Nonsmooth modeling of distributed impacts in spatially discretized continuous structures using the Ivanov transformation

This work deals with the modeling of nonsmooth impacting motions of a structure against a rigid distributed obstacle. Finite element methods can be used to discretize the structure, and this results in a system of ordinary differential equations (ODEs). When these ODEs are subjected to unilateral constraints and velocity jump conditions, one has to use an event detection algorithm to calculate the time of impact accurately. Event detection in the presence of multiple simultaneous impacts is a nontrivial and computationally demanding task. Ivanov (Ivanov, A., 1993. Analytical methods in the theory of vibro-impact systems. Journal of Applied Mathematics and Mechanics, 57(2), pp. 221-236.) proposed a nonsmooth transformation for a vibro-impacting multidegree-of-freedom (MDOF) system subjected to only a single unilateral constraint. This transformation eliminates the unilateral constraints from the problem and, therefore, no event detection is required during numerical integration. This nonsmooth transformation leads to sign function nonlinearities in the equations of motion. However, they can be easily accounted during numerical integration. Ivanov used his transformation to make analytical calculations for the stability and bifurcations of vibro-impacting motions, but did not explore its application to simulating distributed collisions in discretized continuous structures. We adopt the Ivanov transformation to deal with multiple unilateral constraints in discretized continuous structures. The developed method is demonstrated by modeling the distributed collision of a string and a beam against a rigid surface. For validation, we compare our results with the penalty approac

Impact on auxetic and metal foams

Using the finite element method, we investigate the elasto-plastic impact of a rigid sphere on a half-space of auxetic and metal foams. The validity of the Hertz theory for elastic impacts is investigated for both positive and negative Poisson’s ratio. For elastic impacts, the results from Hertz theory are accurate within 20 % with the finite element simulations. The plasticity is modeled using the Deshpande-Fleck metal foam yield criterion. This yield criterion allows for plastic compressibility and can also accommodate materials having a negative Poisson’s ratio. The elasto-plastic simulations reveal that the coefficient of restitution decreases as the impact velocity is increased. The coefficient of restitution is also least for materials having a zero plastic Poisson’s ratio. Our study suggests for maximum energy dissipation the plastic Poisson’s ratio should be close to zero

Impact on auxetic and metal foams

Using the finite element method, we investigate the elasto-plastic impact of a rigid sphere on a half-space of auxetic and metal foams. The validity of the Hertz theory for elastic impacts is investigated for both positive and negative Poisson’s ratio. For elastic impacts, the results from Hertz theory are accurate within 20 % with the finite element simulations. The plasticity is modeled using the Deshpande-Fleck metal foam yield criterion. This yield criterion allows for plastic compressibility and can also accommodate materials having a negative Poisson’s ratio. The elasto-plastic simulations reveal that the coefficient of restitution decreases as the impact velocity is increased. The coefficient of restitution is also least for materials having a zero plastic Poisson’s ratio. Our study suggests for maximum energy dissipation the plastic Poisson’s ratio should be close to zero

Nature-inspired microfluidic propulsion using magnetic artificial cilia

Lab-on-a-chip is a technology that aims at performing analyses of biological samples (such as blood and urine), conventionally performed in a clinical lab, on a small chip. The lab-on-a-chip consists of micro-chambers (where dedicated tests are carried out) connected by micro-channels, through which the bio-fluid has to pass through. In this work, we explore a way to propel fluids through these micro-channels by mimicking the fluid transport mechanisms present in nature at small length scales. Micron-scale fluid propulsion takes place in nature using hair-like motile appendages known as cilia that beat out-of-phase to result in a wave-like motion (metachronal waves). In addition, individual cilia beat in an asymmetric manner with a distinct effective and recovery stroke. During the effective stroke the cilia are straight and push a large amount of fluid, whereas during the recovery stroke they stay closer to the cell surface and pull back a small amount of fluid. The net fluid propelled is in the direction of the effective stroke. In this work we design artificial cilia that can be realized using thin films consisting of a polymer matrix filled with magnetic nano-particles, so that they can be actuated using an external magnetic field. We use a coupled magneto-mechanical solid-fluid numerical model to find under what conditions a magnetic film will mimic the asymmetric motion of natural cilia. The response of the artificial cilia is further studied in terms of the dimensionless parameters that govern their physical behavior and the parameter space in which the cilia can generate maximum flow is identified.

