Metamodel-Based Inverse Design of a Composite Material with Prescribed Interval Effective Elastic Properties

A problem of inverse design of a composite material with prescribed (desired) interval effective elastic constants is formulated and solved. The identified parameters are the interval parameters of the constituent geometry and material properties on the microscale. Such uncertainty falls into the category of epistemic uncertainty, which is frequent in engineering practice and is caused by incomplete knowledge, not allowing for the stochastic description of quantities of interest. Commercial finite element code Ansys is applied to the computational homogenisation with representative volume element (RVE) analysis. The high-fidelity model is replaced by a finely adjusted polynomial response surface to minimise overall computation time. The response surface is used for the interval computations involved in the identification problem. Directed interval arithmetic is applied. It includes cancelation laws for addition and multiplication and is the preferred method in engineering problems. Objective functions also involve differences between the desired and actual effective interval properties and widths of the identified microstructure parameters. The single- and multi-objective evolutionary algorithms are applied to solve the optimisation tasks. In the identification problem, the interval variables are represented as pairs of real numbers (components of the directed intervals). As numerical examples, two problems concerning a unidirectional fibre-reinforced composite with linear-elastic properties are formulated and solved. The first one employs scalarization by combining the objectives with presumed weights. In the second, a more extensive Pareto-frontier approach is considered. The proposed approaches provide feasible solutions to identification problems and provide perspectives for their extension to efficient solutions of more complex ones with epistemic uncertainty: fuzzy representation of uncertain parameters, nonlinear inhomogeneous materials, and others.