Computational homogenisation based multiscale failure modelling: application to cortical bone tissue

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