Deep Material Network for Thermal Conductivity Homogenization

The agile and accurate material simulation model is in demand for rapid material analysis and design. Especially a computational analysis model for multiphysics and multiscale applications is of major interest. Recently, Deep Material Network (DMN) has shown itself to be a powerful approach for the material's reduced-order modeling because of its ability to extrapolate the constitutive equations and its orders of lower computational cost. DMN learns the homogeneous pathway from the linear constitutive relation data and can be used as a reduced-order model for predicting the non-linear constitutive equations. However, currently, all the DMN work has been done only on the elastic mechanical problems. In this study, DMN has been explored to handle thermal conductivity analysis. By building the DMN architecture corresponding to the thermal conductivity homogenization, we have shown that the DMN can be expanded to different physics, which is essential to dealing with multiphysics problems. We had predicted the two-scale problem's homogenized response, corresponding to the thermal conductivity of the woven structure. To consider the woven structures' orthotropic properties, micromechanics-based DMN network parameters have also been updated to reflect the material's orientation. The trade-off of increasing the DMN network parameters, corresponding to the complexity of the homogenization process, has also been studied. We believe our material model will open new chances for multiphysics-multiscale design and analysis for composite materials and, furthermore, to explore the material design space with sufficient agility and accuracy. Sandia National Laboratories is managed and operated by NTESS under DOE NNSA contract DE-NA0003525.