Mechanics of structured materials and their biomedical applications

Abstract

This work is concerned with the mechanics of periodic structures for biomedical applications. Classical work on the apparent elastic properties of infinite planar and cylindrical lattice structures is generalised to the non-linear elasto-plastic regime. The elastic recoil upon unloading is also assessed. Elastic instability behaviour of constrained perforated films upon stretching is studied.

The elasto-plastic response and recoil analysis of two-dimensional honeycomb is presented. The apparent non-linear structural response obtained analytically here is observed to be smooth, even though the material model of the constituent material is elastic-perfectly-plastic. We show that the Poisson's ratio in the non-linear deformation remains the same as that during the elastic phase. A non-trivial scaling transformation for apparent stress and strain, which separates the individual cell wall response from the mechanics of the overall honeycomb sheet, is identified. This leads to a non-linear master deformation profile that fully describes the plastic response of hexagonal honeycomb with different geometries. The effects of material hardening are introduced by using a novel hyperbolic hardening model. This is then generalised for lattices whom struts possess circular cross-section. Such analysis is relevant to lattice materials and scaffolds manufactured using 3D printing techniques, such as fused deposition modelling, that inevitably makes use of cylindrical filaments.

Analytical expressions for the elasto-plastic response of a sinusoidal structure wrapped over a cylinder, as a model of crown found within cardiovascular stents, is developed. The response of the cylinder under internal pressure is well approximated by that of the opened-up flattened configuration under remote stretch. A scaling ansatz that collapses the response for different geometries on a family of 'master-curves' is proposed. We show that the stiffness scales as the cube of the ratio between the amplitude and the wavelength of the sinusoid. Such analysis is then successfully applied to the development of two novel biodegradable stents.

Thin membranes with positive apparent Poisson's ratio wrinkle when stretched. Here we show that membranes with negative apparent Poisson's ratio are wrinkle-free upon stretching, except at the edges where localised wrinkling occurs. Here we develop a simple analytical kinematic model to characterise the amplitude and wavelength of the instability behaviour. The model is then validated experimentally and computationally.

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