Linking microstructure and properties through a predictive multiresolution continuum

Abstract Under the sponsorship of the NSF/Sandia Life Cycle Science-based Engineering Program, the Sandia Predictive Science Program, and the ONR Digital 3D (D3D) program, a multiresolution continuum theory [C. McVeigh, F. Vernerey, W.K. Liu, L.C. Brinson, Comput. Methods Appl. Mech. Engrg. 195 (2006) 5053] is developed to predict material response when spatial and temporal microstructure evolution gives rise to severely inhomogeneous deformation at multiple scales. The proposed theory is applied by concurrently homogenizing the microstructure at each characteristic length scale associated with the inhomogeneous response. A continuum-microstructure work rate equivalence approach is used to develop a set of continuum partial differential governing equations, in terms of multiresolution microstresses (and couple microstresses). Constitutive models relating to each microstress are determined from numerical microstructure models. The multiresolution governing equations can be solved with a conventional finite element approach. Hence numerical and modeling errors analyses, probabilistic and reliability analyses and petaflop computing can be considered using existing approaches (or with transparent modifications). When only a single scale of inhomogeneous deformation (at the scale of the RVE) is considered, the multiresolution theory decomposes to the strain gradient theory of Fleck and Hutchinson. The theory is applied to (i) an alloy with two scales of statistically embedded particles, (ii) a cemented carbide and (iii) adiabatic shear banding in steel alloys. Only the mean constitutive behavior is considered at each scale; the full probabilistic analysis will be presented in a separate paper.