Novel boundary conditions for strain localization analyses in microstructural volume elements

Abstract

SUMMARYMulti-scale modeling frequently relies on microstructural representative volume elements (RVEs) on which macroscopic deformation is imposed through kinematical boundary conditions. A particular choice of these boundary conditions may influence the obtained effective properties. For strain localization and damage analyses, the RVE is pushed beyond the limits of its representative character, and the applied boundary conditions have a significant impact on the onset and the type of macroscopic material instability to be predicted.In this article, we propose a new type of boundary conditions for microstructural volume elements, called percolation-path-aligned boundary conditions. Intrinsically, these boundary conditions capture the constraining effect of the material surrounding the RVE upon developing localization bands. The alignment with evolving localization bands allows the highly strained band to cross the RVE and fully develop with minimal interference of the applied boundary conditions. For an illustration of the performance of the newly proposed boundary conditions, macroscopic deformation has been imposed on a voided elasto-plastic RVE using different types of boundary conditions. It is observed that the new RVE boundary conditions provide a good estimate for the effective stiffness, are not susceptible to spurious localization, and permit the development of a full strain localization band up to failure.

A two‐scale failure model for heterogeneous materials: numerical implementation based on the finite element method

“…To reach this goal, a very important aspect of the methodology is the introduction, after detecting the stability loss at the macro scale, of the hybrid boundary conditions with periodicity aligned with the crack. This concept was taken from Coenen et al [6].…”

“…This methodological approach has been the subject of recent intensive research in the scientific community. A number of novel contributions have been made in this direction, see for example the approaches of Matous et al [21], Verhoosel et al [44], Nguyen et al [27,29] Belytschko and coworkers [2,41], Geers and coworkers [6], Unger [43] and Souza et al [42]. However, the development of a consistent method has remained full of major theoretical challenges.…”

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

“…Mesarovic and Padbidri [238] argued that there is no reason to assume that an RVE with random microstructure behaves as a periodic unit cell and suggested the use of minimal kinematic boundary conditions. However, minimal kinematic boundary conditions are sensitive to spurious localization in regions close to the RVE boundary [239]. A comprehensive comparison of this type of boundary conditions and periodic boundary conditions was made by Inglis et al [240].…”

Regularization of first order computational homogenization for multiscale analysis of masonry structures

“…(8)) are enforced on the boundaries of the RVE. In some applications, the assumption of periodic boundary fluctuations might enforce unphysical constraints on the crack direction [13]. However, for the specific case of masonry the cracks mainly take place following the periodic geometry of the weak mortar joints.…”

“…Another issue related to the loss of representativeness of the RVE is the choice of proper boundary conditions to be applied on the RVE. A study on this topic has been done in [13], where a novel boundary condition has been proposed, using the concept of rotating periodicity to avoid costraining the crack propagation orientation.…”