Size Effects at the Mesoscale: A Concurrent Multi-scale Model for the Thermomechanical Response of Materials
Prof. Julian J. Rimoli
School of Aerospace Engineering
Georgia Institute of Technology
Predictive modeling of material behavior is a problem that necessarily spans several scales: for example, inter-atomic interactions dominate the elastic behavior of materials, point and line defects condition their inelastic response, and planar defects such as grain boundaries could introduce length-dependent macroscopic material properties. With novel manufacturing and material synthesis techniques allowing the manipulation of characteristic material length scales, e.g., grain size and grain size distribution, the possibility of designing microstructures for a desired macroscopic performance is becoming closer to reality. In this context, mesoscale models become key to link the fundamental processes obtained from the lower scales with the continuum models needed by designers and engineers. In this work, we formulate efficient models and numerical schemes for understanding the length-dependent thermomechanical response of ceramics with rich microstructures. Our approach consists of: (i) a sub-micron scale model for the thermal conductivity, (ii) a classic Fourier heat transport model at the mesoscale, and (iii) a continuum model of thermomechanical deformation that explicitly resolves the microscopic geometric features of the material. The capabilities of the model are demonstrated through a series of examples, which highlight the potential that our proposed framework has for designing materials and metamaterials with improved thermomechanical performance. For example, our simulations show that one could tailor the material’s microstructure, e.g. through grading of the grain size, and affect the resulting distribution of thermal stresses within the material.