A numerical investigation of the effect of boundary conditions and representative volume element size for porous titanium

Abstract

To facilitate the design and application of porous titanium and titanium foam, numerical simulation of their mechanical behavior is essential. The concept of a representative volume element (RVE) is essential to obtain accurate estimates of the properties. Because of the high contrast between the properties of the two phases (pore vs. matrix), it is impractical to obtain a single RVE independent of boundary conditions to provide accurate predictions. We suggest that a set of small domain RVEs can be used instead, as long as the average of the small domains provides a convergent result. Two mixed boundary conditions simulating uniaxial proportional loading were designed and implemented on several 2D and 3D finite element models at different length scales, that is, containing different numbers of pores. The two boundary conditions provide opposite biased responses. Convergence of both the macroscopic and the microscopic elastoplastic responses associated with the boundary conditions is demonstrated here. By this approach, RVEs that are prohibitively large according to Hill's definition are divided into reasonably small ones associated with special boundary conditions, and the error of predictions associated with model size can be estimated.