The brain soft tissue is subject to large strains due to the shape changes that occur during growth. The process can be viewed as one in which tissue transforms from a locally stress-free reference configuration to a mature state exhibiting large elastic deformations. The biological growth alters the state of stress and leads to residual fields existing in the equilibrium state of the tissue after morphogenesis. Residual stress fields are inhomogeneous and anisotropic. This resulting stress field typically involves compressive and tensile stresses that vary through the material in a complex fashion. Hence, the mechanical response of residually stressed tissues to finite deformations differs from that of stress-free tissues. Furthermore, considering the role of mechanical properties of the tissues on the regulation of the essential behavior of the cellular structure, the residual fields have a potential role in mechanotransduction at the tissue and cellular scale. The residual fields also should be included when seeking to model the micromechanical mechanisms that give rise to brain injury. While the physical mechanisms of acute and secondary injuries led by extreme events (e.g., blunt impact, blast waves, cavitation, etc.) still remain unclear, it does seem clear that residual stresses could have a significant effect. For example, a preexisting tensile residual stress could accelerate the formation of microfissures during an episode of physical trauma, whereas a preexisting compressive residual stress field could provide some benefit in delaying fissure formation. It is issues of this type that motivate much of this research.Research on residual fields in the cortex is quite limited, despite extensive experimental studies estimating residual stress fields in various tissues. The limited experimental findings generally indicate that gray matter (outer layer) experiences compression, while white matter (inner core) is subject to tension. The findings support the differential growth hypothesis where the gray matter is growing more than the white matter. It should be noted that the experimental insights are limited to specific cutting directions and regions, making a comprehensive assessment of residual stress/strain fields challenging. On the other hand, computational models have been extensively used in order to simulate cortical growth and folding processes to understand various aspects such as folding patterns, developmental abnormalities, underlying growth and folding mechanisms, and the role of physical and material properties on the final morphology. Still, there is a notable scarcity of computational models predicting the mechanical state of brain tissue during cortical growth, particularly including the extended folding regime.The research work presented in this dissertation concerns the study of morphogenesis-induced residual stress fields in hyperelastic materials and the potential effect of these residual stress fields on the material response. This research is generally based on the non-linear theory of elasticity. To address the effect of the residual stress field on the material response, the solution of a finite deformation boundary value problem for a residually stressed elastic spherical shell subject to pressure inflation is first provided. To this end, the general constitutive equation for an isotropic Mooney-Rivlin type of hyperelastic material with a background residual stress field is derived. Four residual stress fields with distinct levels of strength are considered. The problem is then expressed as a compact integral expression including the base response of the material and the response arising from the presence of the residual stress field. An asymptotic analysis is conducted to examine the dependence of residual-stress integrals on a dimensionless measure of radial strain. The results are compared with the base response of the Mooney-Rivlin type material to pressure inflation and the potential effect of the residual stress field on the material response is discussed. The numerical analysis shows that the residual stress fields have the potential to alter the qualitative behavior of the pressure-inflation response of the material.While the just described analysis was quite general for residual stress fields that could arise from a variety of causes, the work then proceeds with the examination of residual stress due to differential growth in adjoining tissue in incompressible isotropic hyperelastic single and bilayer spherical shells. The kinematics of differential volumetric growth utilizing the incompressible hyperelastic framework are presented for each geometry considered, and the growth-induced residual stress fields are computed for five different growth conditions: area, surface, isotropic, and the combination of area and surface growth. Then, the sensitivity of the resultant stress field to the differential growth in adjoining layers is examined for the combination of the five growth conditions. In this analysis, the spherical symmetry is preserved during the growth. To address the residual stress fields generated by the morphogenesis including symmetry-breaking bifurcation and beyond, the study later continues by building an elementary computational model with idealized geometry, boundary conditions, and parameters. This 2D plane strain computational model provides the residual stress/strain fields emerging in a formation resembling sulcus-gyrus structure in a gyrified brain. In the finite element model, an initially flat bilayer rectangular model is utilized, which consists of a relatively stiff outer layer (cortex) and the inner core (subcortex). Following the differential growth hypothesis, the residual stress and strain fields are computed for the domain where the cortex undergoes only tangential (in-plane) growth while the subcortex does not experience any growth. A detailed stress and strain analysis of the resultant sulcus-gyrus formation is performed to understand morphogenesis-induced residual fields specifically for the sulcal floor and gyral crown. The computational results are consistent with previous experimental findings.Due to the specific attention to physical injuries leading to the neuropathies such as Chronic traumatic encephalopathy (CTE) seen in the depth of the sulcus, the analysis is extended to encompass the response of non-residually stressed sulci subjected to intrasulcal deformations. A 2D plane strain computational model of a single sulcus is built to examine the deformations associated with the expansion of a cavitation bubble in the intrasulcal region. Based on the previously obtained experimental data, the quasi-static and transient pressure loading conditions are implemented to the gray matter-cerebrospinal fluid (CSF) boundary, and the response of the sulcus is investigated in detail. The findings demonstrate that cavitation result in sulcal expansion and the formation of localized high strain and strain rates at the depth of sulci. The strain and strain rate localization regions resemble the tauopathy / neurofibrillary tangles patterns seen in early CTE.
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