Predicting stress–strain constitutive relationships: a deep learning approach based on multi-head attention mechanism and long short-term memory networks

The stress–strain constitutive relationship of materials is a critical indicator for assessing their mechanical properties and serves as a vital bridge connecting microstructures with macroscopic mechanical behaviors. This study focuses on 106 metal alloy materials, employing the finite element method to establish uniaxial tensile numerical models, thereby simulating and obtaining a comprehensive dataset of stress–strain relationship curves. Innovatively, this research proposes a MA-LSTM-DLnet prediction model that integrates multi-head attention mechanisms with long short-term memory networks, based on deep learning methodologies. The model utilizes conventional key parameters such as material strain, yield strength, tensile strength, elastic modulus, density, strength coefficient, and stress as input features to construct a multi-dimensional training dataset. It particularly explores the learning capabilities and predictive performance of the MA-LSTM-DLnet model under both complete and limited feature datasets. The results demonstrate that the trained MA-LSTM-DLnet model can accurately predict the stress–strain constitutive relationship curves of new materials by merely acquiring conventional physical parameters like yield strength, tensile strength, and elastic modulus, with a similarity exceeding 95% compared to test data. Compared to traditional empirical formulas and numerical simulation methods, the main innovation of this study lies in eliminating key parameters that are difficult to determine in mathematical models (such as the strength coefficient in the Ludwik isotropic hardening model), significantly reducing repetitive work dependent on experiments to obtain constitutive relationships, and achieving efficient and precise material performance evaluation.