Multiscale constitutive model using data-driven yield function

To overcome inaccurate prediction of yield surface evolution arising from the general use of classical yield functions, a method to formulate data-driven yield functions is established, using machine learning technique operating on the multi-axial yield data that exhibit the unique multi-axial hardening behavior of amorphous polymers. A scheme to generate sufficient data for multi-axial hardening responses is proposed, using molecular dynamics simulations, considering their timescale limitations, on quantitative estimations of mechanical responses. Based on the mined data-driven yield function, a constitutive model is constructed, and the corresponding multi-axial stress evolutions are compared with those of classical models. To examine the possibility of yield function mining by symbolic regression, the development of the classical yield functions von?Mises, Drucker?Prager, Tresca, Mohr?Coulomb, and paraboloidal yield functions was reproduced by using the proposed approach. Additional simulations were undertaken to characterize the influence of noise in the yield data set on the chosen functions.