# K. S. SuranaUniversity of Kansas | KU · Department of Mechanical Engineering

K. S. Surana

BE , MS , Ph.D.

## About

241

Publications

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Introduction

K. S. Surana currently is University Distinguished Professor at the Department of Mechanical Engineering, University of Kansas.
His research areas include Computational Mathematics, Computational Mechanics, Continuum Mechanics, both Classical and Non_Classical Theories including constitutive theories.
Most recent research publications are in Non_Classical Continuum theories for solid and fluent Continua and their applications.

## Publications

Publications (241)

The paper presents k-version of the finite element method for boundary value problems (BVPs) and initial value problems (IVPs) in which global differentiability of approximations is always the result of the union of local approximations. The higher order global differentiability approximations (HGDA/DG) are always p-version hierarchical that permit...

The work presented in a recent paper by the authors [35] for a thermodynamically consistent and kinematic assumption free plate and shell formulation for small deformation and small strain based on the conservation and balance laws of classical continuum mechanics (CCM) is extended here for non-classical continuum mechanics (NCCM). This formulation...

This paper presents a thermodynamically consistent and kinematic assumption free formulation for dynamics of thermoviscoelastic plates/shells based on the conservation and balance laws of classical continuum mechanics (CCM) in which dissipation mechanism has been incorporated through ordered rate constitutive theory for deviatoric stress tensor. In...

In this work, we demonstrate the existence of rotational waves in deforming thermoelastic non-classical solid continua in which the conservation and balance laws consider internal rotations due to the deformation gradient tensor (Jacobian of deformation) as well as their time varying rates. In this non-classical continuum theory, time dependent def...

This paper considers dynamic behavior of non-classical thermoelastic solid continua. The mathematical model consists of the conservation and balance laws of non-classical continuum mechanics that incorporates additional physics of internal rotations arising due to deformation gradient tensor. We consider plane stress behavior with small deformation...

This paper presents a kinematic assumption free and thermodynamically consistent non-linear formulation incorporating finite strain and finite deformation for thermoviscoelastic plates/shells based on the conservation and balance laws of the classical continuum mechanics (CCM) in R3 (see Surana and Mathi, (2020) for linear theory). The conservation...

The work presented in this paper extends the kinematic assumption free and thermodynamically consistent formulation for bending of thermoelastic beams presented by Surana et al. for bending of thermoviscoelastic beams with dissipation mechanism without memory. We consider small strain, small deformation physics in Lagrangian description. Conservati...

This paper considers non-classical continuum theory for thermoviscous fluids without memory incorporating internal rotation rates resulting from the antisymmetric part of the velocity gradient tensor to derive ordered rate constitutive theories for the Cauchy stress and the Cauchy moment tensor based on entropy inequality and representation theorem...

In order to enhance currently used beam theories in \(\mathbb {R}^2\) and \(\mathbb {R}^3\) to include mechanisms of dissipation and memory, it is necessary to establish if the mathematical models for these theories can be derived using the conservation and the balance laws of continuum mechanics in conjunction with the corresponding kinematic assu...

This paper considers conservation and balance laws for non-classical solid continua in the presence of internal rotations (iΘ) due to the Jacobian of deformation and Cosserat rotations (eΘ) at each material point. In these balance laws, internal rotations are completely defined as functions of the displacement gradient tensor, but Cosserat rotation...

A nonclassical internal polar continuum theory for finite deformation and finite strain for isotropic, homogeneous compressible and incompressible solids is presented in this paper. Since the Jacobian of deformation J is a fundamental measure of deformation in solid continua, J in its entirety must be incorporated in the thermodynamic framework. Po...

This paper presents the effects of non-classical kinematic measures in continuum mechanics on common failure theories. Internal polar and Cosserat continuum theories introduce rotations as kinematic variables, in addition to the classical translations. The inclusion of these additional measures of deformation results in new stress, strain, and stra...

