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In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning techniques. We propose to use a collection of connected mechanistic building blocks with analytical homogenization solutions which avoids the loss of essential physics in generic neural networks, and this concept is demonstrated for 2-dimensional RVE problems and network depth up to 7. Based on linear elastic RVE data from offline direct numerical simulations, the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, further enhanced by model compression methods. Importantly, the trained network is valid for any local material laws without the need for additional calibration or micromechanics assumption. Its extrapolations to unknown material and loading spaces for a wide range of problems are validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finitestrain hyperelasticity under large deformations.By discovering a proper topological representation of RVE with fewer degrees of freedom, this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a largescale heterogeneous structure. It also provides a mechanistic understanding of structure-property relations across material length scales and enables the development of parameterized microstructural database for material design and manufacturing. cost and accuracy. Analytical micromechanics methods [9,10,1,11,12,13] can be regarded as one type of reduced-order models with high efficiency. However, due to a loss of detailed physics in the microscale, they normally lose accuracy or require extensive model calibrations when irregular complex morphologies, nonlinear history-dependent properties or large deformations are presented. For heterogeneous hyperelastic materials, manifold-learning methods like isomap are used for nonlinear dimensionality reduction of microscopic strain fields [14]. The model reduction of history-dependent plastic materials can be more complex and challenging. Two examples are non-uniform transformation field analysis (NTFA) [15,16] and variants of the principle component analysis [17] or proper orthogonal decomposition (POD) [18,19,20]. However, they usually require extensive a priori simulations for interpolating nonlinear responses, and their extrapolation capability for new material inputs is usually limited, Recently, the self-consistent clustering analysis (SCA) [21,22] has demonstrated a powerful trade-off between accuracy and efficiency in predicting smallstrain elasto-plastic behavior though clustering techniques, and it only requires linear elastic simulations in the offline stage.Meanwhile, current advanced machine learning models (e.g. artificial neural networks and deep learning) hav...

This paper extends the deep material network (DMN) proposed by Liu et al. (2019) [1] to tackle general 3-dimensional (3D) problems with arbitrary material and geometric nonlinearities. It discovers a new way of describing multiscale heterogeneous materials by a multi-layer network structure and mechanistic building blocks. The data-driven framework of DMN is discussed in detail about the offline training and online extrapolation stages. Analytical solutions of the 3D building block with a two-layer structure in both small-and finite-strain formulations are derived based on interfacial equilibrium conditions and kinematic constraints. With linear elastic data generated by direct numerical simulations on a representative volume element (RVE), the network can be effectively trained in the offline stage using stochastic gradient descent and advanced model compression algorithms. Efficiency and accuracy of DMN on addressing the long-standing 3D RVE challenges with complex morphologies and material laws are validated through numerical experiments, including 1) hyperelastic particle-reinforced rubber composite with Mullins effect; 2) polycrystalline materials with rate-dependent crystal plasticity; 3) carbon fiber reinforced polymer (CFRP) composites with fiber anisotropic elasticity and matrix plasticity. In particular, we demonstrate a threescale homogenization procedure of CFRP system by concatenating the microscale and mesoscale material networks. The complete learning and extrapolation procedures of DMN establish a reliable data-driven framework for multiscale material modeling and design.anisotropic responses, and may require burdensome calibration to find the model parameters. As a result, homogenization based on the concept of representative volume element (RVE) [11] has become an important approach to model multiscale materials [12]. Many analytical methods have been proposed, which adopt some micromechanics assumptions to simplify the full-field RVE problem, such as Hashin-Shtrikman bounds [13,14], the Mori-Tanaka method [15] and self-consistent methods [16]. Since most analytical methods are derived based on the solution for regular geometries and simple material models (e.g. Eshelby's solution for isotropic elastic materials [17]), it is usually difficult for them to consider complex microstructural morphologies, history-dependent materials and large deformations. Additionally, direct numerical simulation (DNS) tools, such as finite element [18], meshfree [19,20] and fast Fourier transform (FFT)-based micromechanics methods [21,22], are both flexible and accurate. However, a DNS model involves a detailed meshing of the RVE microstructures and requires tremendous computational cost, especially for 3D problems. Therefore, one of the fundamental issues in multiscale material modeling and design is how to find an accurate low-dimensional representation of the RVE for arbitrary morphologies and nonlinearities.In the past decade, a plethora of data-driven material modeling methods have been proposed based on exist...

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This paper presents our latest work on comprehensive modeling of process-structure-property relationships for additive manufacturing (AM) materials, including using data-mining techniques to close the cycle of design-predict-optimize. To illustrate the processstructure relationship, the multi-scale multi-physics process modeling starts from the micro-scale to establish a mechanistic heat source model, to the meso-scale models of individual powder particle evolution, and finally to the macro-scale model to simulate the fabrication process of a complex product. To link structure and properties, a highefficiency mechanistic model, self-consistent clustering analyses, is developed to capture a variety of material response. The model incorporates factors such as voids, phase composition, inclusions, and grain structures, which are the differentiating features of AM metals. Furthermore, we propose data-mining as an effective solution for novel rapid design and optimization, which is motivated by the numerous influencing factors in the AM process. We believe this paper will provide a roadmap to advance AM fundamental understanding and guide the monitoring and advanced diagnostics of AM processing.