Table 1 - uploaded by Lukáš Horný
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An anisotropic strain energy density function based on limiting fiber extensibility assumption was suggested. The function
was deduced directly from isotropic Gent model. A material was modeled as a composite reinforced with two families of helical
fibers. The anisotropy of the strain energy function was incorporated via pseudo-invariants I
4 and I...
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Citations
... To have a quantitative insight, we establish a correlation between clinical data on the fracture energy ( Γ ) of the abdominal aorta and the energy release rate (G) predicted by using Gent hyperelastic model, with J m = 1 (Horny et al. 2009). Sommer et al. (2008) reported the dissection energy value to be 76 J∕m 2 in longitudinal and 51 J∕m 2 in circumferential directions for an effective specimen radius of 20 mm. ...
Aortic dissection, a critical cardiovascular condition with life-threatening implications, is distinguished by the development of a tear and its propagation within the aortic wall. A thorough understanding of the initiation and progression of these tears, or cracks, is essential for accurate diagnosis and effective treatment. This paper undertakes a fracture mechanics approach to delve into the mechanics of tear propagation in aortic dissection. Our objective is to elucidate the impact of geometric and material parameters, providing valuable insights into the determinants of this pivotal cardiovascular event. Through our investigation, we have gained an understanding of how various parameters influence the energy release rate for tear propagation in both longitudinal and circumferential directions, aligning our findings with clinical data.
... It is assumed that the matrix and fibers undergo the same deformation at each point of continuum. Another successful fitting of experimental data with the model (1) for human aorta can be found in [11]. ...
An inflation-extension test with human vena cava inferior was performed with the aim to fit a material model. The vein was modeled as a thick-walled tube loaded by internal pressure and axial force. The material was assumed to be an incompressible hyperelastic fiber reinforced continuum. Fibers are supposed to be arranged in two families of anti-symmetric helices. Considered anisotropy corresponds to local orthotropy. Used strain energy density function was based on a concept of limiting strain extensibility. The pressurization was comprised by four pre-cycles under physiological venous loading (0 - 4kPa) and four cycles under nonphysiological loading (0 - 21kPa). Each overloading cycle was performed with different value of axial weight. Overloading data were used in regression analysis to fit material model. Considered model did not fit experimental data so good. Especially predictions of axial force failed. It was hypothesized that due to nonphysiological values of loading pressure and different values of axial weight the material was not preconditioned enough and some damage occurred inside the wall. A limiting fiber extensibility parameter Jm was assumed to be in relation to supposed damage. Each of overloading cycles was fitted separately with different values of Jm. Other parameters were held the same. This approach turned out to be successful. Variable value of Jm can describe changes in the axial force - axial stretch response and satisfy pressure - radius dependence simultaneously.
... It is assumed that the matrix and fibers undergo the same deformation at each point of continuum. Another successful fitting of experimental data with the model (3) for human aorta can be found in [13]. Regression analysis based on least square method gave the estimations for material parameters in the models (1) ...
Coronary artery bypass grafts (CABG) are widely studied with respect to hemodynamic conditions which play important role in presence of a restenosis. However, papers which concern with constitutive modeling of CABG are lacking in the literature. The purpose of this study is to find a constitutive model for CABG tissue. A sample of the CABG obtained within an autopsy underwent an inflation-extension test. Displacements were recoredered by CCD cameras and subsequently evaluated by digital image correlation. Pressure - radius and axial force - elongation data were used to fit material model. The tissue was modeled as one- layered composite reinforced by two families of helical fibers. The material is assumed to be locally orthotropic, nonlinear, incompressible and hyperelastic. Material parameters are estimated for two strain energy functions (SEF). The first is classical exponential. The second SEF is logarithmic which allows interpretation by means of limiting (finite) strain extensibility. Presented material parameters are estimated by optimization based on radial and axial equilibrium equation in a thick-walled tube. Both material models fit experimental data successfully. The exponential model fits significantly better relationship between axial force and axial strain than logarithmic one.
... In [5] this approach was modified to limiting fiber extensibility suitable for composite materials with progressive large strain stiffening. Horny et al. [8] used this model to describe mechanical response of a coronary artery bypass graft and in a constitutive modeling of human aorta [9]. Models mentioned above are capable to describe elastic arterial response. ...
Cyclic uni-axial tensile tests with samples of human aorta were performed with an aim to obtain data describing the Mullins effect of arterial tissue. Due to presumed anisotropy of an aorta, reported widely, both samples oriented longitudinally and circumferentially were tested in each case. Every tested sample underwent cyclic tension limited to a certain value of a stretch four times, consecutively the limit of sustained deformation was increased and subsequent four cycles were performed. Significant stress softening of aortic tissue and residual strains were confirmed. An idealization was made in such a way that reloading and unloading curves are coincident. It was hypothesized that the stress softening observed within reloading of previously loaded tissue may be described by an evolution of material parameters. These parameters should be related to an alternation of internal structure. The model based on changes in limiting fiber extensibility of fibrillar component of the aortic wall, primarily represented by a collagen, was proposed. The arterial wall was assumed to be hyperelastic transversely isotropic material with different response under primary loading and unloading. A stored energy function was additively split into isotropic and anisotropic part. Preferred direction in continuum, defined in referential configuration, was assumed to be unchanged with cyclic loading. Every straining level in the cyclic test had its own value of fiber extensibility. Explicit form of the relation between evolving limiting extensibility of fibers and maximum previously sustained deformation was proposed in such a way that limiting extensibility under primary loading is considered as the limit. The isotropic matrix response was modeled using Neo-Hooke term with shear modulus values different under primary loading and reloading, however all reloading values were held the same. The predictions of the model described above were in good agreement with observations.
... In [5] this approach was modified to limiting fiber extensibility suitable for composite materials with progressive large strain stiffening. Horny et al. [8] used this model to describe mechanical response of a coronary artery bypass graft and in a constitutive modeling of human aorta [9]. ...
Cyclic uni-axial tensile tests with samples of human aorta were performed with an aim to obtain data describing the Mullins
effect of arterial tissue. According to presumed anisotropy, reported widely, both samples oriented longitudinally and circumferentially
were tested. Each of tested samples underwent cyclic tension up to a particular value of a stretch four times, consecutively
maximum limit of reached stretch was increased and subsequent four cycles were performed. Significant stress softening of
aortic tissue and residual strains were confirmed. An idealization was made in such a way that reloading and unloading curves
are coincident. It was hypothesized that the stress softening observed within reloading of previously loaded tissue may be
described by an evolution of material parameters. These parameters should be related to an alternation of internal structure.
We proposed a model based on changes in limiting fiber extensibility of fibrillar component of the aortic wall, primarily
represented by a collagen. The arterial wall was assumed to be hyperelastic transversely isotropic material with different
response under primary loading and unloading. A stored energy function was additively split into isotropic and anisotropic
part. Preferred direction in continuum, defined in referential configuration, was assumed to be unchanged with cyclic loading.
Every straining level in the cyclic test had its own value of fiber extensibility related to strain maximum previously reached.
The isotropic matrix response was modeled using Neo-Hooke term with shear modulus values different under primary loading and
reloading, however all reloading values were held the same. The predictions of the model described above were in good agreement
with observations.