This paper presents two specific thermodynamically consistent non-classical continuum theories for solid and fluent continua. The first non-classical continuum theory for solid continua incorporates Jacobian of deformation in its entirety in the conservation and the balance laws and the derivation of the constitutive theories. The second non-classi...

Classical Continuum Mechanics

The work in this paper is based on a non-classical continuum theory in the Lagrangian description for thermoviscoelastic solids without memory in which the conservation and balance laws are derived by incorporating internal rotations arising from the Jacobian of deformation, as well as Cosserat rotations at a material point. Such non-classical soli...

This paper presents constitutive theories for non-classical thermoviscoelastic solids with dissipation and memory using thermodynamic framework based on entirety of the displacement gradient tensor. Thus, the conservation and the balance laws used in this work incorporate symmetric as well as antisymmetric parts of the displacement gradient tensor....

In the non-classical theories for fluent continua, the presence of internal rotation rates and their gradients arising due to the velocity gradient tensor necessitate existence of moment tensor. The Cauchy moment tensor acting on the faces of the deformed tetrahedron (derived using Cauchy principle) and the gradients of the rates of total rotations...

In the non-classical continuum theories for solid continua the presence of internal rotations and their gradients arising due to Jacobian of deformation and/or consideration of Cosserat rotations as additional unknown degrees of freedom at a material point necessitate existence of moment tensor. For small deformation, small strains theories, in Lag...

This paper considers conservation and balance laws for non-classical fluent continua in the presence of internal rotation rates due to the velocity gradient tensor and the rotation rates due to Cosserat rotations. In these balance laws, the internal rotation rates are completely defined as functions of the velocity gradient tensor, but the Cosserat...

For thermoelastic solids, rate of mechanical work equilibrates with the rate of kinetic energy and rate of strain energy. In this article, this aspect of the physics is utilized to: (i) derive an alternate form of the energy equation based on the first law of thermodynamics and (ii) derive an alternate form of entropy inequality based on the second...

This paper considers conservation and balance laws and the constitutive theories for non-classical viscous fluent continua without memory, in which internal rotation rates due to the velocity gradient tensor are incorporated in the thermodynamic framework. The constitutive theories for the deviatoric part of the symmetric Cauchy stress tensor and t...

If the deforming matter is to be in thermodynamic equilibrium, then all constitutive theories, including those for heat vector, must satisfy conservation and balance laws. It is well known that only the second law of thermodynamics provides possible conditions or mechanisms for deriving constitutive theories, but the constitutive theories so derive...

This paper presents a non-classical continuum theory for fluent continua in which the conservation and balance laws are derived by incorporating both internal rotation rates arising from the velocity gradient tensor and the rotation rates of the Cosserats. Specifically, in this non-classical continuum theory we have (1) the usual velocities ((Formu...

Unlike most finite element books that cover time dependent processes (IVPs) in a cursory manner, The Finite Element Method for Initial Value Problems: Mathematics and Computations focuses on the mathematical details as well as applications of space-time coupled and space-time decoupled finite element methods for IVPs. Space-time operator classifica...

A non-classical internal polar continuum theory for finite deformation and finite strain for isotropic, homogeneous compressible and incompressible solids is presented in this paper. Since the Jacobian of deformation J is a fundamental measure of deformation in solid continua, J in its entirety must be incorporated in the thermodynamic framework. P...

Newton's law of visocosity is a commonly used constitutive theory for deviatoric Cauchy stress tensor. In this constitutive theory originally constructed based on experimental observation, the deviatoric Cauchy stress is proportional to the symmetric part of the velocity gradient tensor. The constant of proportionality is the viscosity of the fluid...

This paper presents a non-classical continuum theory in Lagrangian description for solids in which the conservation and the balance laws are derived by incorporating both the internal rotations arising from the Jacobian of deformation and the rotations of Cosserat theories at a material point. In particular, in this non-classical continuum theory,...

