共查询到20条相似文献，搜索用时 0 毫秒
1.
J. Knap C. Spear K. Leiter R. Becker D. Powell 《International journal for numerical methods in engineering》2016,108(13):1649-1666
A computational framework for scale‐bridging in multi‐scale simulations is presented. The framework enables seamless combination of at‐scale models into highly dynamic hierarchies to build a multi‐scale model. Its centerpiece is formulated as a standalone module capable of fully asynchronous operation. We assess its feasibility and performance for a two‐scale model applied to two challenging test problems from impact physics. We find that the computational cost associated with using the framework may, as expected, become substantial. However, the framework has the ability of effortlessly combining at‐scale models to render complex multi‐scale models. The main source of the computational inefficiency of the framework is related to poor load balancing of the lower‐scale model evaluation We demonstrate that the load balancing can be efficiently addressed by recourse to conventional load‐balancing strategies. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
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M. Gonzalez B. Schmidt M. Ortiz 《International journal for numerical methods in engineering》2010,82(2):205-241
We present a class of integration schemes for Lagrangian mechanics, referred to as energy‐stepping integrators, that are momentum and energy conserving, symplectic and convergent. In order to achieve these properties we replace the original potential energy by a piecewise constant, or terraced approximation at steps of uniform height. By taking steps of diminishing height, an approximating sequence of energies is generated. The trajectories of the resulting approximating Lagrangians can be characterized explicitly and consist of intervals of piecewise rectilinear motion. We show that the energy‐stepping trajectories are symplectic, exactly conserve all the momentum maps of the original system and, subject to a transversality condition, converge to trajectories of the original system when the energy step is decreased to zero. These properties, the excellent long‐term behavior of energy‐stepping and its automatic time‐step selection property, are born out by selected examples of application, including the dynamics of a frozen Argon cluster, the spinning of an elastic cube and the collision of two elastic spheres. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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M. Gonzalez B. Schmidt M. Ortiz 《International journal for numerical methods in engineering》2010,84(12):1407-1450
We formulate an integration scheme for Lagrangian mechanics, referred to as the force‐stepping scheme, which is symplectic, energy conserving, time‐reversible, and convergent with automatic selection of the time‐step size. The scheme also conserves approximately all the momentum maps associated with the symmetries of the system. The exact conservation of momentum maps may additionally be achieved by recourse to the Lagrangian reduction. The force‐stepping scheme is obtained by replacing the potential energy by a piecewise affine approximation over a simplicial grid or regular triangulation. By taking triangulations of diminishing size, an approximating sequence of energies is generated. The trajectories of the resulting approximate Lagrangians can be characterized explicitly and consist of piecewise parabolic motion, or free fall. Selected numerical tests demonstrate the excellent long‐term behavior of force‐stepping, its automatic time‐step selection property, and the ease with which it deals with constraints, including contact problems. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Yong‐Ping Feng Jun‐Zhi Cui 《International journal for numerical methods in engineering》2004,60(11):1879-1910
The two‐scale asymptotic (TSA) expressions of the increment of temperature and the displacement for the structure of composite materials with small periodic configuration under coupled thermoelasticity condition are derived formally in this paper, especially, the two‐scale coupled relation between the increment of temperature and the displacements are set up. Then the approximate solutions and their error estimations are presented, and the multi‐scale finite element algorithm corresponding to TSA is described. Finally, simple numerical results evaluated by multi‐scale FE computation are shown. They demonstrate that the basic configuration and the increment of temperature strongly influence upon local strains and local stresses inside basic cell. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Kenjiro Terada Mao Kurumatani 《International journal for numerical methods in engineering》2010,83(4):426-451
