In this paper, a multiscale computational formulation is developed for modeling two- and three-dimensional gradient elasticity behaviors of heterogeneous structures. To capture the microscopic properties at the macros...
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In this paper, a multiscale computational formulation is developed for modeling two- and three-dimensional gradient elasticity behaviors of heterogeneous structures. To capture the microscopic properties at the macroscopic level effectively, a numerical multiscale interpolation function of coarse element is constructed by employing the oversampling element technique based on the staggered gradient elasticity scheme. By virtue of these functions, the equivalent quantities of the coarse element could be obtained easily, resulting in that the material microscopic characteristics are reflected to the macroscopic scale. Consequently, the displacement field of the original boundary value problem could be calculated at the macroscopic level, and the corresponding microscopic gradient-enriched solutions could also be evaluated by adopting the downscaling computation on the sub-grids of each coarse element domain, which will reduce the computational cost significantly. Furthermore, several representative numerical experiments are performed to demonstrate the validity and efficiency of the proposed multiscale formulation.
By combining the Multiscale Scale Boundary Finite Element Method (MsSBFEM) and the Temporally Piecewise Adaptive Algorithm (TPAA), a new numerical model is presented to reduce the solution scale of the twodimensional ...
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By combining the Multiscale Scale Boundary Finite Element Method (MsSBFEM) and the Temporally Piecewise Adaptive Algorithm (TPAA), a new numerical model is presented to reduce the solution scale of the twodimensional heterogeneous viscoelastic problems. Utilizing TPAA, a spatially and temporally related problem is transformed into a series of recursive spatial problems, which are solved by MsSBFEM. The solution scale can be effectively reduced by recourse of a bridge between small-scale and large-scale via Scaled Boundary Finite Element Method (SBFEM) based numerical base functions, and the solution accuracy can be improved only by increasing nodes of coarse elements without increasing any new node inside. By virtue of singular, polygon and Quadtree elements, SBFEM renders the proposed algorithm more efficient and convenient to tackle with the stress singularity, and to generate SBFE mesh. TPAA provides a measure to secure the temporal computational accuracy via an adaptive process when the step size varies. numerical examples are provided to elucidate the effectiveness of proposed approaches, and satisfactory results are achieved at both the large and small scales.
Extended multiscale finite element method (EMsFEM) has been proved to be an efficient method for the mechanical analysis of heterogeneous materials. The key factor for efficiency and accuracy of EMsFEM is the numerica...
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Extended multiscale finite element method (EMsFEM) has been proved to be an efficient method for the mechanical analysis of heterogeneous materials. The key factor for efficiency and accuracy of EMsFEM is the numerical base functions (NBFs). The paper summarizes the general method for constructing NBFs and proposes a generalized isoparametric interpolation based on the rigid displacement properties (RDPs) of NBFs. We prove that the NBFs constructed by linear, periodic and rotational angle boundary conditions satisfy the RDPs, which is independent with the shape and material properties of unit cells. The properties of NBFs for oversampling technique are also comprehensively discussed. The algorithm complexity is discussed in theoretical and numerical aspects, which concludes that the computation quantity of EMsFEM is much smaller than the direct solutions. The algorithm is validated by linear analysis of the materials with random impurities and holes and the efficiency is improved further by parallel computing.
This paper presents a multiscale finite element method with the embedded strong discontinuity model for the strain localization analysis of homogeneous and heterogeneous saturated porous media. In the proposed method,...
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This paper presents a multiscale finite element method with the embedded strong discontinuity model for the strain localization analysis of homogeneous and heterogeneous saturated porous media. In the proposed method, the strong discontinuities in both displacement and fluid flux fields are considered. For the localized fine element, the mathematical description and discrete formulation are built based on the so-called strong discontinuity approach. For the localized unit cell, numerical base functions are constructed based on a newly developed enhanced coarse element technique, that is, additional coarse nodes are dynamically added as the shear band propagating. Through the enhanced coarse element technique, the multiscale finite element method can well reflect the softening behavior at the post-localization stage. Furthermore, the microscopic displacement and pore pressure are obtained with the solution decomposition technique. In addition, a non-standard return mapping algorithm is given to update the displacement jumps. Finally, through three representative numerical tests comparing with the results of the embedded finite element method with fine meshes, the high efficiency and accuracy of the proposed method are demonstrated in both material homogeneous and heterogeneous cases. Copyright (C) 2017 John Wiley & Sons, Ltd.
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