Search

In this work, virtual fields method (VFM) is applied to extract the constitutive parameter of silicone elastomers under equi-biaxial and general biaxial tests; the influence of missing deformation data near specimen edges and noise introduced by digital image correlation (DIC) on parameter identification using VFM is investigated. The results indicate that the negative impact of the missing data and noise can be mitigated by scaling the load applied to the specimen boundary properly and extracting parameters based on the deformation fields of all loading steps through the least square method. [ABSTRACT FROM AUTHOR]

Background: Quasilinear viscoelasticity (QLV) theory has been widely and successfully used to describe the time-dependent response of connective tissues. Difficulties remain, however, particularly in material parameter estimation and sensitivities. In this study, we introduce a new alternative: the fractional order viscoelasticity (FOV) theory, which uses a fractional order integral to describe the relaxation response. FOV implies a fractal-like tissue structure, reflecting the hierarchical arrangement of collagenous tissues. Method of Approach: A one-dimensional (1-D) FOV reduced relaxation function was developed, replacing the QLV 'box-spectrum' function with a fractional relaxation function. A direct-fit, global optimization method was used to estimate material parameters from stress relaxation tests on aortic valve tissue. Results: We found that for the aortic heart valve, FOV had similar accuracy and better parameter sensitivity than QLV, particularly for the long time constant ([tau]2). The mean (n=5).fractional order was 0.29, indicating that the viscoelastic response of the tissue was strongly fractal-like. Results summary: mean QLV parameters were C=0.079, [tau]1=0.004, [tau]2=76, and mean FOV parameters were [beta]=0.29, [tau]=0.076, and [rho]= 1.84. Conclusions: FOV can provide valuable new insights into tissue viscoelastic behavior. Determining the fractional order can provide a new and sensitive quantitative measure for tissue comparison. [DOI: 10.1115/1.1933900] Keywords: Fractional Calculus, Viscoelasticity, Nonlinear Elasticity, Aortic Valve, Fractals, Soft Tissue

A physiologic constitutive expression is presented in algorithmic format for the nonlinear elastic response of wavy collagen fibrils found in soft connective tissues. The model is based on the observation that crimped fibrils in a fascicle have a three-dimensional structure at the micron scale that we approximate as a helical spring. The symmetry of this wave form allows the force/displacement relationship derived from Castigliano's theorem to be solved in closed form: all integrals become analytic. Model predictions are in good agreement with experimental observations for mitral-valve chordae tendineae. [DOI: 10.1115/1.1934145]