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Cilia are tiny hair-like structures that cover the surfaces of biological cells. One of their functions is to generate flow. Artificial cilia are mechanical actuators that are designed to mimic the motion of natural cilia in order to create fluid transport in microchannels. These fluid propulsion systems have potential for application in lab-on-a-chip devices that are used, e.g., for point-of-care diagnosis. The artificial cilia can be actuated through various means such as light, magnetic fields and electric fields. One of the main challenges in the design of artificial cilia is to find the cilia geometry and spacing, microchannel geometry, external actuation field, and frequency of operation, for which the fluid transported and the pressure generated are maximal. Various researchers have attempted to provide answers to these questions using computational models and experimental studies. The main feature of the computational models is that they accurately capture the interaction between the external actuation field (such as electric or magnetic fields), the motion of the artificial cilia and the fluid flow. In this chapter, we (i) give a brief overview of the existing modeling approaches, (ii) give an in-depth description of a recently developed modeling framework, and (iii) provide an overview of the most important results and insights that has led to our current understanding of the fluid propulsion using magnetically driven artificial cilia.

Manipulation of bio-fluids in microchannels faces many challenges in the development of lab-on-a-chip devices. We propose magnetically actuated artificial cilia which can propel fluids in microchannels. These cilia are magnetic films which can be actuated by an external magnetic field, leading to an asymmetric motion like that of natural cilia. The coupling between different physical mechanisms (magnetostatics, solid mechanics and fluid dynamics) is numerically established. In this work we quantify the flow through a microfluidic channel as a function of its geometry for a characteristic set of dimensionless parameters.

In this paper we develop a mathematical model of the dynamics for an inflatable space reflector, which can be used to design a controller for the shape of the inflatable structure. Inflatable structures have very nice properties, suitable for aerospace applications. We can construct e.g. a huge light weight reflector for a satellite which consumes very little space in the rocket because it can be inflated when the satellite is in the orbit. So with this technology we can build inflatable reflectors which are about 100 times bigger than solid ones. But to be useful for telescopes we have to actively control the surface of the inflatable to achieve the desired surface accuracy. The starting point of the control design is modeling for control, in the case port-Hamiltonian (pH) modeling. We will show how to derive a nonlinear infinite dimensional pH model of a 1-D Euler-Bernoulli beam with piezo actuation. In the future we will also focus on 2-D models.

Strain stiffening of protein networks is explored by means of a finite strain analysis of a two-dimensional network model of cross-linked semiflexible filaments. The results show that stiffening is caused by non-affine network rearrangements that govern a transition from a bending dominated response at small strains to a stretching dominated response at large strains. Thermally-induced filament undulations only have a minor effect; they merely postpone the transition.

Scale effects in cellular metals can develop when the specimen size is of the order of the cell size. Decreasing the relevant specimen dimensions—height, width, and ligament size (the region between notches in notched specimens)—leads to material strengthening in shear, in indentation, and in notched specimens and to reduced strength and stiffness in uniaxial compression. Experimental size-effect studies were reviewed, and it was concluded from discrete modeling results that scale effects are caused by two different microstructural mechanisms: boundary-layer effects and constraint effects. The first mechanism is active in shear (strong boundary layers) and uniaxial compression (weak boundary layers) and vanishes for specimens larger than two cell sizes and seven cell sizes, respectively. The second mechanism is active in indentation and in notched specimens, leading to a strengthening behavior that is inversely proportional to indenter and ligament size.

A micromechanical-based approach is proposed to quantify the effective (in the macroscopic sense) elastic constants of Cosserat materials. The material under investigation (cancellous bone) is cellular and classically elastic at the microscopic level and assumed to be dense Cosserat elastic at the macroscopic level. A homogenization procedure is applied to determine the effective constitutive coefficients of the macroscopic Cosserat medium. The finite element method is used to solve the necessary boundary value problems. The proposed approach is applied to determine the effective constitutive coefficients of two-dimensional cancellous bone. Preliminary results will be shown.

Metallic foams show notch-strengthening behavior when analyzing double-edge notched specimen in compression and tension. A discrete microstructural model has been used to simulate the effect of notch depth and specimen size on the net-section-strength. The non-uniform deformation behavior is analyzed by using a strain mapping procedure, highlighting that strain tends to localize in discrete bands connecting the notch tips. The net-section-strength increases with increasing notch-depth and decreasing specimen size.