If the deforming matter is to be in thermodynamic equilibrium, then all constitutive theories, including those for heat vector, must satisfy conservation and balance laws. It is well known that only the second law of thermodynamics provides possible conditions or mechanisms for deriving constitutive theories, but the constitutive theories so derive...

Various approaches used currently for fluid-solid interaction problems are considered and evaluated. The validity of the associated mathematical models is established based on consistency in the use of basic thermodynamic principles for continuous media and whether interaction physics is inherent in the mathematical models or are created externally...

Written by two well-respected experts in the field, The Finite Element Method for Boundary Value Problems: Mathematics and Computations bridges the gap between applied mathematics and application-oriented computational studies using FEM. Mathematically rigorous, the FEM is presented as a method of approximation for differential operators that are m...

For thermoelastic solids, rate of mechanical work equilibrates with the rate of kinetic energy and rate of strain energy. In this article, this aspect of the physics is utilized to: (i) derive an alternate form of the energy equation based on the first law of thermodynamics and (ii) derive an alternate form of entropy inequality based on the second...

Explore the Computational Methods and Mathematical Models That Are Possible through Continuum Mechanics Formulations Mathematically demanding, but also rigorous, precise, and written using very clear language, Advanced Mechanics of Continua provides a thorough understanding of continuum mechanics. This book explores the foundation of continuum mech...

Polar decomposition of the changing velocity gradient tensor in a deforming fluent continua into pure stretch rates and rates of rotations shows that a location and its neighboring locations can experience different rates of rotations during evolution. Alternatively, we can also consider decomposition of the velocity gradient tensor into symmetric...

The Jacobian of deformation at a material point can be decomposed into the stretch tensor and the rotation tensor. Thus, varying Jacobians of deformation at the neighboring material points in the deforming volume of solid continua would yield varying stretch and rotation tensors at the material points. Measures of strain, such as Green's strain, at...

This paper presents numerical simulations of liquid-solid and solid-liquid phase change processes using mathematical models in Lagrangian and Eulerian descriptions. The mathematical models are derived by assuming a smooth interface or transition region be-tween the solid and liquid phases in which the specific heat, density, thermal conductivity, a...

This work considers initiation of nonlinear waves, their propagation, reflection, and their interactions in thermoelastic solids and thermoviscoelastic solids with and without memory. The conservation and balance laws constituting the mathematical models as well as the constitutive theories are derived for finite deformation and finite strain using...

This article presents constitutive theories for the stress tensor and the heat vector for homogeneous, isotropic thermoelastic solids in Lagrangian description for finite deformation. The deforming solid is assumed to be in thermodynamic equilibrium during the evolution. Since conservation of mass, balance of momenta, and balance of energy are inde...

This paper considers various approaches used currently for the fluid–solid interaction problem and associated computational methodologies. The validity of the mathematical models for fluid–solid interaction is established based on the consistency in the use of continuum mechanics principles and whether the interaction between the solid and the flui...

This paper presents numerical simulation of the evolution of one-dimensional normal shocks, their propagation, reflection and interaction in air using a single diaphragm Riemann shock tube and validate them using experimental results. Mathematical model is derived for one-dimensional compressible flow of viscous and conducting medium. Dimensionless...

This paper presents numerical simulations of liquid-solid and solid-liquid phase change processes using mathematical models in Lagrangian and Eulerian descriptions. The mathematical models are derived by assuming a smooth interface or transition region between the solid and liquid phases in which the specific heat, density, thermal conductivity, an...

The paper presents rate constitutive theories for finite deformation of homogeneous, isotropic, compressible, and incompressible thermoviscoelastic solids without memory in Lagrangian description derived using the second law of thermodynamics expressed in terms of Gibbs potential Ψ. To ensure thermodynamic equilibrium during evolution, the rate con...

