A flexible design framework to design graded porous bone scaffolds with adjustable anisotropic properties.

Since the success of bone regenerative medicine depends on scaffold morphological and mechanical properties, numerous scaffolds designs have been proposed in the last decade, including graded structures that are suited to enhance tissue ingrowth. Most of these structures are based either on foams with a random pore definition, or on the periodic repetition of a unit cell (UC). These approaches are limited by the range of target porosities and obtained effective mechanical properties, and do not permit to easily generate a pore size gradient from the core to the periphery of the scaffold. In opposition, the objective of the present contribution is to propose a flexible design framework to generate various three-dimensional (3D) scaffolds structures including cylindrical graded scaffolds from the definition of a UC by making use of a non-periodic mapping. Conformal mappings are firstly used to generate graded circular cross-sections, while 3D structures are then obtained by stacking the cross-sections with or without a twist between different scaffold layers. The effective mechanical properties of different scaffold configurations are presented and compared using an energy-based efficient numerical method, pointing out the versatility of the design procedure to separately govern longitudinal and transverse anisotropic scaffold properties. Among these configurations, a helical structure exhibiting couplings between transverse and longitudinal properties is proposed and permits to extend the adaptability of the proposed framework. In order to investigate the capacity of common additive manufacturing techniques to fabricate the proposed structures, a subset of these configurations is elaborated using a standard SLA setup, and subjected to experimental mechanical testing. Despite observed geometric differences between the initial design and the actual obtained structures, the effective properties are satisfyingly predicted by the proposed computational method. Promising perspectives are offered concerning the design of self-fitting scaffolds with on-demand properties depending on the clinical application.

Curvature, metric and parametrization of origami tessellations: theory and application to the eggbox pattern.

Origami tessellations are particular textured morphing shell structures. Their unique folding and unfolding mechanisms on a local scale aggregate and bring on large changes in shape, curvature and elongation on a global scale. The existence of these global deformation modes allows for origami tessellations to fit non-trivial surfaces thus inspiring applications across a wide range of domains including structural engineering, architectural design and aerospace engineering. The present paper suggests a homogenization-type two-scale asymptotic method which, combined with standard tools from differential geometry of surfaces, yields a macroscopic continuous characterization of the global deformation modes of origami tessellations and other similar periodic pin-jointed trusses. The outcome of the method is a set of nonlinear differential equations governing the parametrization, metric and curvature of surfaces that the initially discrete structure can fit. The theory is presented through a case study of a fairly generic example: the eggbox pattern. The proposed continuous model predicts correctly the existence of various fittings that are subsequently constructed and illustrated.