This paper presents a new stabilized form of incompressible Navier-Stokes equations for weak enforcement of Dirichlet boundary conditions at immersed boundaries. The boundary terms are derived via the Variational Multiscale (VMS) method which involves solving the fine-scale variational problem locally within a narrow band along the boundary. The fine-scale model is then variationally embedded into the coarse-scale form that yields a stabilized method which is free of user defined parameters. The derived boundary terms weakly enforce the Dirichlet boundary conditions along the immersed boundaries that may not align with the inter-element edges in the mesh. A unique feature of this rigorous derivation is that the structure of the stabilization tensor which emerges is naturally endowed with the mathematical attributes of area-averaging and stress-averaging. The method is implemented using 4-node quadrilateral and 8-node hexahedral elements. A set of 2D and 3D benchmark problems is presented that investigate the mathematical attributes of the method. These test cases show that the proposed method is mathematically robust as well as computationally stable and accurate for modeling boundary layers around immersed objects in the fluid domain.

In the healthy heart, left ventricular (LV) filling generates different flow patterns which have been proposed to optimize blood transport by coupling diastole and systole. This work presents a novel image-based method to assess how different flow patterns influence LV blood transport in patients undergoing cardiac resynchronization therapy (CRT). Our approach is based on solving the advection equation for a passive scalar field from time-resolved blood velocity fields. Imposing time-varying inflow boundary conditions for the scalar field provides a straightforward method to distinctly track the transport of blood entering the LV in the different filling waves of a given cardiac cycle, as well as the transport barriers which couple filling and ejection. We applied this method to analyze flow transport in a group of patients with implanted CRT devices and a group of healthy volunteers. Velocity fields were obtained using echocardiographic color Doppler velocimetry, which provides two-dimensional time-resolved flow maps in the apical long axis three-chamber view of the LV. In the patients under CRT, the device programming was varied to analyze flow transport under different values of the atrioventricular conduction delay, and to model tachycardia (100 bpm). Using this method, we show how CRT influences the transit of blood inside the left ventricle, contributes to conserving kinetic energy, and favors the generation of hemodynamic forces that accelerate blood in the direction of the LV outflow tract. These novel aspects of ventricular function are clinically accessible by quantitative analysis of color-Doppler echocardiograms.

The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.

Tissues change in many ways in the period that they are part of a living organism. Tissues are created in fairly repeatable structural patterns, and the patterns are due to both the genes and the (mechanical) environment, but we do not know exactly what part or percentage of a particular pattern to consider the genes, or the environment, responsible for. We do not know much about the beginning of tissue construction (morphogenesis) and also the methods of tissue construction. When the tissue structure is altered to accommodate a new loading, it is not known how the decision is made for the structural reconstruction. We know that tissues grow or reconstruct themselves without ceasing to continue with their structural function, but we do not understand the processes that permit them to accomplish this. Tissues change their structures to altered mechanical environments, but we are not sure how. Tissues heal themselves and we understand little of the structural mechanics of the process. With the objective of describing the interesting unsolved mechanics problems associated with these biological processes, some aspects of the formation, growth and adaptation of living tissues are reviewed. Beyond the objective is the hope that the work will stimulate new ideas and new observations in developmental biology.

