From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: Special cases of incompressible, uniaxial tension/compression (left) and simple shear (right) for different hyperelastic elastic brain tissue models. The top and bottom figures illustrate the responses for small and large deformations. The material parameters are chosen such that ∂σ11/∂λ|λ=1 is the same for all the models. The remaining material parameters are chosen to be consistent with the experimental data.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: Axial stress versus stretch curves for the Ogden model in incompressible, uniaxial tension/compression loading for varying model parameters N and αi. In tension, the Ogden model displays a strain softening if |αi|<1 for all i=1…N, and a strain stiffening otherwise. In compression, the model predicts a strain stiffening for all the values of αi.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: Time-dependent behavior of the brain tissue under uniaxial loading. The brain tissue displays viscous effects and stress relaxation under constant deformation.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: Multiplicative decomposition model and standard linear solid model. Every component of the deformation gradient is associated with a rheological element: F, Fe, and Fv are related to the main elastic network, the elastic spring, and the viscous damper. These elements require individual constitutive relations to define the elastic stress σe, the viscous stress σv, and the viscous stretch rate dv.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: Hrapko model [15] and Bilston model [14] as examples of multiplicative decomposition models. Both models are popular viscoelastic models for the brain tissue based on multiple parallel configurations.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: Prevost model [16] as example of multiplicative decomposition model. The Provost model is a popular viscoelastic model for the brain tissue based on four configurations.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: History-dependent response of the brain tissue under uniaxial loading–unloading. The brain tissue displays a preconditioning effect that converges after approximately seven preconditioning cycles.

From: Constitutive Modeling of Brain Tissue: Current Perspectives Date of download: 11/10/2017 Copyright © ASME. All rights reserved. From: Constitutive Modeling of Brain Tissue: Current Perspectives Appl. Mech. Rev. 2016;68(1):010801-010801-16. doi:10.1115/1.4032436 Figure Legend: History-dependent response under uniaxial loading–unloading displaying the Mullins effect and residual strains similar to rubberlike materials