In this paper, we introduce a two‐scale diffusion–deformation coupled model that represents the aging material deterioration of two‐phase materials involving micro‐crack propagations. The mathematical homogenization method is applied to relate the micro‐ and macroscopic field variables, and a weak coupling solution method is employed to solve the two‐way coupling phenomena between the diffusion of scalar fields and the deformation of quasi‐brittle solids. The macroscopic mechanical behavior represented by the derived two‐scale two‐way coupled model reveals material nonlinearity due to micro‐scale cracking induced by the scalar‐field‐induced deformation, which can be simulated by the finite cover method. After verifying the fundamental validity of the proposed model and the analysis method, we perform a simple numerical example to demonstrate their ability to predict aging material deterioration. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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Hans Janssen 《International journal for numerical methods in engineering》2010,81(11):1455-1474
Efficient simulation of unsaturated moisture flow in porous media is of great importance in many engineering fields. The highly non‐linear character of unsaturated flow typically gives sharp moving moisture fronts during wetting and drying of materials with strong local moisture permeability and capacity variations as result. It is shown that these strong variations conflict with the common preference for low‐order numerical integration in finite element simulations of unsaturated moisture flow: inaccurate numerical integration leads to errors that are often far more important than errors from inappropriate discretization. In response, this article develops adaptive integration, based on nested Kronrod–Patterson–Gauss integration schemes: basically, the integration order is adapted to the locally observed grade of non‐linearity. Adaptive integration is developed based on a standard infiltration problem, and it is demonstrated that serious reductions in the numbers of required integration points and discretization nodes can be obtained, thus significantly increasing computational efficiency. The multi‐dimensional applicability is exemplified with two‐dimensional wetting and drying applications. While developed for finite element unsaturated moisture transfer simulation, adaptive integration is similarly applicable for other non‐linear problems and other discretization methods, and whereas perhaps outperformed by mesh‐adaptive techniques, adaptive integration requires much less implementation and computation. Both techniques can moreover be easily combined. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
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Hui Wang Haitao Liu Fan He Wenwen Chen Xu Zhang Mengqian Zhao Li Wang Jianhua Qin 《Advanced Materials Technologies》2020,5(6)
Hydrogel capsules are widely applied in materials science, pharmaceutical science, and tissue engineering due to their tunable nature, defined core–shell architecture, and proper biocompatibility. Specially, multi‐core capsules are highly functional carriers with notable advantages for co‐encapsulation of diverse incompatible components without cross‐contamination. However, current approaches for generating such capsules are limited by using gas/oil‐water‐oil systems, leading to poor biocompatibility and functions due to the gas/oil cores. Herein, a simple and new approach is proposed for flexible fabrication of multi‐aqueous core hydrogel capsules (MACHC) using microfluidic aqueous two‐phase system (µATPS). In this system, a flow‐focusing microfluidic device is designed to create a stable laminar flow with two immiscible liquids composed of polyethylene glycol and dextran, which is sheared by oil phase to further effectively produce MACHC. The volume and components of each core can be well tailored by precisely adjusting the distinct flows, while the number of cores is determined by the orifice design of microfluidic chip. The MACHC are successfully used to co‐encapsulate heterogeneous hepatic and endothelial cells, indicating good biocompatibility and multi‐functionality of the multi‐core carriers. The proposed µATPS‐based approach is stable and convenient, holding promise for generation of multi‐responsive materials, tissue engineering, and co‐delivery of diverse drugs. 相似文献
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Dmitri Kavetski Philip Binning Scott W. Sloan 《International journal for numerical methods in engineering》2004,60(12):2031-2043
