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In this work, we numerically study the hydrodynamic permeability of new-generation artificial porous materials used as scaffolds for cell growth in a perfusion bioreactor. We consider two popular solid matrix designs based on triply periodic minimal surfaces, the Schwarz P (primitive) and D (diamond) surfaces, which enable the creation of materials with controlled porosity gradients. The latter property is crucial for regulating the shear stress field in the pores of the scaffold, which makes it possible to control the intensity of cell growth. The permeability of functionally graded materials is studied within the framework of both a microscopic approach based on the Navier-Stokes equation and an averaged description of the liquid filtration through a porous medium based on the equations of the Darcy or Forchheimer models. We calculate the permeability coefficients for both types of solid matrices formed by Schwarz surfaces, study their properties concerning forward and reverse fluid flows, and determine the ranges of Reynolds number for which the description within the Darcy or Forchheimer model is applicable. Finally, we obtain a shear stress field that varies along the sample, demonstrating the ability to tune spatially the rate of tissue growth. [ABSTRACT FROM AUTHOR]

• Nucleation and propagation of fracture in additively manufactured biomedical scaffolds is important for their proper design and performance. • The tensile and compressive stress-strain states of TPMS periodic structures were studied. • The XFEM method with an original multiple-crack-growth algorithm based on cluster detection was applied to unit cells and representative volumes. • The field of strain-concentration factor allowed introduction of three conditional regions: pre-critical, critical and post-critical states. • The analysis demonstrated considerable differences of mechanical properties and performance of scaffolds with similar levels of porosity. In this paper, the mechanical behaviour and failure of porous additively manufactured (AM) polylactide (PLA) scaffolds based on the triply periodic minimal surfaces (TPMS) is investigated using numerical calculations of their unit cells and representative volumes. The strain-amplification factor is chosen as the main parameter, and the most critical locations for failure of different types of scaffold structures are evaluated. The results obtained are presented in comparison with a multiple-crack-growth algorithm using the extended finite element method (XFEM), underpinned by the experimentally obtained fracture properties of PLA. The effect of morphology of TPMS structures on the pre-critical, critical and post-critical behaviours of scaffolds under monotonic loading regimes is assessed. The results provide an understanding of the fracture behaviour and main risk points for crack initiation in structures of AM-PLA scaffolds based on typical commonly used types of TPMS, as well as the influence of structure type and external load on this behaviour. [ABSTRACT FROM AUTHOR]