The failure behavior of geological materials depends heavily on confining pressure and strain rate. Under a relatively low confining pressure, these materials tend to fail by brittle, localized ...fracture, but as the confining pressure increases, they show a growing propensity for ductile, diffuse failure accompanying plastic flow. Furthermore, the rate of deformation often exerts control on the brittleness. Here we develop a theoretical and computational modeling framework that encapsulates this variety of failure modes and their brittle–ductile transition. The framework couples a pressure-sensitive plasticity model with a phase-field approach to fracture which can simulate complex fracture propagation without tracking its geometry. We derive a phase-field formulation for fracture in elastic–plastic materials as a balance law of microforce, in a new way that honors the dissipative nature of the fracturing processes. For physically meaningful and numerically robust incorporation of plasticity into the phase-field model, we introduce several new ideas including the use of phase-field effective stress for plasticity, and the dilative/compactive split and rate-dependent storage of plastic work. We construct a particular class of the framework by employing a Drucker–Prager plasticity model with a compression cap, and demonstrate that the proposed framework can capture brittle fracture, ductile flow, and their transition due to confining pressure and strain rate.
For material modeling and discovery, synthetic microstructures play a critical role as digital twins. They provide stochastic samples upon which direct numerical simulations can be conducted to ...populate material databases. A large ensemble of simulation data on synthetic microstructures may provide supplemental data to inform and refine macroscopic material models, which might not be feasible from physical experiments alone. However, synthesizing realistic microstructures with realistic microstructural attributes is highly challenging. Thus, it is often oversimplified via rough approximations that may yield an inaccurate representation of the physical world. Here, we propose a novel deep learning method that can synthesize realistic three-dimensional microstructures with controlled structural properties using the combination of generative adversarial networks (GAN) and actor-critic (AC) reinforcement learning. The GAN-AC combination enables the generation of microstructures that not only resemble the appearances of real specimens but also yield user-defined physical quantities of interest (QoI). Our validation experiments confirm that the properties of synthetic microstructures generated by the GAN-AC framework are within a 5% error margin with respect to the target values. The scientific contribution of this paper resides in the novel design of the GAN-AC microstructure generator and the mathematical and algorithmic foundations therein. The proposed method will have a broad and substantive impact on the materials community by providing lenses for analyzing structure-property-performance linkages and for implementing the notion of 'materials-by-design'.
The loading of a granular material induces anisotropies of the particle arrangement (fabric) and of the material’s strength, incremental stiffness, and permeability. Thirteen measures of fabric ...anisotropy are developed, which are arranged in four categories: as preferred orientations of the particle bodies, the particle surfaces, the contact normals, and the void space. Anisotropy of the voids is described through image analysis and with Minkowski tensors. The thirteen measures of anisotropy change during loading, as determined with three-dimensional discrete element simulations of biaxial plane strain compression with constant mean stress. Assemblies with four different particle shapes were simulated. The measures of contact orientation are the most responsive to loading, and they change greatly at small strains, whereas the other measures lag the loading process and continue to change beyond the state of peak stress and even after the deviatoric stress has nearly reached a steady state. The paper implements a methodology for characterizing the incremental stiffness of a granular assembly during biaxial loading, with orthotropic loading increments that preserve the principal axes of the fabric and stiffness tensors. The linear part of the hypoplastic tangential stiffness is monitored with oedometric loading increments. This stiffness increases in the direction of the initial compressive loading but decreases in the direction of extension. Anisotropy of this stiffness is closely correlated with a particular measure of the contact fabric. Permeabilities are measured in three directions with lattice Boltzmann methods at various stages of loading and for assemblies with four particle shapes. Effective permeability is negatively correlated with the directional mean free path and is positively correlated with pore width, indicating that the anisotropy of effective permeability induced by loading is produced by changes in the directional hydraulic radius.
We introduce a mathematical framework designed to enable a simple image-to-simulation workflow for solids of complex geometries in the geometrically nonlinear regime. While the material point method ...is used to circumvent the mesh distortion issues commonly exhibited in Lagrangian meshes, a shifted domain technique originated from Main and Scovazzi (J Comput Phys 372:972–995,
2018
) is used to represent the boundary conditions implicitly via a level set or signed distance function. Consequently, this method completely bypasses the need to generate high-quality conformal mesh to represent complex geometries and therefore allows modelers to select the space of the interpolation function without the constraints due to the geometric need. This important simplification enables us to simulate deformation of complex geometries inferred from voxel images. Verification examples on deformable body subjected to finite rotation have shown that the new shifted domain material point method is able to generate frame-indifferent results. Meanwhile, simulations using micro-CT images of a Hostun sand have demonstrated that this method is able to reproduce the quasi-brittle damage mechanisms of single grain without the excessively concentrated nodes commonly displayed in conformal meshes that represent 3D objects with local fine details.
This paper presents a computational framework that generates ensemble predictive mechanics models with uncertainty quantification (UQ). We first develop a causal discovery algorithm to infer causal ...relations among time-history data measured during each representative volume element (RVE) simulation through a directed acyclic graph. With multiple plausible sets of causal relationships estimated from multiple RVE simulations, the predictions are propagated in the derived causal graph while using a deep neural network equipped with dropout layers as a Bayesian approximation for UQ. We select two representative numerical examples (traction-separation laws for frictional interfaces, elastoplasticity models for granular assembles) to examine the accuracy and robustness of the proposed causal discovery method for the common material law predictions in civil engineering applications.
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The triggering and spreading of volumetric waves in soils, namely pressure (P) and shear (S) waves, developing from a point source of a dynamic load, are analyzed. Wave polarization and shear wave ...splitting are innovatively reproduced via a three-dimensional Finite Element research code upgraded to account for fast dynamic regimes in fully saturated porous media. The mathematical–numerical model adopts a u-v-p formulation enhanced by introducing Taylor–Hood mixed finite elements and the stability features of the solution are considered by analyzing different implemented time integration strategies. Particularly, the phenomena have been studied and reconstructed by numerically generating different types of medium anisotropy accounting for (i) an anisotropic solid skeleton, (ii) an anisotropic permeability tensor, and (iii) a Biot’s effective stress coefficient tensor. Additionally, deviatoric-volumetric coupling effects have been emphasized by specifically modifying the structural anisotropy. A series of analyses are conducted to validate the model and prove the effectiveness of the results, from the directionality of polarized vibrations, the anisotropy-induced splitting, up to the spreading of surface waves.
We present a reduced-dimensional proper orthogonal decomposition (POD) solver to accelerate discrete element method (DEM) simulations of the granular mixing problem. We employ the method of snapshots ...to create a low-dimensional solution space from previous DEM simulations. By reducing the dimensionality of the problem, we accelerate the calculations of the incremental solution with fewer degrees of freedom (DOF), while enabling a larger stable time step due to the filtering of low-energy mode. We analyze two feasible strategies to generate the reduced-dimensional basis, one generating by finding the orthogonal basis from the global snapshots captured at the same location in the parametric domains; another one employing the known POD bases from the closest known cases. Our results show that, when POD bases are generated via the local strategy, the reduced-order model is a more efficient alternative to the full-scale simulations for extrapolating behaviors in the parametric domain. Numerical examples of granular mixing problems are presented to demonstrate the efficiency and accuracy of the proposed approach.
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