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Abstract This article introduces a computational design framework for obtaining three‐dimensional (3D) periodic elastoplastic architected materials with enhanced performance, subject to uniaxial or shear strain. A nonlinear finite element model accounting for plastic deformation is developed, where a Lagrange multiplier approach is utilized to impose periodicity constraints. The analysis assumes that the material obeys a von Mises plasticity model with linear isotropic hardening. The finite element model is combined with a corresponding path‐dependent adjoint sensitivity formulation, which is derived analytically. The optimization problem is parametrized using the solid isotropic material penalization method. Designs are optimized for either end compliance or toughness for a given prescribed displacement. Such a framework results in producing materials with enhanced performance through much better utilization of an elastoplastic material. Several 3D examples are used to demonstrate the effectiveness of the mathematical framework.
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A double-yield-surface plasticity theory for transversely isotropic rocks
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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- Award ID(s):
- 1914780
- PAR ID:
- 10336145
- Date Published:
- Journal Name:
- Acta Geotechnica
- ISSN:
- 1861-1125
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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null (Ed.)SUMMARY The yield surfaces of rocks keep evolving beyond the initial yield stress owing to the damage accumulation and porosity change during brittle deformation. Using a poroelastic damage rheology model, we demonstrate that the measure of coupling between the yield surface change and accumulated damage is correlated with strain localization and the Kaiser effect. Constant or minor yield surface change is associated with strong strain localization, as seen in low-porosity crystalline rocks. In contrast, strong coupling between damage growth and the yield surface leads to distributed deformation, as seen in high-porosity rocks. Assuming that during brittle deformation damage occurs primarily in the form of microcracks, we propose that the measured acoustic emission (AE) in rock samples correlates with the damage accumulation. This allows quantifying the Kaiser effect under cyclic loading by matching between the onset of AE and the onset of damage growth. The ratio of the stress at the onset of AE to the peak stress of the previous loading cycle, or Felicity Ratio (FR), is calculated for different model parameters. The results of the simulation show that FR gradually decreases in the case of weak coupling between yield surface and damage growth. For a strong damage-related coupling promoting significant yield surface change, the FR remains close to one and decreases only towards the failure. The model predicts that a steep decrease in FR is associated with a transition between distributed and localized modes of failure. By linking the evolving yield surface to strain localization patterns and the Kaiser effect, the poroelastic damage rheology model provides a new quantitative tool to study failure modes of brittle rocks.more » « less
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Deshpande, Vikram (Ed.)The yield surface of a material is a criterion at which macroscopic plastic deformation begins. For crystalline solids, plastic deformation occurs through the motion of dislocations, which can be captured by discrete dislocation dynamics (DDD) simulations. In this paper, we predict the yield surfaces and strain-hardening behaviors using DDD simulations and a geometric manifold learning approach. The yield surfaces in the three-dimensional space of plane stress are constructed for single-crystal copper subjected to uniaxial loading along the [100] and [110] directions, respectively. With increasing plastic deformation under loading, the yield surface expands nearly uniformly in all directions, corresponding to isotropic hardening. In contrast, under [110] loading, latent hardening is observed, where the yield surface remains nearly unchanged in the orientations in the vicinity of the loading direction itself but expands in other directions, resulting in an asymmetric shape. This difference in hardening behaviors is attributed to the different dislocation multiplication behaviors on various slip systems under the two loading conditions.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11440-022-01605-6
