Model-free data-driven computational mechanics, first proposed by Kirchdoerfer and Ortiz, replaces phenomenological models with numerical simulations based on sample data sets in strain-stress space. Recent literature extended the approach to inelastic problems using structured data sets, tangent space information, and transition rules. From an application perspective, the coverage of qualified data states and calculating the corresponding tangent space is crucial. In this respect, material symmetry significantly helps to reduce the amount of necessary data. This study applies the data-driven paradigm to elasto-plasticity with isotropic hardening. We formulate our approach employing Haigh-Westergaard coordinates, providing information on the underlying material yield surface. Based on this, we use a combined tension-torsion test to cover the knowledge of the yield surface and a single tensile test to calculate the corresponding tangent space. The resulting data-driven method minimizes the distance over the Haigh-Westergaard space augmented with directions in the tangent space subject to compatibility and equilibrium constraints.

翻译：无模型数据驱动计算力学方法由Kirchdoerfer和Ortiz首次提出，以应变-应力空间中的样本数据集替代唯象模型进行数值模拟。近期文献通过使用结构化数据集、切空间信息及转换规则将该方法拓展至非弹性问题。从应用角度而言，合格数据状态的覆盖范围及对应切空间的计算至关重要。在此方面，材料对称性显著有助于减少所需数据量。本研究将数据驱动范式应用于具有各向同性硬化的弹塑性问题。我们采用Haigh-Westergaard坐标构建方法，提供基础材料屈服面的信息。基于此，通过组合拉扭试验覆盖屈服面知识，并利用单轴拉伸试验计算对应切空间。所提数据驱动方法在满足相容性及平衡约束条件下，最小化增强切方向信息的Haigh-Westergaard空间中的距离。