The elastic moduli and viscosity of TMV superlattice were determined to be E 1s = 2.14 GPa, E 2s = 21.3 MPa, and η s = 12.4 GPa∙ms. From the characterized viscoelastic parameters, it can be concluded that the TMV/Ba2+ superlattice was quite rigid at the initial contact and then experienced a large deformation under a constant pressure. Finally, the simulation of the mechanical behavior of TMV/Ba2+ superlattice
under various loading cases, including uniform tension/compression and nanoindentation, were conducted to predict the mechanical response of sample under different loadings. The storage and loss shear moduli were also demonstrated to extend the applicability of the proposed method. With the selleck screening library characterized viscoelastic properties of TMV superlattice, we are now able to predict the process of tissue regeneration around the superlattice where the time-dependent mechanical properties of scaffold interact with the growth of tissue. Appendix Modeling of adhesive contact of viscoelastic
bodies The functional equation method was employed to develop a contact mechanics model for indenting a viscoelastic material with adhesion. A modified standard solid model was used to extract the viscous and elastic parameters of the sample. Several adhesive contact models are available, such as Johnson-Kendall-Roberts (JKR) model , Derjaguin-Muller-Toporov (DMT) model , etc. [51–53]. Detailed comparisons can be selleck chemicals found in reference . As the DMT model results in a simpler differential equation, it was used in this study for the simulation to solve the indentation on an elastic body with adhesion. For the DMT model , the selleck inhibitor relation between the indentation force F and relative approach (-)-p-Bromotetramisole Oxalate δ, shown in Figure 8, can be expressed as Figure 8 Schematic of contact between a rigid sphere and a flat surface (cross-section view). (A.1) where R is the nominal radius of the two contact
spheres of R 1 and R 2, given by R = R 1 R 2/(R 1 + R 2); the adhesive energy density w is obtained from the pull-off force F c , where F c = 3πwR/2; and the reduced elastic modulus E * is obtained from the elastic modulus E s and Poisson’s ratio ν s of the sample by with the assumption that the elastic modulus of the tip is much larger than that of the sample. In Equation (A.1), E * , which governs the contact deformation behavior, is decided by the sample’s mechanical properties. In the functional equation method , E * needs to be replaced by its equivalence in the viscoelastic system, so that the contact deformation behavior can be governed by the viscoelastic properties. To achieve it, the elastic/viscoelastic constitutive equations are needed. As a premise of the functional equation method, quasi-static condition is assumed so that the inertial forces of deformation can be neglected [43, 44]. The general constitutive equations for a linear viscoelastic/elastic system in Cartesian coordinate configuration can be written as (A.2) (A.