Conference Agenda

Modern 3D bioprinting techniques aim at reproducing a specific tissue composition by extruding a bioink, which is a cluster of stem cells embedded into a hosting gel, into the desired pattern. If the extruded structure is fed suitable nutrients, cell differentiation and growth is initiated. However, prior to activating these processes, the gel must first be converted into a polymer construct to provide support and preferential directions to the successive cellular growth phase. There are many ways to accomplish this melt-to-solid transition, most notably photo-polymerisation. The irradiation of a light with suitable intensity and wavelength triggers chemical processes that induce the cross-linking between polymer chains within the printed material, in a time-evolving scheme of structure formation. Controlling this process holds great importance, since cellular motility and nutrient diffusion are greatly affected by the disposition and orientation of the polymer network. As it currently stands, the 3D printing process briefly described above is well known, but in many instances it is not yet adequately optimised and the influence of a variety of parameters hinders a large-scale production basis. For example, the intensity and direction of the UV light has no standard protocol yet, so the definition of an optimal disposition of the light sources can prove essential in minimising the polymerisation times, hence tissue formation times as a whole. This work intends to ground the choice of selected polymerisation parameters to a rational basis. To achieve this, the relevant Physics of what happens after the melted bio-ink is deposited has been represented through multi-physics Finite Element simulations, where the kinetics of polymer cross-linking has been coupled with finite deformation formulations. Viscoelastic behaviour during polymerisation has also been accounted for. To deal with the highly non-linear differential equations representing the problem, a parametrised custom Finite Element variational formulation has been implemented.

Magneto Active Polymers (MAPs) are composite material that combines micron-sized magnetic particles with an elastomer matrix. These materials are notable for their softness and ability to become stiffer in response to an external magnetic field. MAP is prepared by mixing micron-sized iron particles with an elastomeric matrix (i.e., PDMS), which is one of the varieties of silicon rubber. Here we present a study on the mechanical characterization of magneto active polymers prepared by mixing iron particles with a Polydimethylsiloxane (PDMS) (Ecoflex polymers) matrix. The stiffness of PDMS depends on the mixing ratio of these two components. Tensile and relaxation tests were conducted to characterize the mechanical properties of MAP. The experimental data obtained from these tests were used to calibrate the model for the material and to determine the elastic and viscoelastic constants. The results of the study showed that the MAP exhibited desirable mechanical properties and that the external magnetic field can control its response. The calibrated model effectively predicted the mechanical behavior of the material under different loading conditions. The findings of this study have significant implications for the development of magneto active polymers for various applications, such as in the field of soft robotics, where the material's mechanical properties play a crucial role in the design and operation of soft robots.

Magnetorheological elastomers (MREs) with soft matrices have paved the way for new advancements in the fields of soft robotics and bioengineering. The material response is governed by a complex magneto-mechanical coupling, which necessitates the use of computational tools to guide the design process. However, these computational models typically rely on finite element frameworks that oversimplify and idealize the magnetic source and magnetic boundary conditions (BCs), leading to discrepancies with the actual behavior even at a qualitative level. In this study, we comprehensively examine the impact of magnetic BCs and highlight their significance in the modeling process. We present a magneto-mechanical framework that models the response of soft-magnetic and hard-magnetic MREs under various magnetic fields generated by an idealized magnetic source, a permanent magnet, a coil system, and an electromagnet with two iron poles. Our results demonstrate noteworthy differences in magnetostriction depending on the magnetic source used. Furthermore, we implement a virtual testbed to explore the fracture performance of MREs with remanent magnetic fields. To this end, we prescribe remanent magnetization conditions on rectangular samples, and we add a damage phase-field to model crack propagation. In order to maintain the continuity of the magneto-mechanical fields, the damaged material is designed to exhibit the same behavior as the surrounding air. The results show that remanent magnetization enhances the fracture energy and arrests cracks propagation.

Refs:

[1] Lucarini S, Moreno-Mateos MA, Danas K, Garcia-Gonzalez D. "Insights into the viscohyperelastic response of soft magnetorheological elastomers: Competition of macrostructural versus microstructural players". International Journal of Solids and Structures, Vol. 256, 2022.

[2] Moreno-Mateos MA, Hossain M, Steinmann P, Garcia-Gonzalez D. “Hard magnetics in ultra soft magnetorheological elastomers enhance fracture toughness and delay crack propagation”. Journal of the Mechanics and Physics of Solids, Vol. 173, 2023.

Two decades ago, new experiments accompanied by the modernization of magnetoelastic theory have spawned a great amount of theoretical, numerical but also experimental developments on magnetoelastic composites such as magnetorheological elastomers (MREs). Thanks to extensive research efforts, their coupled magnetoelastic response is well understood nowadays. However, this applies only to MREs and related materials based on sufficiently stiff matrix material. Indeed, as the shear modulus of the matrix material is reduced further and further, magnetoelasticity turns out to be an insufficient theoretical framework at the macroscopic scale as demonstrated in this contribution. Even when neglecting the dissipation in the constituents, one may observe significant dissipation.

In composites based on very soft matrix material that can only store rather small amounts of elastic energy, the magnetic energy may dominate the total energy of the system. Multiple (meta-)stable configurations are the consequence, which render the composite material "magneto-pseudoelastic" even when both the inclusions and the matrix material are practically non-dissipative. While such “magnetodeformal shape-memory” effects can be found in mainly experimental literature, we are not aware of quantitatively predictive simulations in this regard.

In this talk we present ongoing work pushing the limits of finite element and re-meshing technologies in order to render the complicated processes extremely soft MREs accessible by computational means.