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About Karan S. Surana's Research

sorem Deane E. Ackers Distinguished Professor
(Ph. D., Wisconsin)
3138 Learned Hall
Phone: (785) 864-2988
Continuum Mechanics, Computational Mathematics, Computational Mechanics, Finite Element Methods and Software

Research Interests

Continuum Mechanics:

Classical and non-classical continuum theories, associated thermodynamic frameworks, and ordered rate constitutive theories for compressible and incompressible solid and fluent continua.  Finite deformation internal polar continuum theories and associated constitutive theories for solid continua. Classical and non-classical mixture theories for fluid-fluid and fluid-solid mixtures, associated constitutive theories, and determination of mixture transport properties. Determination of material coefficients in higher order rate constitutive theories in classical and non-classical continuum theories. Applications of new continuum theories. Mathematical models for fluid-solid interaction physics for stationary and time dependent processes.

Computational Mathematics and Computational Mechanics:

Computational mathematics and computational mechanics research leading to development of computational methods and techniques, formulations, algorithms, software systems, and software engineering for boundary value problems (BVPs) and initial value problems (IVPs) describing steady or stationary, transient, and unsteady processes. Operator classification, methods of approximation, and unconditionally stable finite element computational processes for BVPs and IVPs in h,p,k – framework.  Higher order global differentiability approximations, convergence rates, error computation, error estimation, adaptive and self-adaptive computational processes for BVPs and IVPs.  The specific areas of research in computational mathematics and computational mechanics are:

  • Computational fluid dynamics: Incompressible Newtonian and generalized Newtonian fluid flows.  High speed compressible flows including high pressure, high temperature gas dynamics with real gas models and variable transport properties, flows of polymeric viscoelastic fluids using various constitutive models (Maxwell, Oldroyd, Giesekus, PTT, etc.).
  • Solid mechanics, composite mechanics, and viscoelastic solids: Development of computational techniques in solid mechanics, structural mechanics, composite mechanics, and viscoelastic solid mechanics with and without memory. Delamination, free edge effects, interlamina behavior, damping assessment, and damage mechanics in composites.  Impact and wave propagation.  Finite deformation of solids.  Fluid-solid interaction.


Computational Mechanics Laboratory

The Computational Mechanics Laboratory (CML) is the focal point of computational mechanics research and development in linear and non-linear solid mechanics (elastic solids with and without dissipation and memory), structural mechanics, composite mechanics, fluid dynamics (Newtonian, generalized Newtonian, and viscoelastic fluids, error estimation, h,p,k – adaptive methods, numerical simulation of moving fronts such as: elastic and inelastic wave propagation, in isotropic, orthotropic, and composite materials, acoustic waves, low speed and high speed compressible flows, reacting flows, phase transition, mixture theories, and fluid-solid interaction.

Various research and development activities in the Laboratory foster new theories, methodologies, innovative formulations and concepts, and algorithms in computational mathematics and mechanics that are primarily focused in the Finite element area.

The nature of the Laboratory, breadth of various diverse research activities, expertise of the individuals involved, availability of up-to-date computing facilities and many software tools provide an attractive, conducive, and efficient environment for research and development in various areas of computational mechanics.

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