Data-Driven Problems in Elasticity
Data-Driven Problems in Elasticity
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DOI：
10.1007/s00205-017-1214-0
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发表时间：
2018-07-01
影响因子：
2.5
通讯作者：
Ortiz, M.
中科院分区：
文献类型：
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作者：
Conti, S.;Mueller, S.;Ortiz, M.
我们考虑弹性中的一类新问题，称为数据驱动问题，定义在应变-应力场对空间或相空间上。该问题包括最小化给定材料数据集与平衡状态下相容应变场和应力场子空间之间的距离。我们发现，在线性弹性情况下，经典解是恢复的。我们确定了与近似材料数据集序列相对应的数据驱动解决方案的收敛条件。对恒定材料数据集序列的专门化依次建立了适当的松弛概念。我们发现这种数据驱动框架中的松弛与经典的能量函数松弛有根本的不同。例如，我们表明，在数据驱动框架中，双稳态材料的松弛导致材料数据集不是图形。
We consider a new class of problems in elasticity, referred to as Data-Driven problems, defined on the space of strain-stress field pairs, or phase space. The problem consists of minimizing the distance between a given material data set and the subspace of compatible strain fields and stress fields in equilibrium. We find that the classical solutions are recovered in the case of linear elasticity. We identify conditions for convergence of Data-Driven solutions corresponding to sequences of approximating material data sets. Specialization to constant material data set sequences in turn establishes an appropriate notion of relaxation. We find that relaxation within this Data-Driven framework is fundamentally different from the classical relaxation of energy functions. For instance, we show that in the Data-Driven framework the relaxation of a bistable material leads to material data sets that are not graphs.