Data-driven computational mechanics
Data-driven computational mechanics
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DOI：
10.1016/j.cma.2016.02.001
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发表时间：
2016-06-01
影响因子：
7.2
通讯作者：
Ortiz, M.
中科院分区：
文献类型：
--
作者：
Kirchdoerfer, T.;Ortiz, M.
我们开发了一种新的计算范式，我们称之为数据驱动计算，根据这种计算直接从实验材料数据和相关的约束和守恒定律（如相容性和平衡）进行，从而完全绕过了传统计算的经验材料建模步骤。数据驱动的求解器试图从预先指定的数据集中为每个物质点分配最接近满足守恒定律的状态。等价地，数据驱动的求解器旨在找到最接近数据集的满足守恒定律的状态。由此产生的数据驱动的问题，从而包括在相空间中的数据集的距离函数的最小化受到守恒定律引入的约束。我们激励数据驱动的范例，并通过两个应用程序的例子，即，非线性三维桁架的静态平衡和线性弹性的数据驱动的求解器的性能进行调查。在这些测试中，数据驱动的求解器表现出良好的收敛性能，无论是相对于数据点的数量和相对于本地数据分配。数据驱动问题的可变结构也使其易于分析。我们表明，随着数据集越来越接近相空间中的经典物质定律，数据驱动的解决方案收敛到经典的解决方案。我们还说明了空间离散化的数据驱动的求解器的鲁棒性。特别是，我们表明，数据驱动的解决方案的有限元离散线弹性收敛联合相对于网格大小和近似的数据集。(C)2016爱思唯尔B.V.保留所有权利。
We develop a new computing paradigm, which we refer to as data-driven computing, according to which calculations are carried out directly from experimental material data and pertinent constraints and conservation laws, such as compatibility and equilibrium, thus bypassing the empirical material modeling step of conventional computing altogether. Data-driven solvers seek to assign to each material point the state from a prespecified data set that is closest to satisfying the conservation laws. Equivalently, data-driven solvers aim to find the state satisfying the conservation laws that is closest to the data set. The resulting data-driven problem thus consists of the minimization of a distance function to the data set in phase space subject to constraints introduced by the conservation laws. We motivate the data-driven paradigm and investigate the performance of data-driven solvers by means of two examples of application, namely, the static equilibrium of nonlinear three-dimensional trusses and linear elasticity. In these tests, the data-driven solvers exhibit good convergence properties both with respect to the number of data points and with regard to local data assignment. The variational structure of the data-driven problem also renders it amenable to analysis. We show that, as the data set approximates increasingly closely a classical material law in phase space, the data-driven solutions converge to the classical solution. We also illustrate the robustness of data-driven solvers with respect to spatial discretization. In particular, we show that the data-driven solutions of finite-element discretizations of linear elasticity converge jointly with respect to mesh size and approximation by the data set. (C) 2016 Elsevier B.V. All rights reserved.