Abstract
Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states. Most of its complexity arises from the nontrivial dependence of the yield loci on the complete strain history of a material and its microstructure. This motivated 3 ingenious simplifications that underpinned a century of developments in this field: 1) yield criteria describing yield loci location; 2) associative or nonassociative flow rules defining the direction of plastic flow; and 3) effective stress-strain laws consistent with the plastic work equivalence principle. However, 2 key complications arise from these simplifications. First, finding equations that describe these 3 assumptions for materials with complex microstructures is not trivial. Second, yield surface evolution needs to be traced iteratively, i.e., through a return mapping algorithm. Here, we show that these assumptions are not needed in the context of sequence learning when using recurrent neural networks, diverting the above-mentioned complications. This work offers an alternative to currently established plasticity formulations by providing the foundations for finding history- and microstructure-dependent constitutive models through deep learning.
Highlights
Plasticity theory aims at describing the yield loci and work hardening of a material under general deformation states
We propose to address this challenge by using deep learning to find history- and microstructure-dependent plasticity models when abundant data of material behavior is available
To other fields where, for example, machine learning is helping to design new materials [15, 16] and to predict protein behavior [17], the key to learning constitutive models of materials is to generate data about material behavior. This has been achieved for nonlinear elastic constitutive laws where data are created by finite element analysis (FEA) of representative volume elements (RVEs) [18, 19] and, more recently, to determine property maps obtained from plasticity and fracture simulations of RVEs [19]
Summary
Finding plasticity models can follow the recently proposed 3-module data-driven framework [19] that integrates: 1) design of experiments to sample the input space; 2) computational analyses to create a database of outputs corresponding to each input configuration; and 3) machine learning to find the constitutive law that links inputs and outputs. SI Appendix contains a comparative analysis between the 3 RNN architectures considered, where we demonstrate why we recommend the one shown in Fig. 2C for learning plasticity-constitutive models In this architecture, a GRU formulation with a secondary hidden state is proposed to carry nontemporal inputs. Note that the training set does not include any linear strain path because it is constructed via Gaussian process regression of fluctuating paths, but Fig. 4 E and F demonstrates that our RNN model is still able to predict these average stress states and plastic energy. The inputs to the RNN model are the nontemporal microstructure descriptors, as well as the temporal deformation paths, and the outputs are temporal stresses and plastic energy over 100 increments for each RVE. This was not observed when the deformation paths were sampled with GP regression due to its smoothness
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