Physical phenomena can be modeled at varying degrees of complexity and at different scales. Multiscale modeling provides a framework, based on fundamental principles, for constructing mathematical and computational models of such phenomena, by examining the connection between asphalt/cement concrete models at different scales.

Concrete is composite construction material, which is composed primarily of coarse aggregates, sand and cement paste. The fracture processes in concrete are complicated, because of the multiscale and multiphase nature of the material. The fracture properties of cement paste, mortar and concrete are highly related in nature. In this topic, the lattice fracture model is coupled with the parameter-passing multiscale modeling scheme to study the relationship of the fracture processes in cement paste, mortar and concrete. A multiscale fracture modeling procedure is proposed and demonstrated. Three levels of characters are defined, including micrometer scale for cement paste, millimeter scale for mortar and centimeter scale for concrete. The lattice fracture model is applied at lower scale, while the finite element analysis is applied at the higher scale, respectively. The inputs required at a certain scale are obtained by the simulation at a lower scale. At the lowest scale, the micrometer scale for cement paste, inputs are determined by laboratory experiments and nanomechanics modeling from atomistic modeling.

The multiscale modeling scheme proposed in this topic can be used by researchers in concrete community, to study the various factors which influence the mechanical performance of cementitious materials. It can also be adapted with other computational models to form a complete fully multiscale modeling framework, from nano to macro scale.

Build 3-D image model and spherical harmonic-based model of random microstructures

This work bridges the gap between heterogeneous microstructure and computer-aided engineering finite element analysis.

Cement Paste at Microscale

The microstructure of materials determines its global performance. Start from microscale, the microstructure of cement paste can be obtained either experimentally or numerically. The micro X-ray computed tomography (CT) offers a nondestructive experimental technique to collect microstructure information of cement paste in terms of digitized voxels. Computer modeling packages are also available to simulate the cement hydration and microstructure formation processes, for example, the HYMOSTRUC3D model developed by TU Delft [1], the NIST CEMHYD3D toolkit [2] and the Mic model by EPFL [3].

After obtaining the microstructure of cement paste, the 3D lattice fracture model can be employed to simulate the fracture behavior of the cement paste. For example, a uniaxial tensile test can be set up and simulated on the cement paste to predict its Young's modulus, tensile strength and fracture energy, as well as the microcracks propagation and cracks pattern in the final failure state.

The cement hydration and microstructure formation model, HYMOSTRUC3D model, and the mechanical performance evaluation model, 3D lattice fracture model, can be combined to study the influences of various factors on the mechanical properties of cement paste, including but not limited to the influences of degree of hydration, cement fineness, water/cement ratio and mineral composition of cement.

Simulated microstructures of cement paste

In the HYMOSTRUC3D model, the cement particles are modeled as spheres and these spherical particles grow during the hydration process.

In general the hydrating cement particle contains three layers from center to outward surface, namely unhydrated cement, inner product and outer product, as shown in the Figure.The cement grain dissolves and the hydration products are generated gradually during the hydration process, which yields expansion and layer thickness change of the cement particle, as shown in the Figure. The amount of unhydrated cement is decreasing, while inner product and outer product are being produced.

Hydration of a single cement particle

The initial microstructure of cement paste can be created by parking multiple spherical particles into an empty container, as shown in Figure (a). The microstructures at the curing ages of 28 days and 365 days are shown in Figure (b) and (c) respectively, the corresponding degrees of hydration are 69% and 88 %. Periodic material boundary conditions apply.

Microstructures of cement paste at different degrees of hydration

The cement paste of curing age 28 days is usually of interest, as the strength at 28 days is commonly used in many structural design codes, hence the microstructure in above Figure is converted to a voxel-based digital image, as shown in the following Figure. It can be decomposed to four phases, including a pore phase, and three solid phases namely unhydrated cement, inner product, and outer product.

Voxel-based image of the microstructure of cement paste (100 µm X 100 µm X 100 µm)

Individual phases of the microstructure of cement paste.

The volume percentage of every individual phase is indicated in the note.

Computational multiscale modeling approach and its integration with experimental materials characterization

This aim can only be achieved by developing new methods for the simulation of the onset of the initiation propagation and coalescence of cracks in the structure. The project’s objectives are as follows:

• Predict the roughness of the surface obtained by the cracking process

• Accurately predict the initiation of the micro cracks (nucleation point, direction)

• Accurately predict the multiple micro crack paths until coalescence

• Explain the deviation of the crack inside the bulk of the material as a function of material and interfacial properties

Project related with the Petroleum industry:

Investigate and analyze downhole tool dynamics and the associated failures.

Specifically working on the following 3 topics:

• Evaluation of various crack growth rules, and their effects on fluid flow in fractured porous media,

• Probabilistic analysis of stochastic loading,

• Assessment of the effect of variability in material properties on structural durability using the Finite Element Method.

[1] Klaas van Breugel. Simulation of Hydration and Formation of Structure in Hardening Cement-based Materials. PhD thesis, Delft University of Technology, 1997. 2nd edition. 26, 69

[2] D.P. Bentz. CEMHYD3D: A Three-Dimensional Cement Hydration and Microstructure Development Modeling Package. Version 3.0. NISTIR 7232. Interagency report, National Institute of Standards and Technology, June 2005. 69

[3] Shashank Bishnoi and Karen L. Scrivener. Mic: A new platform for modelling the hydration of cements. Cement and Concrete Research, 39(4):266-274, 2009. 69