ANU College ofEngineering & Computer Science

Multiscale Modeling of Advanced Composite MaterialsBy Changyong Cao∗, ANU CECS Biomechanics Group, changyong.cao@anu.edu.au. Supervisor: Qinghua Qin∗.

Figure 1: Multiscale Nature of Materials

1 Introduction

Industrial and engineering materials, as well as natural materials, areheterogeneous at a certain scale (Figure 1).This heterogeneous na-ture has a significant impact on the observed macroscopic behaviorof composite materials. The overall behavior of micro-heterogeneousmaterials depends strongly on the size, shape, spatial distribution andproperties of the microstructural constituents and their respective in-terfaces.

For composite materials involving thermal-electro-mechanical field-s, the coupling behavior is more complex and usually different fromthose when only one single field applied, such as MEMS, biomedicaldevices, stretchable/flexible electronics (Figure 2), flexible Piezoelec-tric Sensor (Figure 2). Consequently, it is necessary to developmenta more comprehensive multi-scale multi-field methodology for accu-rate and robust prediction the coupling behaviors of these advancedcomposites.

(a) 50% of the primary structure - including the fuselage and wing - on Boeing 787 made ofcomposite materials.

(b) Flexible Sensor Array Wraps Beating Hearts to Map Cardiac Activity in Real Time

Figure 2: Applications of the advanced composite materials

∗Biomechanics Group, Research School of Engineering, College of Engineering & ComputerScience, Australian National University

(c) Army’s Helmet Sensors Measure Hits to Head

Figure 2: Applications of the advanced composite materials

2 Objective

The goal of this contribution is to develop an effective multiscalemultifield framework, which has the capability to bridging the nano-,micro-, and macroscales, and combining mechanical, thermal, andelectric fields to predict the response of advanced composite mate-rials. The failure mechanism of model for the composites will be en-riched by the damage models and the cohesive zone interface model.Micromechanical structures, such as defects,cracks and pore holeswill be involved by the proposed methodology in order to do a moreaccurate and realistic simulation. The effect of these microstructureswill be investigated to reveal its relationship with the desirable macroproperties such as reduction of thermal and mechanical stress con-centration, improved stress redistribution, maximization of output dis-placement etc.

3 Methodology

Three interacting length scales are involved in this project:• The molecular interface level, needed to assess the dissipative

contribution of bonding structures that are too small to fit in a con-tinuum approach. Dedicated molecular mechanisms will be coarsegrained to the fine scale model (Figure 3).

• The microscopic level, at which a detailed temperature-dependentcontinuum model including geometrical and physical defects bothon interface and matrix will be used to capture the influence of adistributed adhesion, and irregularities and defects.RepresentativeVolume Element (RVE) is employed.

• The macroscopic level, in which the mechanisms identified at themicro-scale, will be modeled at a constitutive level in terms of bulkconstitutive properties and cohesive zone models.

Carbon Nanotube

Interface

Matrix

Figure 3: Schematic of CNT-Matrix interface

Two scale transitions are required: The first one relies on the coarsegraining of the molecular dynamics results, which will be used in thefailure model at the microscale model. The fine scale model, with aconsiderable level of physical and geometrical complexity, will be ho-mogenized to the coarse scale, using HTFEM/HFS-FEM method.

4 Results and discussion

Currently, effective elastic properties of heterogeneous composite withisotropic and orthotropic fibers were investigated based on the ho-mogenization method combining with the newly developed Hybrid Tr-efftz FEM (HTFEM) and Hybrid Fundamental Solution based FEM(HFS-FEM). The representative volume element (RVE) models withperiodic boundary conditions were established and employed. It isfound that combined with homogenization technique, HTFEM andHFS-FEM is not sensitive to mesh density and Mesh distortion (Fig-ure 4). It may be concluded that we can employ linear elements andcoarser meshes to improve the computational efficiency without de-caying the accuracy when performing micromechanical analysis.

Figure 4: Contour plots of deformation and stresses of the RVE withideal bonded interface

5 Future Work

1. Enrich the current micromechanical model by cohesive interfacemodel to simulate the failure of composites.

2. Scale up the micromechanical model to the macro-scale using ho-mogenization scheme.

3. Combining the nano-, micro- and macro-scale models into a wholescheme.

4. Verification of the multiscale model using a full-resolution simula-tion.

6 References

1. Cao, C., Q.-H. Qin, et al. (2011). "Micromechanical analysis ofheterogeneous composites using HTFEM and HFS-FEM." Compos-ite Structures submitted.2. I. Temizer, P. Wriggers (2009): An Adaptive Multiscale ResolutionStrategy for the Finite Deformation Analysis of MicroheterogeneousStructures., Comput. Methods Appl. Mech. Engrg.