The Connection Between Strain Components In Uniaxial Tests: A Comparative Analysis

From an investigation of the connection between strain components in uniaxial tests, this research conducted a mixture of experimental and numerical analysis to determine the damage constitutive constraints of the brain tissue by exploiting nonlinear optimization method. To do that, a mixture of the gray and white matters of the brain tissue were imaged using MRI and then the tractography approached was used to determine the angle of collagen fibers in them. Finally, the tissue samples were subjected to a set of axial and transversal compressive loads. The constitutive damage model of the brain tissue was optimized using the experimental data and the unknown coefficients of the brain tissue were reported. Finally, the agreement of the proposed
4). Similarly, it has been shown that the behavior of the brain tissue in unconfined compression is intrinsically nonlinear at finite deformation [55]. The brain tissue in here also presented statistically significant higher elastic modulus as well as maximum stress in the axial direction compared to that of the transversal one (n = 10 samples for each direction, *p < 0.01, post hoc Scheffe method). The reason of this stiffness in here is related to the distribution of the collagen fibers in the tissue as presented in Figs. 2 and 3. That is, the contribution of the collagen fibers in the axial direction of loading is more than that of the transversal one and, this is why, a stiffer behavior in that direction was observed (Fig. 5). This mechanical difference implies that there must be a strong connection between the mechanical properties of the brain tissue with the distribution of the collagen fibers. This is why it is of vital important to perform a numerical analysis to figure out how the distribution of collagen fibers, in here their orientations, can contribute to the load bearing. In addition, it is worth knowing that how the collagen fibers can contribute to the softening and stiffening behaviors of the brain tissue under the applied load thru a damage constitutive
To address this issue, in the current study a combination of Ogden as well as Holzapfel-Gasser-Ogden damage model was used to address the mechanical response of the brain tissue under the unconfined compressive loading. Twenty-five variables of the model were optimized using the written program (Fig. 6). In the optimization approach, the variable were minimized under the imposed constraints to minimize the function value. The results were well calculated under 2000 iterations to be able to have the least amount of function value (Tables 1 and 2). After calculating the model coefficients, the agreements of the proposed model with that of the experimental data under both loading directions were examined (Fig. 7). The model enabled to well address the initial softening and later stiffening behaviors of the brain tissue under both loading directions. The coefficients of the Ogden model in Table 2 implies the delicate soft behavior of the brain tissue under the applied load. In addition, the results of the damage parameters, rf and mf, depicted a severe damage in the fibers at a fast pace. That is, the brain tissue is so vulnerable to the compressive load