Francesco Costanzo

Surface acoustic wave microfluidics

The recent introduction of surface acoustic wave (SAW) technology onto lab-on-a-chip platforms has opened a new frontier in microfluidics. The advantages provided by such SAW microfluidics are numerous: simple fabrication, high biocompatibility, fast fluid actuation, versatility, compact and inexpensive devices and accessories, contact-free particle manipulation, and compatibility with other microfluidic components. We believe that these advantages enable SAW microfluidics to play a significant role in a variety of applications in biology, chemistry, engineering and medicine. In this review article, we discuss the theory underpinning SAWs and their interactions with particles and the contacting fluids in which they are suspended. We then review the SAW-enabled microfluidic devices demonstrated to date, starting with devices that accomplish fluid mixing and transport through the use of travelling SAW; we follow that by reviewing the more recent innovations achieved with standing SAW that enable such actions as particle/cell focusing, sorting and patterning. Finally, we look forward and appraise where the discipline of SAW microfluidics could go next.

A continuum thermodynamic analysis of cohesive zone models

A global thermodynamic analysis of the running crack problem is presented. The crack is modeled as an evolving partially cohesive interface endowed with a thermodynamic structure distinct from that of the surrounding body. Constitutive relationships for the cohesive part of the crack surface are formulated in a general way that allows one to account for various dissipative mechanisms and to recover most of the cohesive zone models available from the literature. Particular attention is focused on some of the fundamental and necessary requirements for formulating cohesive zone models. The relationship between such requirements and the interface evolution is discussed and analysed.

A study of dynamic crack growth in elastic materials using a cohesive zone model

Abstract The problem of a semi-infinite mode III crack dynamically propagating in a two-dimensional linear elastic infinite body is considered. The crack tip is assumed to be a cohesive zone whose (finite) size is determined so as to cancel the classical crack tip stress singularity caused by the applied loads. The cohesive zone behavior is assumed rate dependent and is characterized by a thermodynamically based constitutive equation. A new semi-analytical solution method has been formulated to solve the resulting initial value problem. The proposed solution method offers the capability to analyze the entire crack growth phenomenon (acceleration-steady state-arrest), without requiring special assumptions, neither on the crack propagation mode (e.g. steady state or assigned crack tip velocity), nor on the space-time discretization, so to obtain solutions that are not affected by grid size effects. Several solutions, corresponding to various values of the initial and boundary conditions as well as cohesive zone constitutive properties, are presented and analyzed.

On the use of space–time finite elements in the solution of elasto-dynamic problems with strain discontinuities

Abstract The use of a discontinuous Galerkin (DG) formulation for the solution of elasto-dynamic problems with discontinuities in the displacement gradients is examined. Comparisons with exact solutions are presented. The paper demonstrates that space–time finite element methods based on a DG formulation can be very effective in the study of dynamic solid/solid phase transitions as well as dynamic fracture.

Investigation of acoustic streaming patterns around oscillating sharp edges

Oscillating sharp edges have been employed to achieve rapid and homogeneous mixing in microchannels using acoustic streaming. Here, we used a perturbation approach to study the flow around oscillating sharp edges in a microchannel. This work extends prior experimental studies to numerically characterize the effect of various parameters on the acoustically induced flow. Our numerical results match well with the experimental results. We investigated multiple device parameters such as the tip angle, oscillation amplitude, and channel dimensions. Our results indicate that, due to the inherent nonlinearity of acoustic streaming, the channel dimensions could significantly impact the flow patterns and device performance.

On the constitutive relations of materials with evolving microstructure due to microcracking

This paper discusses the practical implementation of a thermodynamically based procedure for the derivation of the effective nonlinear constitutive relations for composites with evolving microstructure. Examples of the procedure for the case of an elastic periodic composite with several growing cracks are presented. These examples are intended to show how the use of this procedure differs from the traditional global-local analysis approach and how well suited it is for use with general purpose structural analysis packages.

Variational implementation of immersed finite element methods

Dirac-δ distributions are often crucial components of the solid–fluid coupling operators in immersed solution methods for fluid–structure interaction (FSI) problems. This is certainly so for methods like the immersed boundary method (IBM) or the immersed finite element method (IFEM), where Dirac-δ distributions are approximated via smooth functions. By contrast, a truly variational formulation of immersed methods does not require the use of Dirac-δ distributions, either formally or practically. This has been shown in the finite element immersed boundary method (FEIBM), where the variational structure of the problem is exploited to avoid Dirac-δ distributions at both the continuous and the discrete level. In this paper, we generalize the FEIBM to the case where an incompressible Newtonian fluid interacts with a general hyperelastic solid. Specifically, we allow (i) the mass density to be different in the solid and the fluid, (ii) the solid to be either viscoelastic of differential type or purely elastic, and (iii) the solid to be either compressible or incompressible. At the continuous level, our variational formulation combines the natural stability estimates of the fluid and elasticity problems. In immersed methods, such stability estimates do not transfer to the discrete level automatically due to the non-matching nature of the finite dimensional spaces involved in the discretization. After presenting our general mathematical framework for the solution of FSI problems, we focus in detail on the construction of natural interpolation operators between the fluid and the solid discrete spaces, which guarantee semi-discrete stability estimates and strong consistency of our spatial discretization.

Enriching Nanoparticles via Acoustofluidics

Focusing and enriching submicrometer and nanometer scale objects is of great importance for many applications in biology, chemistry, engineering, and medicine. Here, we present an acoustofluidic chip that can generate single vortex acoustic streaming inside a glass capillary through using low-power acoustic waves (only 5 V is required). The single vortex acoustic streaming that is generated, in conjunction with the acoustic radiation force, is able to enrich submicrometer- and nanometer-sized particles in a small volume. Numerical simulations were used to elucidate the mechanism of the single vortex formation and were verified experimentally, demonstrating the focusing of silica and polystyrene particles ranging in diameter from 80 to 500 nm. Moreover, the acoustofluidic chip was used to conduct an immunoassay in which nanoparticles that captured fluorescently labeled biomarkers were concentrated to enhance the emitted signal. With its advantages in simplicity, functionality, and power consumption, the acoustofluidic chip we present here is promising for many point-of-care applications.

A classical mechanics approach to the determination of the stress–strain response of particle systems

This paper presents the numerical implementation of a Lagrangian-based approach for the determination of the stress–strain behaviour of solids via molecular dynamics (MD). This approach is based on continuum homogenization and it offers a framework in which the notions of effective stress and effective deformation for a particle system can be said to have the same meaning that they have in a continuum context. Since the effective stress response of the system is not based on the notion of virial stress, the paper presents three MD calculations to demonstrate how the continuum-based notion of effective stress differs from that of virial stress.

Numerical simulations of a dynamically propagating crack with a nonlinear cohesive zone

Numerical solutions of a dynamic crack propagation problem are presented. Specifically, a mode III semi-infinite crack is assumed to be moving in an unbounded homogeneous linear elastic continuum while the crack tip consists of a nonlinear cohesive (or failure) zone. The numerical results are obtained via a novel semi-analytical technique based on complex variables and integral transforms. The relation between the properties of the failure zone and the resulting crack growth regime are investigated for several rate independent as well as rate dependent cohesive zone models. Based on obtained results, an hypothesis is formulated to explain the origin of the crack tip velocity periodic fluctuations that have been detected in recent dynamic crack propagation experiments.