M Scale Cement
Multi Scale Cement ICME Project
Ultra-High Performance Concrete (UHPC) is a class of concrete that can provide superior performance versus normal strength Portland cement concretes. UHPCs are a family of materials that typically exhibit compressive strengths in excess of 21,000 psi (150 MPa) and high durability due to negligible interconnected porosity. They are a highly heterogeneous material with a w/cm lower than 0.30 and a microstructure consisting of hydrated cement paste, unhydrated cement grains, fine aggregates, pores ranging from nanometers to millimeters in size, and potentially steel and/or polymer fibers . Experimentally, concrete is generally quantified on the macro scale (i.e. Unconfined Compressive Strength, Flexural Strength, etc.) with minimal characterization, as classical methods to characterize at the lower length scales are difficult. As UHPCs become more widely used within the civil and military infrastructures it has become increasingly important to develop and validate multi-scale models to accurately assist for the design and optimization of UHPC structures to survive long term and dynamic events when given a particular set of constituent materials.
When considering UHPCs at the macro scale the mechanical properties (both dynamic and quasi-static) and loading conditions are of interest. Ellis and McDowell  concluded that at this, “structural,” scale combinations of panel thickness, quasi-static fiber-reinforced tensile strength, and dissipated energy density could change the response of the UHPC system from brittle to ductile. Type, size, shape, and volume fraction of fiber reinforcement greatly influences tensile and flexural strength , while the cementitious matrix controls most other properties such as the young’s moduli, compressive strength, void volume fraction, and porosity.
Ellis and McDowell looked at modeling of UHPCs with fibers at three scales; “structural,” “multi-fiber,” and “single-fiber”. These for information regarding multiple fiber interaction within a UHPC we look to the continuum “multi-fiber” scale, while relying on the meso scale “single-fiber” for the material/physical properties of the fiber, Inerfacial Transition Zones (ITZ), and cementitious matrix. However, affective for their purpose, this approach does not fully encompass the complex microstructure of the UHPC cementitious matrix.
At the multiple fiber length scale information relating to the fiber volume fraction and fiber orientation relative to a predefined crack plane can be passed up to the macro-scale. Information regarding the fiber, Interfacial Transition Zone (ITZ) and plastic deformation due to granular flow of the ITZ and matrix must be received from the single fiber or meso scale. Fiber interaction with crack propagation can be observed at this level. Kumaresan  demonstrated modeling success of UHPC crack propagation using lattice models. Also, information regarding volume fractions, porosity, and surface area of the aggregate are supplied from the meso scale.
Similar to the macro scale the continuum scale needs information regarding the young’s and bulk moduli and other yield stresses is required. The bonding strength between each phase is required too. Simulations in DFT and Molecular Dynamics at the micro and nano scales can supply this.
Void volume fractions are often observed at the meso scale. These sites can have great influence on crack nucleation. Pore structure is highly related to the degree of hydration. In UHPCs the degree of hydration is driven by the formation of Calcium Silicate Hydrate (CSH) created during cement hydration and the pozzolanic reaction of Calcium Hydroxide with Silica Fume. Hydration phenomena occur at the microscale.
Other crack nucleation sites that are seen on this scale are in the ITZ between the hydrated cement paste and aggregates and fiber reinforcement. The dissipation mechanisms at the single fiber level include the deformation of the fiber, friction at the fiber-ITZ interface, and plastic deformation due to granular flow of the ITZ and matrix. Fiber morphology influences the resistance of fibers against pullout from the cementitious matrix .
Hydration occurs at the micro scale. The w/cm, Ca/Si ratios, age, and use of additives are inputs necessary for hydration models. These models are able to generate void volume fraction and porosity to supply the meso scale, but are also able to predict a proposed crystal structure of the CSH hydration products. To account for detrimental actions during hydration such as thermal cracking the thermal diffusion coefficients must be acquired from the nano scale.
At this scale DFT can be used to calculate bond strength between the solid phases, which can supply the moduli to the continuum and macro scales. Molecular Dynamic Simulations and Energy Minimization are able to calculate diffusion coefficients.
 Moser, R. D., P. G. Allison, and M. Q. Chandler. "Characterization of Impact Damage in Ultra-High Performance Concrete Using Spatially Correlated Nanoindentation/SEM/EDX." Journal of Materials Engineering and Performance 22.12 (2013): 3902-908. Web.
 Ellis, Brett D., and David L. McDowell. Multiscale Modeling and Design of Ultra-high-performance Concrete. Diss. Mechanical Engineering, Georgia Institute of Technology, 2013. N.p.: n.p., n.d. Print.
 Scott, D., Long, W., Green, B., Moser, R., Williams, B., O’Daniel, J. “Impact of Steel Fiber Size and Shape on the Mechanical Properties of Ultra-‐High Performance Concrete;” ERDC Technical Report; to Be Published 2015;
 Kumaresan, Karthik. Ultra-high Performance Concrete and Lattice Models. Thesis. Virginia Polytechnic Institute and State University, 2011. N.p.: n.p., n.d. Print.