Data driven modeling of plastic deformation

Abstract In this paper the application of machine learning techniques for the development of constitutive material models is being investigated. A flow stress model, for strain rates ranging from 10 −4 to 10 12 (quasi-static to highly dynamic), and temperatures ranging from room temperature to over 1000 K, is obtained by beginning directly with experimental stress–strain data for Copper. An incrementally objective and fully implicit time integration scheme is employed to integrate the hypo-elastic constitutive model, which is then implemented into a finite element code for evaluation. Accuracy and performance of the flow stress models derived from symbolic regression are assessed by comparison to Taylor anvil impact data. The results obtained with the free-form constitutive material model are compared to well-established strength models such as the Preston–Tonks–Wallace (PTW) model and the Mechanical Threshold Stress (MTS) model. Preliminary results show candidate free-form models comparing well with data in regions of stress–strain space with sufficient experimental data, pointing to a potential means for both rapid prototyping in future model development, as well as the use of machine learning in capturing more data as a guide for more advanced model development.

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