Modeling of long-term fatigue damage of soft tissue with stress softening and permanent set effects

Abstract

One of the major failure modes of bioprosthetic heart valves is non-calcific structural deterioration due to fatigue of the tissue leaflets. Experimental methods to characterize tissue fatigue properties are complex and time-consuming. A constitutive fatigue model that could be calibrated by isolated material tests would be ideal for investigating the effects of more complex loading conditions. However, there is a lack of tissue fatigue damage models in the literature. To address these limitations, in this study, a phenomenological constitutive model was developed to describe the stress softening and permanent set effects of tissue subjected to long-term cyclic loading. The model was used to capture characteristic uniaxial fatigue data for glutaraldehyde-treated bovine pericardium and was then implemented into finite element software. The simulated fatigue response agreed well with the experimental data and thus demonstrates feasibility of this approach.

Fig. 1

Illustration of the effects of alpha on the (a) number of cycles to failure, and the (b) degree of stress softening accrued during one loading cycle. The effects of beta on the (c) number of cycles to failure, (d) and the amount of stress softening during one loading cycle

Fig. 2

Illustration of the effects of (a and c) alpha and (b and d) beta on the permanent set accrued in the principal directions during one loading cycle

Fig. 3

Illustration of the effects of beta on the stress–strain response (only the 11 direction is shown for clarity) at different cycle levels up to n = 50 × 10⁶

Fig. 4

Uniaxial response of GLBP in the LD at different fatigue states with (a) no permanent set included and with (b) permanent set included

Fig. 5

(a) Equi-biaxial response of GLBP specimen at the unfatigued state (Sun et al. 2004). (b) Contour plot of equivalent strain with ψ_min = 4.67 $\frac{\sqrt[]{\mathrm{kN}}}{\mathrm{m}}$ and ψ_max = 4.32 × 10⁵ $\frac{\sqrt[]{\mathrm{kN}}}{\mathrm{m}}$ marking the damage evolution region

Fig. 6

Uniaxial failure test data for 5 GLBP specimens with a mean failure strain of approximately 0.45 corresponding to ψ_max = 4.32 × 10⁵ $\frac{\sqrt[]{\mathrm{kN}}}{\mathrm{m}}$

Fig. 7

The simulated uniaxial fatigue specimen with a contour plot of the stress softening factor, D_s, after (a) 0 cycles (unfatigued state), (b) 20 × 10⁶ cycles, (c) 30 × 10⁶ cycles at zero LD displacement, and (d) 30 × 10⁶ cycles at the stress-free state

Fig. 8

(a) The simulated stress–strain response during the cyclic uniaxial displacement control loading (only cycles 1 × 10⁶, 5 × 10⁶, 10 × 10⁶, 15 × 10⁶, 20 × 10⁶, 25 × 10⁶ and 30 × 10⁶ are shown for clarity).(b) The 1-0.1 protocol biaxial stress–strain response of the simulated specimen compared to the actual specimen at the 0 state and the 30 × 10⁶ cycle state