Kentucky Random Structures Toolkit (KRaSTk)

KRaSTk is a software package for generating and computing properties of sets of model representative volume elements (mRVEs) constructed from geometric seed descriptions tuned to represent complex or randomly structured materials.

KRaSTk is developed and maintained by the Beck Research Group.

To collaborate with the Beck Group in developing or applying KRaSTk, please email Dr. Beck.

The “Random Structures” Problem

Computational modeling has had a dramatic impact on our understanding of and ability to design, fabricate, and process many engineering materials. Continuum methods allow us to model materials that can be describe in terms of uniform regions, while atomistic or particle-based methods allow us to model the behavior of materials at the level of atoms or molecules. In addition, nearly all computational methods focus on modeling either periodic materials, or materials whose behavior can be deduced from studying small “representative volumes” of the bulk material.

Increasingly, though, the forefront of materials research is focusing on materials with complex mesoscale structures: nano crystalline multi-phase alloys, additive manufactured allows with complex microstructures, porous materials constructed from fibers or particles, composite materials with complex and critical interface structures. All of these materials are characterized by internal structures that cannot be represented by a uniform field, and for which there is no single small representative volume.

KRaSTk: Physics-based stochastic sampling of properties in complex and/or randomly structured materials.

Computational Stochastic Sampling

To address this limitation on computational modeling the Beck Group has developed the Kentucky Random Structures Toolkit (KRaSTk), which enables stochastic sampling of local materials properties, and the calculation of effective bulk properties for complex or randomly structured materials.

KRaSTk is under rapid and continuing development. The Beck Group is actively seeking collaborators with whom to partner to demonstrate, validate, and extend the capabilities of KRaSTk.

If you are interested in collaborating with the Beck Group, please email Dr. Beck!


  • M.N. Seif, D.J. Richardson, K.M. Moody, M. Martin, M. Turner, S.W. Mays, T.J. Balk, M.J. Beck. Stochastic approach for determining properties of randomly structured materials: Effects of network connectivity. Acta Materialia (2021): 117382
  • M.N. Seif, J. Puppo, M. Zlatinov, D. Schaffarzick, A. Martin, M.J. Beck. Stochastic mechanical modeling of Duocel foam from micro-to macro-length scales. In AIAA SCITECH 2022 Forum, 2022.

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