دندانه مواد hyperelastic ضخامت محدود: بررسی پارامتریک با اشاره به عضله قلب
Abstract: Indentation experiments on myocardium demonstrated specific relationships between the applied in-plane stress and the transverse stiffness, defined as the slope of the indentation force-displacement curve. Theoretical derivations confirmed these relationships in axisymmetric semi-infinite bodies for Mooney-Rivlin and exponential hyperelastic materials. Nonlinear finite element analysis was used to model the indentation of finite thickness hyperelastic specimens, using 12 combinations of indenter radii (0.5-3.0 mm) and slab thicknesses (5.0-20.0 mm) and various boundary conditions to demonstrate specific relationships between the parameters of indentation and the limitations of the assumptions used in both the theoretical development and experimental studies. The indentation force-displacement relations were found to be linear for the Mooney-Rivlin and exponential materials for small indentation strains. The marked difference between the thresholds for nonlinearity between the materials will facilitate differentiation between passive and actively contracting myocardium. The transverse stiffness increased significantly as the ratio of the indenter radius to the specimen thickness increased. This demonstrated limitations due to the combined effects of the support boundary conditions and the finite thickness of the specimens. As the r/t ratio approached zero, the transverse stiffness approached the value for a semi-infinite body. Nonequibiaxial in-plane loading confirmed the accuracy of using stretch and stress scalar indices to represent the in-plane states of stretch and stress. Hydrostatic pressure supporting the specimen verified that the transmural pressure makes only a small contribution to the transverse stiffness, and that the effects the finite thickness of the specimen are amplified. Translation of the specimen during indentation was identified as a source for atypical increases in transverse stiffness with increasing indentation load. Finally, a mathematical technique for extracting in-plane stress and material properties from transverse stiffness and in-plane stretch measurement was developed and validated.