Constrained sequential lamination: a sub-grid multiscale material model
Matt Fago, California Institute of Technology
A central problem in mechanics concerns the prediction of material processes on multiple lengthscales and their cumulative effect on material behavior. Constitutive models that incorporate effects from several lengthscales are important tools both in circumstances in which the model is directly applicable and in the development of high fidelity models at larger scales. Two such multiscale material models will be presented.
A practical algorithm has been developed to construct, through sequential lamination, the partial relaxation of multiwell energy densities such as those characteristic of shape memory alloys. The resulting microstructures are in static and configurational equilibrium, and admit arbitrary deformations. The laminate topology evolves during deformation through branching and pruning operations, while a continuity constraint provides a simple model of metastability and hysteresis. In cases with strict separation of lengthscales the method may be integrated, at the sub-grid level, into finite element calculations. This capability is demonstrated with a calculation of the indentation of an Cu-Al-Ni shape memory alloy by a spherical indenter. The performance of the algorithm is also compared to tension test experimental results at several crystallographic orientations.
The second algorithm is an ab initio method based on Density Functional Theory. Material properties are computed in real-time during a finite element calculation, with the mesh integration points modeled as non-interacting unit cells under the Cauchy-Born assumption. This approach allows for the prediction of dislocation emission using localization analysis, prediction of phase changes through basis optimization, simulation of high pressures, and studies of alloy composition. The model is illustrated with the simulation of dislocation emission during the indentation of aluminum at two orientations.
Abstract Author(s): Matt Fago