Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the data set is minimized, subject to equilibrium and compatibility constraints. Although this method operates well for non-linear elastic problems, there are challenges dealing with history-dependent materials, since one and the same point in stress-strain space might correspond to different material behaviour.In recent literature, this issue has been treated by including local histories into the data set. However, there is still the necessity to include models for the evolution of specific internal variables. Thus, a mixed formulation of classical and data-driven modeling is obtained. In the presented approach, the data set is augmented with directions in the tangent space of points in stress-strain space. Moreover, the data set is divided into subsets corresponding to different material behaviour. Based on this classification, transition rules map the modeling points to the various subsets. The approach will be applied to non-linear elasticity and elasto-plasticity with isotropic hardening.

翻译：以无模型数据驱动的计算力根据压力-压力空间有代表性样本的数据集进行数字模拟,取代苯球构成功能。根据平衡和兼容性的限制,将压力和压力配对与数据集的距离最小化。虽然这种方法在非线性弹性问题方面运作良好,但在历史依赖材料方面存在着挑战,因为压力-压力-压力空间的同一点可能与不同的物质行为相对应。在最近的文献中,这一问题是通过将当地历史纳入数据集来处理的。然而,仍然有必要将特定内部变量的演变模型纳入其中。因此,获得经典和数据驱动模型的混合配方。在现行方法中,数据集以压力-压力-压力-压力空间点相近空间的方向扩大。此外,数据集被分为与不同物质行为相对应的子集。根据这一分类,过渡规则将模型绘制到各种子集中。该方法将适用于非线性弹性和偏差的等离硬化。