and material parameters. The stability curves are invaluable in determining the precise range of excitation pressure and frequency values required for the EB to exhibit finite amplitude nonspherical oscillations.