We present a double-yield-surface plasticity theory for transversely isotropic rocks that distinguishes between plastic deformation through the solid matrix and localized plasticity along the weak bedding planes. A recently developed anisotropic modified Cam-Clay model is adopted to model the plastic response of the solid matrix, while the Mohr-Coulomb friction law is used to represent the sliding mechanism along the weak bedding planes. For its numerical implementation, we derive an implicit return mapping algorithm for both the semi-plastic and fully plastic loading processes, as well as the corresponding algorithmic tangent operator for finite element problems. We validate the model with triaxial compression test data for three different transversely isotropic rocks and reproduce the undulatory variation of rock strength with bedding plane orientation. We also implement the proposed model in a finite element setting and investigate the deformation of rock surrounding a borehole subjected to fluid injection. We compare the results of simulations using the proposed double-yield-surface model with those generated using each single yield criterion to highlight the features of the proposed theory.
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On the Transversely Isotropic, Hyperelastic Response of Central Nervous System White Matter Using a Hybrid Approach
Abstract A numerical and experimental hybrid approach is developed to study the constitutive behavior of the central nervous system white matter. A published transversely isotropic hyperelastic strain energy function is reviewed and used to determine stress–strain relationships for three idealized, simple loading scenarios. The proposed constitutive model is simplified to a three-parameter hyperelastic model by assuming the white matter's incompressibility. Due to a lack of experimental data in all three loading scenarios, a finite element model that accounts for microstructural axons and their kinematics is developed to simulate behaviors in simple shear loading scenarios to supplement existing uniaxial tensile test data. The parameters of the transversely isotropic hyperelastic material model are determined regressively using the hybrid data. The results highlight that a hybrid numerical virtual test coupled with experimental data, can determine the transversely isotropic hyperelastic model. It is noted that the model is not limited to small strains and can be applied to large deformations.
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- Award ID(s):
- 1763005
- NSF-PAR ID:
- 10359672
- Date Published:
- Journal Name:
- Journal of Engineering and Science in Medical Diagnostics and Therapy
- Volume:
- 4
- Issue:
- 1
- ISSN:
- 2572-7958
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract The most widely-used representation of the compressible, isotropic, neo-Hookean hyperelastic model is considered in this paper. The version under investigation is that which is implemented in the commercial finite element software ABAQUS, ANSYS and COMSOL. Transverse stretch solutions are obtained for the following homogeneous deformations: uniaxial loading, equibiaxial loading in plane stress, and uniaxial loading in plane strain. The ground-state Poisson’s ratio is used to parameterize the constitutive model, and stress solutions are computed numerically for the physically permitted range of its values. Despite its broad application to a number of engineering problems, the physical limitations of the model, particularly in the small to moderate stretch regimes, are not explored. In this work, we describe and analyze results and make some critical observations, underlining the model’s advantages and limitations. For example, a snap-back feature of the transverse stretch is identified in uniaxial compression, a physically undesirable behavior unless validated by experimental data. The domain of this non-unique solution is determined in terms of the ground-state Poisson’s ratio and the state of stretch and stress. The analyses we perform are essential to enable the understanding of the characteristics of the standard, compressible, isotropic, neo-Hookean model used in ABAQUS, ANSYS and COMSOL. In addition, our results provide a framework for the parameter-fitting procedure needed to characterize this standard, compressible, isotropic neo-Hookean model in terms of experimental data.
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Abstract Traumatic brain injury (TBI), particularly from explosive blasts, is a major cause of casualties in modern military conflicts. Computational models are an important tool in understanding the underlying biomechanics of TBI but are highly dependent on the mechanical properties of soft tissue to produce accurate results. Reported material properties of brain tissue can vary by several orders of magnitude between studies, and no published set of material parameters exists for porcine brain tissue at strain rates relevant to blast. In this work, brain tissue from the brainstem, cerebellum, and cerebrum of freshly euthanized adolescent male Göttingen minipigs was tested in simple shear and unconfined compression at strain rates ranging from quasi-static (QS) to 300 s−1. Brain tissue showed significant strain rate stiffening in both shear and compression. Minimal differences were seen between different regions of the brain. Both hyperelastic and hyper-viscoelastic constitutive models were fit to experimental stress, considering data from either a single loading mode (unidirectional) or two loading modes together (bidirectional). The unidirectional hyper-viscoelastic models with an Ogden hyperelastic representation and a one-term Prony series best captured the response of brain tissue in all regions and rates. The bidirectional models were generally able to capture the response of the tissue in high-rate shear and all compression modes, but not the QS shear. Our constitutive models describe the first set of material parameters for porcine brain tissue relevant to loading modes and rates seen in blast injury.more » « less
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Calibration and validation of constitutive models and numerical modeling techniques used in analysis of soil liquefaction and its effects are often based on extensive comparisons with the results of element tests and centrifuge experiments. While good quality experimental data are available to understand and quantify the stress-strain-strength response of liquefiable soils in monotonic and cyclic drained/undrained element (triaxial and direct simple shear) tests, the results of these experiments are often less repeatable when the soil approaches liquefaction state and relatively large deviatoric strains suddenly develop within a few cycles of loading. The main source of these less repeatable patterns of soil behavior appears to be instability rather than the attainment of a state of material failure. The goal of this paper is to investigate the role of instability on the stress-strain response of liquefiable soils by using a critical state sand plasticity model that is enriched with an internal length scale representing the potential shear bands that may develop during monotonic or cyclic loading conditions. Through a series of numerical simulations, it is shown that the global stress-strain response measured in the element tests is a good approximation of the soil constitutive response before an unstable condition such as shear banding or liquefaction develops in the soil specimen.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1115/1.4049168
