Research

While the ultimate goal is to develop constitutive models for engineering materials in conjunction with the practical applications of these models, there are several different areas of research in the background to build a strong basis for that development and beyond. In particular, I have been trying to push forward my understanding of micro-mechanical processes (in various engineering materials), together with extending constitutive modelling frameworks to accommodate the obtained micro-mechanical details. There should be a balance between the two as adding more internal variables to a model based on the framework of classical continuum theory may at best lead to better phenomenological descriptions, but not always better predictive capabilities.

A multi-scale constitutive modelling framework

  1. The aim is to develop thermo-mechanically consistent frameworks that allow the incorporation of length scales in constitutive models. This is essential for capturing the mechanics and physics of localised failure in engineering materials. Examples include nonlocal models with evolving length scale (or nonlocal interaction). Recent research leads to a multi-scale constitutive modelling framework that possesses an embedded localisation zone and its associated constitutive behaviour. This departs from traditional approaches that have either no length scale (e.g. classical continuum models based on plasticity/damage theory...) or a rather ad hoc one (e.g. nonlocal/gradient theories). The new approach retains the local nature of the model, while possessing an intrinsic length scale related to the width of the localisation zone. Of course this is just a start, and on-going research has been well underway to further extend/improve the new framework.Nguyen, G.D., Einav, I., Korsunsky, A.M., 2012, How to connect two scales of behaviour in constitutive modelling of geomaterials, Geotechnique Letter (Special issue on Geomechanics Across the Scales) 2, 129-134 (pdf).

  2. Nguyen, G.D., Korsunsky, A.M., Einav, I., 2013, A constitutive modelling framework featuring two scales of behaviour: fundamentals and applications to quasi-brittle failure, Engineering Fracture Mechanics, under review.

  3. Nguyen G.D., 2013, An Enriched Constitutive Model for Fracture Propagation Analysis using the Material Point Method, 1st Australasian Conference on Computational mechanics (ACCM2013), 03-04 October 2013, Sydney, Australia (pdf).

  4. Nguyen, G.D., 2011, A damage model with evolving nonlocal interactions, International Journal of Solids and Structures 48(10), 1544-1559 (pdf).

Micro-mechanics based constitutive modelling

Describing/analysing solids/structures with full details of the micro-mechanical failure processes is not always feasible in engineering, due to limitation in current computing power. Instead, continuum mechanics views these nonhomogeneous materials as continua and uses only a few internal variables to represent the heterogeneous failure processes at lower scales. Obtaining a constitutive model with a physical basis, identifiable parameters, and able to capture both the macroscopic stress-strain behaviour and the evolving micro-structure of a material requires identifying key internal variables, and quantifying their links with micro-mechanical processes. “An internal variable inferred from the phenomenological evidence and selected to fit a particular stress-strain curve may provide a result that pleases the eye but seldom contributes to the understanding of the processes represented by the fitted curve” (Krajcinovic, Mech Mater. 1998; 28: 165-79). Therefore constitutive modelling to me is both an art and a science!!!

This work runs in parallel with and is integrated in the above development of multi-scale constitutive modelling framework, although sometimes it's better to make a separation/isolation to have more focus on one issue. However, the main focus is the abstract of the rich micro-mechanical details and then embed the obtained micro-mechanics based mechanisms in constitutive models. These mechanisms will give constitutive models predictive capability while minimising the use of empirical or ad hoc parameters that are hard to identify, let alone to quantify. In this respect, a constitutive model not based on intrinsic material properties and correct micro-mechanics of failure cannot be expected to possess any predictive capability out of the loading regimes and experimental conditions under which they are designed and calibrated.

This is where I have collaborations with many people (seen in my Publications), across the continents, on various issues associated with different engineering materials and/or problems. While the main thrust over the years is quasi-brittle failure starting from my PhD study (with Guy Houlsby, Oxford), others include (in time order):

Computational failure mechanics

This is a tool in the background to help gain more micro-mechanical insights into an issue, or to implement any constitutive models for practical applications. While there have been outstanding contributions in the development and applications of advanced methods like the eXtended Finite Element Methods (XFEM) and its derivatives, or the Enhanced Assumed Strain (EAS),... I am more inspired, due to my background and more interests in Constitutive Modelling, by the Material Point Method (MPM; Sulsky et al, 1994) as a versatile tool to analyse a wide range of problems across the scales. This came from the period working as a postdoc under Deborah Sulsky and "Buck" Schreyer at UNM Albuquerque. This is also where I was inspired by issues with very large scale problems (e.g. hundred kilometre size of the ice sheet in the Arctic, and now kilometre size of the block cave mining). These involve several branching/intersecting cracks/discontinuities at various (nested) scales that we have to capture in the simulations. While XFEM and its derivatives are a great option, it could require a lot of efforts and advanced techniques that I may not be good at. Instead, treating these issues as constitutive modelling issues in conjunction with the MPM modelling is an easier and less time consuming way for me. Of course, one method has its own advantages, disadvantages and limitations and it's all up to our capacity, and also personal view to pick one for the research. In brief, to go with the MPM, the kinematics of constitutive models (not Finite Element) is enhanced to account for discontinuities associated with cracking or compaction. This allows to keep all details of the failure at the material point, including crack opening/sliding coupling with the bulk elastic behaviour. However in doing so I have to sacrifice the great accuracy (that XFEM can bring in a few cases) for the easiness, performance and versatility that the MPM offers. The examples below show what I mean.

Mixed mode fracture of concrete: This is the MPM simulation of the mixed mode test performed by Nooru-Mohamed et al (1993). We used a simple isotropic damage model developed earlier integrated in the proposed multi-scale constitutive modelling framework. As seen, the combined behaviour is becoming anisotropic leading to a more realistic behaviour.

Failure of cement matrix composite: the versatility of the MPM allows the explicit modelling of inclusio

ns, matrix and their Interfacial Transition Zone (ITZ) without much pain (of course FEM type modelling is only an issue for a guy like me, as it's nothing to smart ones!!!). These two examples show the diffuse to localised failure process. The active FPZ on the left shows where current micro-cracking activities are, while the FPZ itself indicates the total (cumulative) damage to the RVE. The transition from diffuse to localised failure is different under different loading paths. Tension:

and shear followed by tension:

Failure of a (probably too small) RVE made of cemented granular materials: Again we take advantage of the MPM in generating the sample (consisting of circular grains and cement bridges). This is my alternative to the Discrete Element Modelling (DEM) that many have been using. Of course there is a sacrifice on the sample size (about 30 grains in this example) for more realistic behaviour including cement fracture and grain crushing that are hard (or impossible???) to capture using DEM.

Impact and penetration

Compaction of foam material

Rock fragmentation