A new approach for optimizing the mechanical behavior of porous microstructures for porous materials by design

A high-fidelity generalized method of cells (HFGMC) model for the micromechanical behavior of porous and composite microstructures has been previously developed. Based on this model, a new approach has been developed to optimize porous microstructures for 'porous materials by design'. This approach uses a combination of genetic algorithms (GA) (stochastic), coarse (periodic) and Newton-Raphson (gradient) optimization methods. In order to parametrize the unit cell of the microstructure for optimization and satisfy continuity conditions for the method of cells, lines of mass are used in each direction of the unit cell. Due to the nature of the optimization problem for porous microstructures, there can be multiple choices of mechanical and microstructural characteristics (e.g. axial stress, transverse strain, and mass) for the objective function (i.e. multi-objective) implying a Pareto optimality problem. For the porous materials by design problem based on mechanical characteristics, a predescribed mechanical response was chosen for a random distribution of mass to fit via a least squares objective function. The effects of implementing the combination of optimization methods on their convergence rate and optimized solutions were then studied, as well as variations in the weighting of the objective functions. A hyperelastic material behavior, Mooney-Rivlin, typically associated with natural and synthetic rubbers, is chosen to demonstrate the ability to optimize an engineered microstructure for a new class of super-lightweight energy-absorbing materials. These results indicate that the combination of the GA, coarse search and Newton-Raphson optimization techniques can substantially accelerate the convergence rate. Also, there is significant variability in the optimized microstructure depending on the choice of the weights for the associated Pareto optimality, as well as the choice of terms for the objective function. Parametrizing the porous microstructure using multiple lines of mass can create a more complex microstructure, but common centers of mass should be employed to minimize mass while improving convergence rates and optimal constitutive behavior. This new approach was applied to identify microstructures for three new porous materials by design: (a) a superelastic polymer, (b) an incompressible material and (c) an auxetic material.