MEAM Seminar: “Learning Memory and Material Dependent Constitutive Laws”

The theory of homogenization provides a systematic approach to the derivation of macroscale constitutive laws, obviating the need to repeatedly resolve complex microstructure. However, the unit cell problem which defines the constitutive model is typically not amenable to analytical solution. It is therefore of interest to learn constitutive models from data generated by the unit cell problem. Many viscoelastic and elastoviscoplastic materials are characterized by memory-dependent constitutive laws. Furthermore, in order to amortize the computational investment in finding such memory-dependent constitutive laws, it is desirable to learn their dependence on the material microstructure.
Whilst the learning of memory dependence and material dependence have been considered separately, their joint learning has not been considered. This talk is focused on the joint learning problem and proposes a novel neural operator framework to address it

In order to provide firm foundations, the homogenization problem for linear Kelvin–Voigt viscoelastic materials is studied. The theoretical properties of the cell problem, in this Kelvin–Voigt setting, are used to motivate the proposed general neural operator framework; these theoretical properties are also used to prove a universal approximation theorem for the learned macroscale constitutive model. This formulation of learnable constitutive models is then deployed beyond the Kelvin–Voigt setting. Numerical experiments are presented showing that the resulting data-driven methodology accurately learns history- and microstructure-dependent linear viscoelastic and nonlinear elastoviscoplastic constitutive models; numerical results also demonstrate that the resulting constitutive models can be deployed in macroscale simulation of material deformation.

Joint work with Kaushik Bhattacharya, Lianghao Cao, George Stepaniants and Margaret Trautner (all Caltech).