The consistency and stability of a Thomas–Gladwell family of multistage time‐stepping schemes for the solution of first‐order non‐linear differential equations are examined. It is shown that the consistency and stability conditions are less stringent than those derived for second‐order governing equations. Second‐order accuracy is achieved by approximating the solution and its derivative at the same location within the time step. Useful flexibility is available in the evaluation of the non‐linear coefficients and is exploited to develop a new non‐iterative modification of the Thomas–Gladwell method that is second‐order accurate and unconditionally stable. A case study from applied hydrogeology using the non‐linear Richards equation confirms the analytic convergence assessment and demonstrates the efficiency of the non‐iterative formulation. Copyright © 2004 John Wiley & Sons, Ltd. 相似文献
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Dmitri Kavetski Philip Binning Scott W. Sloan 《International journal for numerical methods in engineering》2002,53(6):1301-1322
An automatic time stepping scheme with embedded error control is developed and applied to the moisture‐based Richards equation. The algorithm is based on the first‐order backward Euler scheme, and uses a numerical estimate of the local truncation error and an efficient time step selector to control the temporal accuracy of the integration. Local extrapolation, equivalent to the use of an unconditionally stable Thomas–Gladwell algorithm, achieves second‐order temporal accuracy at minimal additional costs. The time stepping algorithm also provides accurate initial estimates for the iterative non‐linear solver. Numerical tests confirm the ability of the scheme to automatically optimize the time step size to match a user prescribed temporal error tolerance. An important merit of the proposed method is its conceptual and computational simplicity. It can be directly incorporated into existing or new software based on the backward Euler scheme (currently prevalent in subsurface hydrologic modelling), and markedly improves their performance compared with simple fixed or heuristic time step selection. The generality of the approach also makes possible its use for solving PDEs in other engineering applications, where strong non‐linearity, stability or implementation considerations favour a simple and robust low‐order method, or where there is a legacy of backward Euler codes in current use. Copyright © 2001 John Wiley & Sons, Ltd. 相似文献
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Fei Han Junzhi Cui Yan Yu 《International journal for numerical methods in engineering》2010,84(8):972-988
A class of random composite materials with statistically inhomogeneous microstructure, for example, functionally graded materials is considered in this paper. The microstructures inside a component are gradually varying in the statistical sense. In view of this particularity, a novel statistical second‐order two‐scale (SSOTS) method is presented to predict the mechanical properties, including stiffness, and elastic limit. To develop this method, the microstructures of statistically homogeneous, and inhomogeneous materials are represented. In addition the SSOTS formulas are derived based on normalized cell depending on the position variables by a constructing way, and the algorithm procedure is described. The mechanical properties of the different inhomogeneous materials are evaluated. The numerical results are compared with the experimental findings. It shows that the SSTOS method is effective. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献
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C. T. Wu Wei Hu G. R. Liu 《International journal for numerical methods in engineering》2014,100(5):374-398
This paper presents a bubble‐enhanced smoothed finite element formulation for the analysis of volume‐constrained problems in two‐dimensional linear elasticity. The new formulation is derived based on the variational multi‐scale approach in which unequal order displacement‐pressure pairs are used for the mixed finite element approximation and hierarchical bubble function is selected for the fine‐scale displacement approximation. An area‐weighted averaging scheme is employed for the two‐scale smoothed strain calculation under the framework of edge‐based smoothed FEM. The smoothed fine‐scale solution is shown to naturally contain the stress field jump of the smoothed coarse‐scale solution across the boundary of edge‐based smoothing domain and thus provides the possibility to stabilize the global solution for volume‐constrained problems. A global monolithic solution strategy is employed, and the fine‐scale solution is solved without the consideration of approximating the strong form of the fine‐scale equation. Several numerical examples are analyzed to demonstrate the accuracy of the present formulation. Copyright © 2014 John Wiley & Sons, Ltd. 相似文献
12.
