Minimal kinematic boundary conditions for simulations of disordered microstructures

Authors: Mesarovic, Sinisa Dj.1; Padbidri, Jagan1

Source: Philosophical Magazine, Volume 85, Number 1, January 1, 2005 , pp. 65-78(14)

Publisher: Taylor and Francis Ltd

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Abstract:

In simulations of representative volume elements (RVEs) of materials with disordered microstructures, commonly used rigid and periodic boundary conditions (BCs) introduce additional constraints, causing: (i) boundary effects, (ii) unrealistic stiff response, (iii) artificial wavelengths in the solution fields, and (iv) suppression of solutions with localized deformation that otherwise may occur in the simulation. In this paper we define the minimal kinematic boundary conditions such that only the desired overall strain is imposed on the RVE, with no other undesirable constraints. We prove that such BCs result in a unique solution for the linear elastic case, and that the uniqueness for nonlinear problems is dependent on the pointwise positive definiteness of the incremental stiffness tensor. Upon incorporating the minimal BCs into the finite element framework, we consider, as an example, two-dimensional, linear elastic, disordered polycrystals and perform a systematic study of the effects of boundary conditions while varying the RVE size and controlling the sampling error. The results demonstrate that the minimal BCs, applicable to a RVE of any shape, are superior to other BCs, in that they give more realistic overall behaviour, reduce the required size of the RVE, and eliminate the superficial wavelengths in the solution field, ubiquitous in simulations with other boundary conditions.

Document Type: Research article

DOI: 10.1080/14786430412331313321

Affiliations: 1: School of Mechanical and Materials Engineering Washington State University PO Box 642920 Pullman WA 99164-2920 USA

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