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 …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 …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