In this article we propose a novel mathematical description of biomass growth that combines poroelastic theory of mixtures and cellular population models. The formulation, potentially applicable to general mechanobiological processes, is here used to study the engineered cultivation in bioreactors of articular chondrocytes, a process of Regenerative Medicine characterized by a complex interaction among spatial scales (from nanometers to centimeters), temporal scales (from seconds to weeks) and biophysical phenomena (fluid-controlled nutrient transport, delivery and consumption; mechanical deformation of a multiphase porous medium). The principal contribution of this research is the inclusion of the concept of cellular "force isotropy" as one of the main factors influencing cellular activity. In this description, the induced cytoskeletal tensional states trigger signalling transduction cascades regulating functional cell behavior. This mechanims is modeled by a parameter which estimates the influence of local force isotropy by the norm of the deviatoric part of the total stress tensor. According to the value of the estimator, isotropic mechanical conditions are assumed to be the promoting factor of extracellular matrix production whereas anisotropic conditions are assumed to promote cell proliferation. The resulting mathematical formulation is a coupled system of nonlinear partial differential equations comprising: conservation laws for mass and linear momentum of the growing biomass; advection-diffusion-reaction laws for nutrient (oxygen) transport, delivery and consumption; and kinetic laws for cellular population dynamics. To develop a reliable computational tool for the simulation of the engineered tissue growth process the nonlinear differential problem is numerically solved by: (1) temporal semidiscretization; (2) linearization via a fixed-point map; and (3) finite element spatial approximation. The biophysical accuracy of the mechanobiological model is assessed in the analysis of a simplified 1D geometrical setting. Simulation results show that: (1) isotropic/anisotropic conditions are strongly influenced by both maximum cell specific growth rate and mechanical boundary conditions enforced at the interface between the biomass construct and the interstitial fluid; (2) experimentally measured features of cultivated articular chondrocytes, such as the early proliferation phase and the delayed extracellular matrix production, are well described by the computed spatial and temporal evolutions of cellular populations.

The fluid-structure interaction mechanisms of a coating composed of flexible flaps immersed in a periodically oscillating channel flow is here studied by means of numerical simulation, employing the Euler-Bernoulli equations to account for the flexibility of the structures. A set of passively actuated flaps have previously been demonstrated to deliver favourable aerodynamic impact when attached to a bluff body undergoing periodic vortex shedding. As such, the present configuration is identified to provide a useful test-bed to better understand this mechanism, thought to be linked to experimentally observed travelling waves. Having previously validated and elucidated the flow mechanism in Paper 1 of this series, we hereby undertake a more detailed analysis of spectra obtained for different natural frequency of structures and different configurations, in order to better characterize the mechanisms involved in the organized motion of the structures. Herein, this wave-like behaviour, observed at the tips of flexible structures via interaction with the fluid flow, is characterized by examining the time history of the filaments motion and the corresponding effects on the fluid flow, in terms of dynamics and frequency of the fluid velocity. Results indicate that the wave motion behaviour is associated with the formation of vortices in the gaps between the flaps, which itself are a function of the structural resistance to the cross flow. In addition, formation of vortices upstream of the leading and downstream of the trailing flap is seen, which interact with the formation of the shear-layer on top of the row. This leads to a phase shift in the wave-type motion along the row that resembles the observation in the cylinder case.

During the flight of birds, it is often possible to notice that some of the primaries and covert feathers on the upper side of the wing pop-up under critical flight conditions, such as the landing approach or when stalking their prey (see Fig. 1) . It is often conjectured that the feathers pop up plays an aerodynamic role by limiting the spread of flow separation . A combined experimental and numerical study was conducted to shed some light on the physical mechanism determining the feathers self actuation and their effective role in controlling the flow field in nominally stalled conditions. In particular, we have considered a NACA0020 aerofoil, equipped with a flexible flap at low chord Reynolds numbers. A parametric study has been conducted on the effects of the length, natural frequency, and position of the flap. A configuration with a single flap hinged on the suction side at 70 % of the chord size (from the leading edge), with a length of [Formula: see text] matching the shedding frequency of vortices at stall condition has been found to be optimum in delivering maximum aerodynamic efficiency and lift gains. Flow evolution both during a ramp-up motion (incidence angle from [Formula: see text] to [Formula: see text] with a reduced frequency of [Formula: see text], [Formula: see text] being the free stream velocity magnitude), and at a static stalled condition ([Formula: see text]) were analysed with and without the flap. A significant increase of the mean lift after a ramp-up manoeuvre is observed in presence of the flap. Stall dynamics (i.e., lift overshoot and oscillations) are altered and the simulations reveal a periodic re-generation cycle composed of a leading edge vortex that lift the flap during his passage, and an ejection generated by the relaxing of the flap in its equilibrium position. The flap movement in turns avoid the interaction between leading and trailing edge vortices when lift up and push the trailing edge vortex downstream when relaxing back. This cyclic behaviour is clearly shown by the periodic variation of the lift about the average value, and also from the periodic motion of the flap. A comparison with the experiments shows a similar but somewhat higher non-dimensional frequency of the flap oscillation. By assuming that the cycle frequency scales inversely with the boundary layer thickness, one can explain the higher frequencies observed in the experiments which were run at a Reynolds number about one order of magnitude higher than in the simulations. In addition, in experiments the periodic re-generation cycle decays after 3-4 periods ultimately leading to the full stall of the aerofoil. In contrast, the 2D simulations show that the cycle can become self-sustained without any decay when the flap parameters are accurately tuned.

