Symmetric high order microplane model for damage localization and size effect in quasi‐brittle materials

Abstract

This paper presents the so‐called symmetric high‐order microplane (SYHOM) model for the simulation of damage localization and size effect in quasi‐brittle materials. Contrarily to its predecessor, the high order microplane (HOM) model, SYHOM is formulated without rotational degrees of freedom, does not require couple stresses, and solves stability issues created by the antisymmetric components of stress and high order stress tensors. Furthermore, the formulation features variable, damage‐dependent localization limiter and nonlocal characteristic length that allows reproducing correctly size and shape of the fracture process zone during the entire softening process: from crack initiation to the formation of a stress‐free fracture. The paper highlights the implementation of SYHOM via isogeometric analysis with quadratic shape functions and presents several numerical simulations to demonstrate SYHOM's ability to simulate damage evolution during softening. Finally, SYHOM is validated by simulating experimental data relevant to the size effect on structural strength of notched concrete samples.

Stabilization of Notched Elements' Fracture by Using a Control Algorithm

“…Additionally, some numerical simulations require adaptive load-increment (reduction of load increment) beyond post-peak in order to get softening branch encountered while simulating three-point bending test. Especially for the analysis of bigger specimen without notch or specimen with a significantly smaller notch in comparison to the its size (Ayhan, et al, 2021;Lale & Gianluca, 2021). For these kind of difficulties, corresponding control algorithm can be used in order to have more control on crack-mouth opening versus load relation.…”