We present a dual-horizon peridynamics (DH-PD) formulation for fracture in granular and rock-like materials. In contrast to discrete crack methods such as XFEM, DH-PD does not require any ...representation of the crack surface and criteria to treat complex fracture patterns such as crack branching and coalescence. The crack path is the natural outcome of the simulation. In this manuscript, a new penalty method to model the contact for compressive fractures and constraining the penetration conditions is developed. The new method is applied to several benchmark problems in geomechanics including the four-point shear test, the indirect tensile (Brazilian) test of rock disks with one or multiple initial cracks. By using an appropriate damping coefficient, the quasi-static solution for rock failure is obtained when the dynamic formulation is used. A good agreement is obtained between the results given by DH-PD and those by the experiments.
•Novel dual-horizon peridynamics formulation•The method accounts for crack opening as well as crack closure.•The method is validated through several numerical examples.
Compressive-shear fracture is commonly observed in rock-like materials. However, this fracture type cannot be captured by current phase field models (PFMs), which have been proven an effective tool ...for modeling fracture initiation, propagation, coalescence, and branching in solids. The existing PFMs also cannot describe the influence of cohesion and internal friction angle on load–displacement curve during compression tests. Therefore, to develop a new phase field model that can simulate well compressive-shear fractures in rock-like materials, we construct a new driving force in the evolution equation of phase field. Strain spectral decomposition is applied and only the compressive part of the strain is used in the new driving force with consideration of the influence of cohesion and internal friction angle. For ease of implementation, a hybrid formulation is established for the phase field modeling. Then, we test the brittle compressive-shear fractures in uniaxial compression tests on intact rock-like specimens as well as those with a single or two parallel inclined flaws. All numerical results are in good agreement with the experimental observation, validating the feasibility and practicability of the proposed PFM for simulating brittle compressive-shear fractures.
•A new phase field model for brittle compressive-shear fracture in rock-like materials is proposed.•A new driving force is presented in the phase field modeling.•The influence of cohesion and internal friction angle can be accounted for.•Fracture coalescence and branching for multiple flaws/cracks can be captured.
We present a method for solving partial differential equations using artificial neural networks and an adaptive collocation strategy. In this procedure, a coarse grid of training points is used at ...the initial training stages, while more points are added at later stages based on the value of the residual at a larger set of evaluation points. This method increases the robustness of the neural network approximation and can result in significant computational savings, particularly when the solution is non-smooth. Numerical results are presented for benchmark problems for scalar-valued PDEs, namely Poisson and Helmholtz equations, as well as for an inverse acoustics problem.
Machine learning (ML) methods have shown powerful performance in different application. Nonetheless, designing ML models remains a challenge and requires further research as most procedures adopt a ...trial and error strategy. In this study, we present a methodology to optimize the architecture and the feature configurations of ML models considering a supervised learning process. The proposed approach employs genetic algorithm (GA)-based integer-valued optimization for two ML models, namely deep neural networks (DNN) and adaptive neuro-fuzzy inference system (ANFIS). The selected variables in the DNN optimization problems are the number of hidden layers, their number of neurons and their activation function, while the type and the number of membership functions are the design variables in the ANFIS optimization problem. The mean squared error (MSE) between the predictions and the target outputs is minimized as the optimization fitness function. The proposed scheme is validated through a case study of computational material design. We apply the method to predict the fracture energy of polymer/nanoparticles composites (PNCs) with a database gathered from the literature. The optimized DNN model shows superior prediction accuracy compared to the classical one-hidden layer network. Also, it outperforms ANFIS with significantly lower number of generations in GA. The proposed method can be easily extended to optimize similar architecture properties of ML models in various complex systems.
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Silicene, germanene and stanene likely to graphene are atomic thick material with interesting properties. We employed first-principles density functional theory (DFT) calculations to ...investigate and compare the interaction of Na or Li ions on these films. We first identified the most stable binding sites and their corresponding binding energies for a single Na or Li adatom on the considered membranes. Then we gradually increased the ions concentration until the full saturation of the surfaces is achieved. Our Bader charge analysis confirmed complete charge transfer between Li or Na ions with the studied 2D sheets. We then utilized nudged elastic band method to analyze and compare the energy barriers for Li or Na ions diffusions along the surface and through the films thicknesses. Our investigation findings can be useful for the potential application of silicene, germanene and stanene for Na or Li ion batteries.
In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep ...learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.
Borophene, the boron atom analogue to graphene, being atomic thick have been just recently experimentally fabricated. In this work, we employ first-principles density functional theory calculations ...to investigate the interaction of Ca, Mg, Na or Li atoms with single-layer and free-standing borophene. We first identified the most stable binding sites and their corresponding binding energies as well and then we gradually increased the ions concentration. Our calculations predict strong binding energies of around 4.03 eV, 2.09 eV, 2.92 eV and 3.28 eV between the borophene substrate and Ca, Mg, Na or Li ions, respectively. We found that the binding energy generally decreases by increasing the ions content. Using the Bader charge analysis, we evaluate the charge transfer between the adatoms and the borophene sheet. Our investigation proposes the borophene as a 2D material with a remarkably high capacity of around 800 mA h/g, 1960 mA h/g, 1380 mA h/g and 1720 mA h/g for Ca, Mg, Na or Li ions storage, respectively. This study can be useful for the possible application of borophene for the rechargeable ion batteries.
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•We studied the application of borophene for the rechargeable ion batteries.•Borophene presents a remarkably high capacity for Mg, Na or Li ions storage.•Ions diffusion on the borophene are fast with low energy barriers.
The fracture energy is a substantial material property that measures the ability of materials to resist crack growth. The reinforcement of the epoxy polymers by nanosize fillers improves ...significantly their toughness. The fracture mechanism of the produced polymeric nanocomposites is influenced by different parameters. This paper presents a methodology for stochastic modelling of the fracture in polymer/particle nanocomposites. For this purpose, we generated a 2D finite element model containing an epoxy matrix and rigid nanoparticles surrounded by an interphase zone. The crack propagation was modelled by the phantom node method. The stochastic model is based on six uncertain parameters: the volume fraction and the diameter of the nanoparticles, Young’s modulus and the maximum allowable principal stress of the epoxy matrix, the interphase zone thickness and its Young’s modulus. Considering the uncertainties in input parameters, a polynomial chaos expansion surrogate model is constructed followed by a sensitivity analysis. The variance in the fracture energy was mostly influenced by the maximum allowable principal stress and Young’s modulus of the epoxy matrix.
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