Mechanical properties of the idealized inverse opal lattice

The mechanical properties of an idealized inverse opal lattice have been investigated using analytical and FE formulation. It is a cubic lattice structure and it’s unit-cell consists of 32 struts. The three independent elastic constants are calculated through a unit-cell analysis using finite element method applying periodic boundary conditions. It is found that elastic and shear moduli vary quadratically with relative density of the lattice under uni-axial stressing and pure shear deformation whereas the bulk modulus varies linearly under hydrostatic loading. The plastic collapse mechanisms under plane stress, multi-axial shear, and axisymmetric loading are also analysed for this structure using the upper bound theorem of plasticity. These results are then verified using FE simulations. We also report on the buckling of the lattice under hydrostatic loadin

The Detachment of an Inclined Micro-Pillar Adhered to a Dissimilar Substrate

We investigate the mechanics of the detachment of an inclined micro-pillar adhered to a dissimilar substrate when subjected to a combination of an axial load and end moment. When the micro-pillar has adhered to the substrate, singular stress fields exist at the bi-material corners. The order of singularity is estimated using asymptotic analysis. The first two terms in the asymptotic expansion lead to singular stress fields. The magnitude of the singularity is evaluated in terms of the elastic mismatch between the pillar and substrate and the micro-pillar inclination. The asymptotic stress due to the moment loading is more sensitive to the micro-pillar inclination when compared to that due to the axial loading. They are insensitive to the micro-pillar inclination when the micro-pillar is rigid when compared to the substrate. A short interfacial crack is further assumed to exist at the bi-material corner. This crack is embedded in the corner singularity region and is loaded by the singular fields due to axial and bending loads. A boundary layer analysis is performed on the singular zone to estimate the stress intensity factor when a short crack embedded in it is subjected to the singular fields. The stress intensity factors are also calculated for a long interfacial crack at the bi-material corner, which extends beyond the singular zone. By using the aforementioned results, we investigate the detachment of the inclined micro-pillar under the combination of an axial load and end moment. © 2021 by ASM

Modelling and Analysis of Magnetosensitive Elastomers

Magnetosensitive Elastomers (MSEs) are micron-sized ferrous particle embedded rubber materials whose mechanical properties can be controlled by the application of an external magnetic field. The magnetic properties and the elastic properties of these magnetosensitive elastomers are dependent on each other. This coupled magneto-mechanical behavior is a non-linear multi-physics phenomenon and has a wide number of applications in the engineering field. To be able to design devices based on these magnetosensitive elastomers, it is required to model their behavior when they are subjected to either magnetic field loading, mechanical loading, or both combined. In this work, first, the boundary integral approach is used to compute the induced magnetic field for a 2D geometry when an external magnetic field is applied, using which we could solve for the deformations and stresses generated. As the boundary integral approach was being computationally expensive, so a UEL User Subroutine was defined in Abaqus for the linear model first and then modified for the neo-Hookean material model

Numerical modelling of fluid-structure interaction using fictitious domain method: application towards compressible fluid flow

The interactions between a deformable solid and surrounding fluid are non-linear multiphysics prob- lem that are crucial for the design of many engineering systems. The fictitious domain method is one of the numerical methods to solve FSI problems and has been successfully implemented for FSI problems involving incompressible flows. The objective of the present work is to adopt the fictitious domain method to study fluid-structure interaction problems involving compressible fluids. For this method we are employing Eulerian and Lagrangian finite element formulation for the fluid and solid, respectively, and both bodies are coupled using a Lagrange multiplier. This multiplier allows the solid not to be integral part of the fluid mesh, thus avoiding the need of mesh updating as in case of other numerical methods for FSI problems