In the first part of this paper, a universal fluid velocity based algorithm for simulating hydraulic fracture with leak-off, previously demonstrated for the PKN and KGD models, is extended to obtain solutions for a penny-shaped crack. The numerical scheme is capable of dealing with both the viscosity and toughness dominated regimes, with the fracture being driven by a power-law fluid. The computational approach utilizes two dependent variables; the fracture aperture and the reduced fluid velocity. The latter allows for the application of a local condition of the Stefan type (the speed equation) to trace the fracture front. The obtained numerical solutions are carefully tested using various methods, and are shown to achieve a high level of accuracy.

The aim of this paper is to put the problem of vibroacoustic imaging into the mathematical framework of inverse problems (more precisely, coefficient identification in PDEs) and regularization. We present a model in frequency domain, prove uniqueness of recovery of the spatially varying nonlinearity parameter from measurements of the acoustic pressure at multiple frequencies, and derive Newton as well as gradient based reconstruction methods.

This paper studies the prototype development for the self-propelled capsule system which is driven by autogenous vibrations and impacts under external resistance forces. This project aims for proof-of-concept of its locomotion in pipeline environment in order to mitigate the technical complexities and difficulties brought by current pressure-driven pipeline inspection technologies. Non-smooth multibody dynamics is applied to describe the motion of the capsule system, and two non-smooth nonlinearities, friction and impact, are considered in modelling. The prototype of the self-propelled capsule system driven by a push-type solenoid with a periodically excited rod has been designed to verify the modelling approach. The prototype contains a microcontroller, a power supply, and a wireless control module, which has been tested in a clear uPVC pipe via remote control. Various control parameters, e.g. impact stiffness, frequency and amplitude of excitation, are studied experimentally, and finally, the fastest progression of the system is obtained.

We discuss spontaneously bent configurations of pre-stretched bilayer sheets that can be obtained by tuning the pre-stretches in the two layers. The two-dimensional nonlinear plate model we use for this purpose is an adaptation of the one recently obtained for thin sheets of nematic elastomers, by means of a rigorous dimensional reduction argument based on the theory of Gamma-convergence (Agostiniani and DeSimone in Meccanica. doi:10.1007/s11012-017-0630-4, 2017, Math Mech Solids. doi:10.1177/1081286517699991, arXiv:1509.07003, 2017). We argue that pre-stretched bilayer sheets provide us with an interesting model system to study shape programming and morphing of surfaces in other, more complex systems, where spontaneous deformations are induced by swelling due to the absorption of a liquid, phase transformations, thermal or electro-magnetic stimuli. These include bio-mimetic structures inspired by biological systems from both the plant and the animal kingdoms.

A numerical and theoretical study of yield-stress fluid flows in two types of model porous media is presented. We focus on viscoplastic and elastoviscoplastic flows to reveal some differences and similarities between these two classes of flows. Small elastic effects increase the pressure drop and also the size of unyielded regions in the flow which is the consequence of different stress solutions compare to viscoplastic flows. Yet, the velocity fields in the viscoplastic and elastoviscoplastic flows are comparable for small elastic effects. By increasing the yield stress, the difference in the pressure drops between the two classes of flows becomes smaller and smaller for both considered geometries. When the elastic effects increase, the elastoviscoplastic flow becomes time-dependent and some oscillations in the flow can be observed. Focusing on the regime of very large yield stress effects in the viscoplastic flow, we address in detail the interesting limit of 'flow/no flow': yield-stress fluids can resist small imposed pressure gradients and remain quiescent. The critical pressure gradient which should be exceeded to guarantee a continuous flow in the porous media will be reported. Finally, we propose a theoretical framework for studying the 'yield limit' in the porous media.

