We model grain level phenomena linked with contact driven mechanical deformation. The three key phenomena being modeled are microstructure evolution, elasto-plastic deformation of the multi-grain aggregates, and contact modeling of the interface friction.

In collaboration with Prof. Izabela Szlufarska (MSE). Funded by ARO.

Seashells are an important model system for understanding mechano-morphological basis of the evolution of exoskeleton in invertebrates. In this work, we study the effect of mantle geometry, growth rate and calcification rate on the resulting elastic deformation modes. Connections are made to a variety of antimarginal and commarginal ornamentations, including complex patterns like hierarchical buckling and folding back modes.

In collaboration with Derek Moulton (Oxford), Alain Goriely (Oxford) and Krishna Garikipati (UM).

We present a phenomenological treatment of diffusion driven martensitic phase transformations in multi-component crystalline solids that arise from non-convex free energies in mechanical and chemical variables. The treatment describes diffusional phase transformations that are accompanied by symmetry-breaking structural changes of the crystal unit cell and reveals the importance of a mechanochemical spinodal, defined as the region in strain–composition space, where the free-energy density function is non-convex. The approach is relevant to phase transformations wherein the structural order parameters can be expressed as linear combinations of strains relative to a high-symmetry reference crystal. Specifically, phase transformations in shape memory alloys, electrode materials for Li-ion batteries and certain high-temperature ceramics are of interest.

In collaboration with Krishna Garikipati (UM) and Anton Van der Ven (UCSB).

*S. Rudraraju*, A van der Ven, K. Garikipati,
``Mechano-chemical spinodal decomposition: A phenomenological theory of phase transformations in multi-component, crystalline solids'',
Nature npj Computational Materials, 2016, doi:10.1038/npjcompumats.2016.12.
[journal]
[arXiv]

Cubic spinel LiTiO is a promising electrode material because it exhibits a high lithium diffusivity and undergoes minimal changes in lattice parameters during lithiation and delithiation, thereby ensuring favorable cyclability. This work is a multiphysics and multiscale study of LiTiO that combines first-principles computations of thermodynamic and kinetic properties with continuum scale modeling of lithiation−delithiation kinetics. Several case studies explore the temporal evolution of peak stresses and the potential for crack initiation, during lithiation and delithiation.

In collaboration with Krishna Garikipati (UM) and Michael Falk (JHU).

T. Jiang, *S. Rudraraju*, A. Roy, A. Van der Ven, K. Garikipati, M. L. Falk, ``Multi-physics simulations of lithiation-induced stress in LiTiO electrode particles'', Journal of Physical Chemistry C, 2016, [journal] [arXiv]

Classical elasticity is scale invariant: it does not admit length scales intrinsic to the material. The only length scale which may manifest itself arises from the problem geometry. However, real materials do posses intrinsic length scales (i.e., interatomic distance, dislocation cells, grain sizes, etc). If the deformation varies on these scales, size effects may arise. One framework that is appropriate for treating such problems is the strain gradient formulation of elasticity. We have developed a comprehensive numerical framework for Toupin’s theory of nonlinear gradient elasticity and obtained the first complete three-dimensional numerical solutions to a broad range of boundary value problems in gradient elasticity at finite strain. The governing equation is a fourth order partial differential equation with complex boundary conditions. Studies conducted using the framework include gradient length scale effects on microscale/nanoscale structural problems, regularization of crack tip solutions and modeling of mechanically induced microstructure.

In collaboration with Krishna Garikipati (UM) and Anton Van der Ven (UCSB).

*S. Rudraraju*, A van der Ven, K. Garikipati,
``Three-dimensional iso-geometric solutions to general boundary value problems of Toupin's gradient elasticity theory at finite strains'', Computer Methods in Applied Mechanics and Engineering (CMAME), Vol 278, Pages 705-728, 2014. [journal][arXiv]

Z. Wang, *S. Rudraraju*, K. Garikipati,``A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains'', Journal of the Mechanics and Physics of Solids (JMPS), Vol. 94: 336-361, 2016, doi:10.1016/j.jmps.2016.03.028.[journal][arXiv]

The dynamical processes of chemistry, transport and mechanics that govern tumor growth can be broadly classified into three distinct spatial scales: the tumor scale, the cell-extracellular matrix (ECM) interactions and the sub-cellular processes. In this work, we focus on tumor scale investigations, and model the emergent morphology of tumors to gain system-level insights into their progression. The evolution of various constituents (cancer cells, stem cells, necrotic cells, nutrients, byproducts, etc) is modelled with reaction-advection-diffusion equations coupled with finite strain mechanics.

In collaboration with Kristen Mills (Max Planck Institute for Intelligent Systems, now at RPI), Ralf Kemkemer (Max Planck Institute for Intelligent Systems) and Krishna Garikipati (UM)

*S. Rudraraju*, K.L.Mills, R Kemkemer, K. Garikipati,
``Multiphysics Modeling of Reactions, Mass Transport and Mechanics of Tumor Growth''
Computer Models in Biomechanics, Pages 293-303, 2013.
[journal]

K.L.Mills, R Kemkemer, *S. Rudraraju*, K. Garikipati,
``Elastic free energy drives the shape of prevascular solid tumors'',
PLoS ONE, 9(7), 2014.
[journal]
[arXiv]