Ceramics can be defined as inorganic crystalline materials. Advanced ceramics are materials made by refining naturally occurring ceramics and other special processes. Advanced ceramics are used in substrates that house computer chips, sensors, and actuators, capacitors, wireless communications, spark plugs, inductors, and electrical insulation.  New processing techniques make ceramics sufficiently resistant to fracture that they can be used in load-bearing applications. Ceramics have exceptional strength under compression.
In ceramic materials, the ionic or covalent bonds permit little or no slip. Consequently, failure is a result of brittle fracture. Most crystalline ceramics fail by cleavage along widely space, closely packed planes. The fracture surface typically is smooth and frequently no characteristic surface features point to the origin of the fracture. The tensile and flexural strength values have considerable variation since the strength of ceramics is dependent on the distribution of flaw sizes and is not affected by dislocation motion. On the contrary to popular belief, ceramics are not always brittle. At low strain rates and at high temperatures, many ceramics with a very fine grain size show superplastic behavior.
The average grain size is often closely related to the primary particle size. An exception to this is if there is grain growth due to long sintering time or exaggerated or abnormal grain growth. Typically, ceramics with a small grain size are stronger than coarse-grained ceramics. Finer grain sizes help minimize stresses that develop at grain boundaries due to anisotropic expansion and contraction.
Pores represent the most important defect in polycrystalline ceramics. The presence of pores is usually detrimental to the mechanical properties of bulk ceramics, since pores provide a pre-existing location from which a crack can grow. The presence of pores is one of the reasons why ceramics show such brittle behavior under tensile loading. Since there is a distribution of pore sizes and the overall level of porosity changes, the mechanical properties of ceramics vary.
Multiscale modeling of ceramics can provide valuable tools to understand the mechanics and physics of the brittle material inelastic response. Experimental observations at each of the spatiotemporal scales can be used for validation of the computational models developed at that scale. The computational modeling linkage from the atomistic to the continuum scales of homogeneous and discrete deformation mechanisms (twinning, cleavage, micro-cracking, stacking faults, et cetera), nano- and microstructure and defects. to dynamic failure processes in brittle materials should provide pathways to designing improved mechanical performance through controlled processing.
The computational bridge between the atomistic and continuum length scales is addressed in a hierarchical fashion through development of:
1) a first principles unit cell model to predict the anisotropic elastic properties,
2) a classical molecular dynamics model through period replication of the unit cell model for the study of single crystal slip and twinning dynamics,
3) a single crystal anisotropic plasticity model to account for the kinematics of crystal slip and twinning mechanisms,
4) a mesoscopic polycrystalline computational finite element model that incorporates single crystal deformation kinematics, and explicitly includes microcracks that are represented on the grain boundaries using cohesive interface laws that allow investigation of crack nucleation, growth, and coalescence, and
5) a continuum computational finite element model with the particular challenge of development of algorithms for transitioning microcrack coalescence behavior at the mesoscale to the continuum.
A multiscale constitutive and failure model for A1ON that illustrates the spatiotemporal dependence of the scales