Data Analysis Biaxial Tensile Tests
Different stress and strain definitions have been used to study the biomechanics of soft tissue [24]. The 2nd Piola-Kirchhoff stress and Green strain definitions have been employed in this study, which are described briefly in the following.
The Green strain tensor is defined as E=1/2(F^T F-1), where F is the gradient deformation tensor. For the case of in-plane biaxial stretching in directions 1 and 2, the Green strain in these directions can be written as E_i=(λ_i^2-1)/2,=(〖〖(L〗_i/L_i0)〗^2-1)/2,i=1,2, with λi (i=1, 2, 3) the stretch values in the deformed equilibrium configuration and L_i and L_i0 the length between gauge marks in the deformed and initial configurations, respectively.
The 2nd-Piola Kirchhoff stress tensor, denoted by S, is a symmetric tensor relating force to areas in the reference configuration. By assuming the specimens as rectangular plates with uniform thicknesses subjected to axial loads on their edges and with no shear stresses, the stresses in directions 1 and 2 are given by
S_1=F_11/(A_1^0 λ_1 )=F_11/(A_1^0 √(2E_1+1)),〖 and S〗_2=F_22/(A_2^0 λ_2 )=F_22/(A_2^0 √(2E_2+1)), Eq. 3
where A_1^0 and A_2^0 are the initial areas, and F11 and F22 are correspondingly the loads in directions 1 and 2. The load and strain values were assumed to be zero at the beginning of the test cycles; therefore, the stretches were adjusted to 1 at the beginning of these cycles in the calculations (E_i0=0,i=1,2). The thickness and the lengths between the sutures measured before the experiments were used to obtain A_1^0 and A_2^0. The incremental moduli of the samples were obtained and compared at arbitrary strain values of 10%, in the physiological range, by fitting first order polynomials to the stress-strain results at the strain range of 10±1%. Toughness Tests The work done on the samples during the two phases of the toughness tests were evaluated to find the energy required for inducing a stable controlled-path crack per unit area. Figure 2 depicts the load and displacement data of the blade, obtained during a toughness test. At the beginning of the cutting process, the load increases linearly with the displacement of the blade until it reaches a region with a lower gradient or 'plateau ' region; the crack initiations region were excluded from the toughness calculations since, in this region, a fraction of the applied load can deform samples. The stable crack propagation happens in the plateau section of the load-displacement curves, illustrated in gray in Figure 2; this section is used for the toughness calculations. The work required to cut through the samples, W_i, was found from the area under Path 1, determined during phase (i) of the tests; and, the work of friction, W_ii, was measured from the area under Path 2, acquired during the second non-cutting pass of the blade (phase (ii)). These works …show more content…
Then, the samples were paraffin embedded, cut into thin sections, and mounted on microscopic slides. The slides were stained by a Modified Movat 's Pentachrome staining protocol. Three representative images, each of which covered approximately 1/3 of the media layer, were captured and used to obtain the average contents of the tissue components in this layer. Aortic aneurysms are attributed to medial degeneration [25]; hence, the collagen and elastin contents were determined for this layer. The characterizations of the components were performed by an individual blinded to the mechanical
Different stress and strain definitions have been used to study the biomechanics of soft tissue [24]. The 2nd Piola-Kirchhoff stress and Green strain definitions have been employed in this study, which are described briefly in the following.
The Green strain tensor is defined as E=1/2(F^T F-1), where F is the gradient deformation tensor. For the case of in-plane biaxial stretching in directions 1 and 2, the Green strain in these directions can be written as E_i=(λ_i^2-1)/2,=(〖〖(L〗_i/L_i0)〗^2-1)/2,i=1,2, with λi (i=1, 2, 3) the stretch values in the deformed equilibrium configuration and L_i and L_i0 the length between gauge marks in the deformed and initial configurations, respectively.
The 2nd-Piola Kirchhoff stress tensor, denoted by S, is a symmetric tensor relating force to areas in the reference configuration. By assuming the specimens as rectangular plates with uniform thicknesses subjected to axial loads on their edges and with no shear stresses, the stresses in directions 1 and 2 are given by
S_1=F_11/(A_1^0 λ_1 )=F_11/(A_1^0 √(2E_1+1)),〖 and S〗_2=F_22/(A_2^0 λ_2 )=F_22/(A_2^0 √(2E_2+1)), Eq. 3
where A_1^0 and A_2^0 are the initial areas, and F11 and F22 are correspondingly the loads in directions 1 and 2. The load and strain values were assumed to be zero at the beginning of the test cycles; therefore, the stretches were adjusted to 1 at the beginning of these cycles in the calculations (E_i0=0,i=1,2). The thickness and the lengths between the sutures measured before the experiments were used to obtain A_1^0 and A_2^0. The incremental moduli of the samples were obtained and compared at arbitrary strain values of 10%, in the physiological range, by fitting first order polynomials to the stress-strain results at the strain range of 10±1%. Toughness Tests The work done on the samples during the two phases of the toughness tests were evaluated to find the energy required for inducing a stable controlled-path crack per unit area. Figure 2 depicts the load and displacement data of the blade, obtained during a toughness test. At the beginning of the cutting process, the load increases linearly with the displacement of the blade until it reaches a region with a lower gradient or 'plateau ' region; the crack initiations region were excluded from the toughness calculations since, in this region, a fraction of the applied load can deform samples. The stable crack propagation happens in the plateau section of the load-displacement curves, illustrated in gray in Figure 2; this section is used for the toughness calculations. The work required to cut through the samples, W_i, was found from the area under Path 1, determined during phase (i) of the tests; and, the work of friction, W_ii, was measured from the area under Path 2, acquired during the second non-cutting pass of the blade (phase (ii)). These works …show more content…
Then, the samples were paraffin embedded, cut into thin sections, and mounted on microscopic slides. The slides were stained by a Modified Movat 's Pentachrome staining protocol. Three representative images, each of which covered approximately 1/3 of the media layer, were captured and used to obtain the average contents of the tissue components in this layer. Aortic aneurysms are attributed to medial degeneration [25]; hence, the collagen and elastin contents were determined for this layer. The characterizations of the components were performed by an individual blinded to the mechanical