The spreading of the virus-containing droplets exhaled during respiratory events, e.g., cough, is an issue of paramount importance for the prevention of many infections such as COVID-19. According to the scientific literature, remarkable differences can be ascribed to several parameters that govern such complex and multiphysical problem. Among these, a particular influence appears associated with the different airflows typical of male and female subjects. Focusing on a typical cough event, we investigate this aspect by means of highly-resolved direct numerical simulations of the turbulent airflow in combination with a comprehensive Lagrangian particle tracking model for the droplet motion and evaporation. We observe and quantify major differences between the case of male and female subjects, both in terms of the droplet final reach and evaporation time. Our results can be associated with the different characteristics in the released airflow and thus confirm the influence of the subject gender (or other physical properties providing different exhalation profiles) on both short-range and long-range airborne transmission.

This paper presents a conceptual design and implementation of a soft, compliant 3D printed gripper (SurgGrip), conceived for automated grasping of various surgery-based thin-flat instruments. The proposed solution includes (1) a gripper with a resilient mechanism to increase safety and better adaptation to the unstructured environment; (2) flat fingertips with mortise and tenon joint to facilitate pinching and enveloping based grasping of thin and random shape tools; (3) a soft pad on the fingertips to enable the high surface area to maintain stable grasping of the surgical instruments; (4) a four-bar linkage with a leadscrew mechanism to provide a precise finger movement; (5) enable automated manipulation of surgical tools using computer vision. Our gripper model is designed and fabricated by integrating soft and rigid components through a hybrid approach. The SurgGrip shows passive adaptation through inherent compliance of linear and torsional spring. The four-bar linkage mechanism controlled by a motor-leadscrew-nut drive provides precise gripper opening and closing movements. The experimental results show that the SurgGrip can detect, segment through a camera, and grasp surgical instruments (maximum 606.73 gs), with a 67% success rate (grasped 10 out of 12 selected tools) at 3.21 mm/s grasping speed and 15.81 s object grasping time autonomously. Besides, we demonstrated the pick and place abilities of SurgGrip on flat and nonflat surfaces in real-time.

The use of bistable laminates is a potential approach to realize broadband piezoelectric based energy harvesting systems. In this paper the dynamic response of a piezoelectric material attached to a bistable laminate plate is examined based on the experimental generated voltage time series. The system was subjected to harmonic excitations and exhibited single-well and snap-through vibrations of both periodic and chaotic character. To identify the dynamics of the system response we examined the frequency spectrum, bifurcation diagrams, phase portraits, and the 0-1 test.

In the first part of this paper a universal fluid velocity based algorithm for simulating hydraulic fracture with leak-off was created for a penny-shaped crack. The power-law rheological model of fluid was assumed and the final scheme was capable of tackling both the viscosity and toughness dominated regimes of crack propagation. The obtained solutions were shown to achieve a high level of accuracy. In this paper simple, accurate, semi-analytical approximations of the solution are provided for the zero leak-off case, for a wide range of values of the material toughness and parameters defining the fluid rheology. A comparison with other results available in the literature is undertaken.

In this work, starting from an approach previously proposed by the Authors, we put forward an extension to the large deformation regime of the dimensionally-reduced formulation for peridynamic thin plates, including both hyperelasticity and fracture. In particular, the model, validated against numerical simulations, addresses the problem of the peeling in nonlocal thin films, which when attached to a soft substrate highlights how nonlocality of the peeled-off layer might greatly influence the whole structural response and induce some unforeseen mechanical behaviours that could be useful for engineering applications. Through a key benchmark example, we in fact demonstrate that de-localization of damage and less destructive failure modes take place, these effects suggesting the possibility of  conceiving specific networks of nonlocal interactions between material particles, corresponding to lattice-equivalent structure of the nonlocal model treated, of interest in designing new material systems and interfaces with enhanced toughness and adhesive properties.