Author: Wenjin Xing
Xing, Wenjin, 2020 Computational homogenisation based multiscale failure modelling: application to cortical bone tissue, Flinders University, College of Science and Engineering
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Computational approaches to the fracture of engineering components or structures
are of ongoing research interest. The development of an accurate, robust and
efficient computational fracture framework is not an easy task. To properly account
for the effect of material microstructure on the overall response and to understand
structure-property connections, multiscale modelling is deemed necessary. However,
conventional multiscale approaches have limitations when simulating highly nonlinear
phenomena, such as strain localisation. In the presence of strain localisation, at
the macroscale the governing equations of equilibrium lose ellipticity, leading to the
mesh sensitivity of finite element solutions; furthermore, the homogenised response
with standard averaging methods depends on the size of a Representative Volume
Element (RVE).
This thesis aims to develop computational multiscale failure approaches for linking
fracture or failure events across scales in a manner that alleviates the difficulties
mentioned previously. To this end, two different continuous-discontinuous multiscale
approaches based on computational homogenisation are proposed. Both are capable
of capturing the hardening and softening portions of the material response prior
to and after the strength limit. This is accomplished by coupling intact RVE models
with Gauss points within the predefined critical regions of macroscopic structures
at the beginning of analysis. After the material becomes unstable due to softening,
a new crack segment is inserted for which cohesive RVE models are assigned to
crack integration points. Such cohesive RVE models are associated with extended
computational homogenisation schemes in order to resolve RVE size dependence
in the presence of strain localisation.
Inspired by the classical crack band model of Bazant and Oh, the first multiscale
failure approach is developed on the basis of an extended computational homogenisation
scheme called macro-discontinuity enhanced FE2. The weakly periodic BCs
that are aligned with the localisation direction are employed to minimise the boundary
effects. One major advantage of this model is its simplicity since it does not require
the knowledge of evolution details of strain localisation at the microscale. However, it
does not strictly enforce the kinematical consistency between the macroscopic crack
and microscopic strain localisation band. To this end, the second multiscale failure
approach is developed on the basis of the Failure-Oriented Multiscale Variational
Formulation (FOMVF) proposed in the literature. The FOMVF is built upon the
requirement of kinematic admissibility and the principle of multiscale virtual power.
For both multiscale failure approaches, the crack at the macroscale is represented
with the XFEM method to address mesh sensitivity issues. A series of numerical
studies are illustrated to show both multiscale failure approaches are capable of
handling strain localisation or fracture problems.
Multiscale failure modelling is then applied to explore the failure mechanisms of
cortical bone tissue. The effects of fracture properties of the cement line on the
effective fracture strength and toughness are investigated by means of microscopic
modelling. The extrinsic toughening mechanisms observed in the RVE models are
discussed. A three-point bending test for the cortical bone specimen is simulated
with the first multiscale failure modelling approach.
Keywords: computational homogenisation, multiscale failure modelling, strain localisation, cortical bone fracture, weakly periodic boundary conditions, cohesive zone model, XFEM
Subject: Engineering thesis
Thesis type: Doctor of Philosophy
Completed: 2020
School: College of Science and Engineering
Supervisor: Stuart Wildy and Tony Miller