![Sample our Medicine, Dentistry, Nursing & Allied Health journals, sign in here to start your FREE access for 14 days]({"type":"image" , "src" : "/sda/5944/TOC-Subject-Sample-2021-Medicine-Dentistry-Nursing-Allied-Health.jpg"})
Abstract
A variety of uniaxial constitutive laws have been proposed for the characterization of the aorta's nonlinear passive response, but a detailed comparison of them appears to be lacking. In this study, a systematic presentation of all available phenomenological formulations is undertaken and explicit formulae of constitutive laws are provided for simple elongation tests performed on healthy aortic strips. Common to all derived laws is the use of three analytical functions to approximate the low, physiologic, and high-stress parts of the aortic response, and the very close and essentially equally accurate fits that they give to the experimental data over the full range of stresses. Another feature of the three-part laws is their compatibility with the biphasic nature of the aortic tissue under passive conditions, allowing direct microstructural interpretation of their parameters. Importantly, although it is found that the aorta displays strain softening, i.e. its passive response is dependent on the highest previously experienced stress, the three-part character of the laws seems to be unaffected by the preconditioning procedure.
| List of symbols | ||
| λ | = | Extension ratio |
| T | = | First Piola-Kirchhoff stress |
| σ = Tλ | = | Cauchy stress |
| S = T/λ | = | Second Piola-Kirchhoff stress |
| ϵ = λ – 1 | = | Infinitesimal strain |
| E = 1/2(λ2−1) | = | Green strain |
| e = 1/2(1−λ−2) | = | Almansi strain |
| ν = ln λ | = | Hencky strain |
| B | = | Cauchy-Green deformation tensor |
| IB,IIB | = | First and second invariants of B |
| I | = | Second-rank unit tensor |
| μ | = | Lagrange multiplier |
| W | = | Strain energy density |
| Mt = dT/dϵ | = | Tangent modulus |
| Ms = T/ϵ | = | Secant modulus |
| p0, p1, …, p7 | = | Parameters of the polynomial formulation |
| k, q, a, b, c, d | = | Parameters of the Mt−T formulation |
| k, q, a, b, c, d | = | Parameters of the Ms – T formulation |
| log kˆ′ = kˆ, qˆ, log â′ = â, bˆ, log ĉ′ = ĉ, dˆ | = | Parameters of the log T – log ϵ formulation |
| = | Parameters of the ln T−ϵ formulation | |
| = | Parameters of the dW/dIB−(IB−3) formulation | |
| (ϵI, TI), (ϵII, TII) | = | First and second transition point of the Mt−T formulation |
| = | First and second transition point of the Ms−T formulation | |
| = | First and second transition point of the log T−log ϵ formulation | |
| = | First and second transition point of the ln T−ϵ formulation | |
| = | First and second transition point of the dW/dIB−(IB−3) formulation | |
| (ϵf,Tf) | = | Upper limit of validity for all formulations |
| r | = | Correlation coefficient |
| List of symbols | ||
| λ | = | Extension ratio |
| T | = | First Piola-Kirchhoff stress |
| σ = Tλ | = | Cauchy stress |
| S = T/λ | = | Second Piola-Kirchhoff stress |
| ϵ = λ – 1 | = | Infinitesimal strain |
| E = 1/2(λ2−1) | = | Green strain |
| e = 1/2(1−λ−2) | = | Almansi strain |
| ν = ln λ | = | Hencky strain |
| B | = | Cauchy-Green deformation tensor |
| IB,IIB | = | First and second invariants of B |
| I | = | Second-rank unit tensor |
| μ | = | Lagrange multiplier |
| W | = | Strain energy density |
| Mt = dT/dϵ | = | Tangent modulus |
| Ms = T/ϵ | = | Secant modulus |
| p0, p1, …, p7 | = | Parameters of the polynomial formulation |
| k, q, a, b, c, d | = | Parameters of the Mt−T formulation |
| k, q, a, b, c, d | = | Parameters of the Ms – T formulation |
| log kˆ′ = kˆ, qˆ, log â′ = â, bˆ, log ĉ′ = ĉ, dˆ | = | Parameters of the log T – log ϵ formulation |
| = | Parameters of the ln T−ϵ formulation | |
| = | Parameters of the dW/dIB−(IB−3) formulation | |
| (ϵI, TI), (ϵII, TII) | = | First and second transition point of the Mt−T formulation |
| = | First and second transition point of the Ms−T formulation | |
| = | First and second transition point of the log T−log ϵ formulation | |
| = | First and second transition point of the ln T−ϵ formulation | |
| = | First and second transition point of the dW/dIB−(IB−3) formulation | |
| (ϵf,Tf) | = | Upper limit of validity for all formulations |
| r | = | Correlation coefficient |