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Abstract A seamless and lossless transition of the constitutive description of the elastic response of materials between atomic and continuum scales has been so far elusive. Here we show how this problem can be overcome by using artificial intelligence (AI). A convolutional neural network (CNN) model is trained, by taking the structure image of a nanoporous material as input and the corresponding elasticity tensor, calculated from molecular statics (MS), as output. Trained with the atomistic data, the CNN model captures the size- and pore-dependency of the material’s elastic properties which, on the physics side, derive from its intrinsic stiffness as well as from surface relaxation and non-local effects. To demonstrate the accuracy and the efficiency of the trained CNN model, a finite element method (FEM)-based result of an elastically deformed nanoporous beam equipped with the CNN as constitutive law is compared with that obtained by a full atomistic simulation. The trained CNN model predicts the elasticity tensor in the test dataset with a root-mean-square error of 2.4 GPa (3.0% of the bulk modulus) when compared to atomistic calculations. On the other hand, the CNN model is about 230 times faster than the MS calculation and does not require changing simulation methods between different scales. The efficiency of the CNN evaluation together with the preservation of important atomistic effects makes the trained model an effective atomistically informed constitutive model for macroscopic simulations of nanoporous materials, optimization of nanostructures, and the solution of inverse problems.

Abstract The complex interplay between chemistry, microstructure, and behavior of many engineering materials has been investigated predominantly by experimental methods. Parallel to the increase in computer power, advances in computational modeling methods have resulted in a level of sophistication which is comparable to that of experiments. At the continuum level, one class of such models is based on continuum thermodynamics, phase-field methods, and crystal plasticity, facilitating the account of multiple physical mechanisms (multi-physics) and their interaction during microstructure evolution. This paper reviews the status of simulation approaches and software packages in this field and gives an outlook towards promising research directions.

Abstract We propose a deep neural network (DNN) as a fast surrogate model for local stress calculations in inhomogeneous non-linear materials. We show that the DNN predicts the local stresses with 3.8% mean absolute percentage error (MAPE) for the case of heterogeneous elastic media and a mechanical contrast of up to factor of 1.5 among neighboring domains, while performing 103 times faster than spectral solvers. The DNN model proves suited for reproducing the stress distribution in geometries different from those used for training. In the case of elasto-plastic materials with up to 4 times mechanical contrast in yield stress among adjacent regions, the trained model simulates the micromechanics with a MAPE of 6.4% in one single forward evaluation of the network, without any iteration. The results reveal an efficient approach to solve non-linear mechanical problems, with an acceleration up to a factor of 8300 for elastic-plastic materials compared to typical solvers.