3D couple-stress moduli of porous polymeric biomaterials using µCT image stack and FE characterization

The purpose of the current work is to develop a homogeneous, anisotropic couple-stress continuum model as a substitute of the 3D solid phases of porous natural-polymeric biomaterials used for tissue engineering. Consideration of the second gradient of deformation such as in couples stress continuum theories addresses the size dependency that is observed in such porous structures. The equivalent properties of these biomaterials are presently obtained based on the response of different representative volume elements under mixed prescribed boundary conditions comprising both controlled traction and displacement. The elastic mechanical constants of the effective couple-stress continuum are deduced at the representative volume element level by an equivalent strain energy method. We conduct this study computationally using a finite element approach. For this purpose, 3D high-resolution micro-computed tomography (µCT) scans are performed on formerly fabricated specimens. Loadings of representative volume elements include uniaxial extension, biaxial extension, and shear deformation in order to evaluate the first stiffness tensor. Besides, uniaxial twist, biaxial twist, and bending curvature are also imposed in order to obtain an estimation of the second couple stress stiffness tensor. The computed Young's moduli are similar to measurements obtained from uniaxial compression tests performed on circular cylindrical samples.