The role of inclusions in thin functionalized elastic or viscoelastic sheets, films, and membranes

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One benefit of reinforcing elastic materials by fibers is that the overall dimension of an item can be reduced due to the increased mechanical stiffness. In extreme cases, bulky components may be replaced by thin membranes, films, or sheets. Our long-term goal is to develop theoretical-analytical tools and methods to readily and effectively describe such thin elastic composite materials. As an initial step in this direction, we here consider the role of rigid particulate inclusions in thin elastic sheets. First, the mutual interactions between the inclusions via deformations of the elastic environment and their influence on the overall behavior are described for different surface conditions of the membrane. To allow for a later holistic and adjustable characterization, tools for various different situations are then formulated. Besides the pure role of static effects of elasticity, we investigate dynamic viscoelasticity, thermal and thermophoretic effects when inclusions are heated from outside, as well as related actuation. Elements of adsorption and binding to a membrane together with the resulting bending shall likewise be considered. While, initially, we need to confine ourselves to flat and linearly elastic membranes, also nonlinear elasticity and curved membranes shall be addressed afterwards. The described functionalization by particulate inclusions already promises a broad range of tailored applications. Examples may extend to tuned loudspeaker diaphragms, addressable membranes for on-demand drug release, or thin actuation devices. In a wider context, our results will support, for example, the interpretation of data obtained by AFM (atomic force microscopy) measurements and be relevant in the field of biological membrane engineering. Building on the present results, our long-term objective is the characterization of fiber-reinforced thin elastic sheets and membranes.