Neural operator accelerated atomistic to continuum concurrent multiscale simulations of viscoelasticity

Abstract

We present a neural-operator-accelerated concurrent multiscale framework that couples atomistic simulations with continuum finite-element analysis for history-dependent materials, thereby making atomistic-continuum multiscale simulations of viscoelastic materials tractable. The approach replaces direct molecular dynamics (MD) evaluation of the constitutive response with a Recurrent Neural Operator (RNO) surrogate trained on atomistic simulations. The surrogate learns the strain-history-to-stress operator from molecular dynamics simulations and provides a discretization-independent approximation of the atomistic constitutive mapping, enabling efficient evaluation of stresses and latent internal variables at each quadrature point. The framework is implemented within an explicit finite-element solver, where the constitutive update reduces to inexpensive operator evaluations rather than repeated MD solves. Memory effects are represented through learned internal states, and transfer learning across temperature enables the surrogate to capture thermally dependent viscoelastic behavior. The method is assessed using polyurea through cyclic loading, Taylor impact, and plate impact simulations and compared with an experimentally calibrated viscoelastic polyurea model and a Johnson-Cook model. The neural-operator surrogate reproduces correct viscoelastic response while enabling atomistically informed dynamic simulations at scales that are not tractable with direct MD-FEM coupling.

Figures (17)

• Figure 1: Neural network diagram of discretized RNO at the $n^{th}$ time step.
• Figure 2: (a) shows the chemical formula of polyurea. Here $n$ is the number of repeating monomer units and $m$ is the number of repeating soft segments within a monomer unit. (b) shows the multiscale nature polyurea composites. The polyurea chain, atomistic representative volume element, and continuum modeling is shown.
• Figure 3: (a) shows the dependence of bulk modulus on the cell size of the RVE. (b) shows the dependence of stress on volumetric strain of polyurea at temperatures $300$, $400$, and $500$ K.
• Figure 4: (a) Dependence of relative error on the number of internal variables for temperatures $300$ K, $400$ K, $500$ K. (b) shows the convergence of relative error over the number of epochs for temperatures $300$ K, $400$ K, $500$ K. Both training and testing errors are shown.
• Figure 5: Components of strain tensor shown for five trajectories. The normal strains are shown in the top panel, and shear strains are shown in the bottom panel.