Effects of Multi‐Scale Patterning on the Run‐In Behavior of Steel–Alumina Pairings under Lubricated Conditions 
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下载免费PDF全文 Philipp G. Grützmacher Andreas Rosenkranz Adam Szurdak Carsten Gachot Gerhard Hirt Frank Mücklich 《Advanced Engineering Materials》2018,20(1)
In nature, many examples of multi‐scale surfaces with outstanding tribological properties such as reduced friction and wear under dry friction and lubricated conditions can be found. To determine whether multi‐scale surfaces positively affect the frictional and wear performance, tests are performed on a ball‐on‐disk tribometer under lubricated conditions using an additive‐free poly‐alpha‐olefine oil under a contact pressure of around 1.29 GPa. For this purpose, stainless steel specimens (AISI 304) are modified by micro‐coining (hemispherical structures with a structural depth of either 50 or 95 μm) and subsequently by direct laser interference patterning (cross‐like pattern with 9 μm periodicity) to create a multi‐scale pattern. The comparison of different sample states (polished reference, laser‐patterned, micro‐coined, and multi‐scale) shows a clear influence of the fabrication technique. In terms of the multi‐scale structures, the structural depth of the coarser micro‐coining plays an important role. In case of lower coining depths (50 μm), the multi‐scale specimens show an increased coefficient of friction compared to the purely micro‐coined surfaces, whereas larger coining depths (95 μm) result in stable and lower friction values for the multi‐scale patterns. 相似文献
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J. Knap N. R. Barton R. D. Hornung A. Arsenlis R. Becker D. R. Jefferson 《International journal for numerical methods in engineering》2008,76(4):572-600
We propose an adaptive sampling methodology for hierarchical multi‐scale simulation. The method utilizes a moving kriging interpolation to significantly reduce the number of evaluations of finer‐scale response functions to provide essential constitutive information to a coarser‐scale simulation model. The underlying interpolation scheme is unstructured and adaptive to handle the transient nature of a simulation. To handle the dynamic construction and searching of a potentially large set of finer‐scale response data, we employ a dynamic metric‐tree database. We study the performance of our adaptive sampling methodology for a two‐level multi‐scale model involving a coarse‐scale finite element simulation and a fine‐scale crystal plasticity‐based constitutive law. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
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Abstract A decentralized stabilization problem for a large‐scale system composed of a number of subsystems is investigated. Using Lyapunov stability and the bounds of the solution of the Lyapunov equation, we derive two main results. The first result (Theorem 1) requires checking the negativity of a matrix containing two free parameters to test the decentralized stabilizability of the whole system. The second result (Theorem 2) determines the ranges of two free parameters to satisfy Theorem 1 such that the decentralized local state feedbacks guarantee the whole large‐scale system is stabilized. The matching condition for each subsystem is not necessary in this paper. The results are also summarized using a flow chart which represents the algorithm for decentralized stabilization. 相似文献
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Abstract A design method to achieve robust stability and performance criteria for discrete two‐time‐scale systems controlled by low‐order observer‐based compensators is proposed. Sufficient conditions for stability and performance robustness are established by an easy extension of the small gain theorem. The theoretical analysis is illustrated by a numerical example. 相似文献
18.
Qianbin Wang Bin Su Huan Liu Lei Jiang 《Advanced materials (Deerfield Beach, Fla.)》2014,26(28):4889-4894
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Sangmin Lee Veera Sundararaghavan 《International journal for numerical methods in engineering》2011,85(6):784-804
Problems involving reaction and species diffusion involve field and flux jumps at a moving reaction front. In multi‐scale problems such as carbon fiber composite oxidation, these effects need to be tracked at the microscopic scale of individual carbon fibers. A multi‐scale model is derived in this paper for predicting species distribution in such problems using a fully coupled multi‐scale homogenization approach. The homogenized fluxes from the micro‐scale are derived using Hill's macro‐homogeneity condition accounting for both flux jumps and species density field jumps at the reacting interface in the micro‐scale unit cell. At the macro‐scale, the competition between the transport of reacting species (oxygen) and the reaction product (carbon dioxide) is modeled using homogenized mass conservation equations. The moving reaction front in carbon fibers at the micro‐scale is tracked using level set method and an adaptive meshing strategy. The macroscopic weight loss of the composite when exposed to oxygen is simulated as a function of time using a coupled finite element methodology at various locations in a validated macroscopic model. Copyright © 2010 John Wiley & Sons, Ltd. 相似文献