This paper presents derivation of Giesekus constitutive model in Eulerian description based on ordered rate constitutive theories for thermoviscoelastic fluids for compressible and incompressible cases in contra-, co-variant and Jaumann bases. The ordered rate constitutive theories for thermoviscoelastic fluids of orders (m, n) consider convected t...

This paper presents ordered rate constitutive theories in Lagrangian description for compressible as well as incompressible homogeneous, isotropic thermoviscoelastic solids without memory in which the deviatoric stress tensor and heat vector as dependent variables in the constitutive theories are functions of temperature, temperature gradient, and...

The paper considers developments of constitutive theories in Eulerian description for compressible as well as incompressible ordered homogeneous and isotropic thermofluids in which the deviatoric Cauchy stress tensor and the heat vector are functions of density, temperature, temperature gradient, and the convected time derivatives of the strain ten...

This paper presents constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential. Since conservation of mass, balance of momenta and the energy equation are independent of the constitution of the matter, the second law of thermodynamics, that is, entropy inequality, must...

This paper presents development of rate constitutive theories for compressible as well as in incompressible ordered thermoviscoelastic fluids, i.e., polymeric fluids in Eulerian description. The polymeric fluids in this paper are considered as ordered thermoviscoelastic fluids in which the stress rate of a desired order, i.e., the convected time de...

This paper presents constitutive theories for finite deformation of homogeneous, isotropic thermoelastic solids in Lagrangian description using Gibbs potential. Since conservation ofmass, balance ofmomenta and the energy equation are independent of the constitution of the matter, the second law of thermodynamics, that is, entropy inequality, must f...

This work presents the development of mathematical models based on conservation laws for a saturated mixture of ν homogeneous, isotropic, and incompressible constituents for isothermal flows. The constituents and the mixture are assumed to be Newtonian or generalized Newtonian fluids. Power law and Carreau–Yasuda models are considered for generaliz...

This paper presents numerical computations of evolutions described by the initial value problems (IVPs) in isothermal incompressible viscous and viscoelastic flows in open domains using space-time finite element model in hpk framework with space-time variationally consistent (STVC) integral forms. The mathematical models for viscous and viscoelasti...

This paper considers multi-media interaction processes in which the interacting media are incompressible elastic solids and incompressible liquids such as Newtonian fluids, generalized Newtonian fluids, dilute polymeric liquids described by Maxwell, and Oldroyd-B models or dense polymeric liquids with Giesekus constitutive model. The mathematical m...

When the mathematical models for the deforming solids are constructed using the Eulerian description, the material particle displacements and hence the strain measures are not known. In such cases the constitutive theory must utilize convected time derivatives of the strain measures. The entropy inequality provides a mechanism for determining const...

When the mathematical models for the deforming solids are constructed using Eulerian description, the material particle displacements and the strain measures are not known. Thus the constitutive theories for elastic solid matter based on Eulerian strain measures are not usable. In such cases the constitutive theory must utilize convected time deriv...

Purpose – Most studies of power-law fluids are carried out using stress-based system of Navier-Stokes equations; and least-squares finite element models for vorticity-based equations of power-law fluids have not been explored yet. Also, there has been no study of the weak-form Galerkin formulation using the reduced integration penalty method (RIP)...

This research considers developments of constitutive theory for compressible as well as incompressible ordered homogeneous and isotropic thermofluids in which the deviatoric Cauchy stress tensor and the heat vector are functions of density, temperature, temperature gradient and the convected time derivatives of the strain tensors of up to a desired...

The present study considers mathematical classification of the time differential operators and then applies methods of approximation in time such as Galerkin method (GM), Galerkin method with weak form (/ GM WF), Petrov-Galerkin method (PGM), weighted residual method (WRY), and least squares method or process (LSM or LSP) to construct finite elemen...

This paper presents development of mathematical models for multi-physics interaction processes in which the physics of solids, liquids and gases are described using conservation laws, appropriate constitutive equations and equations of state in Eulerian description. The use of conservation laws in Eulerian description for all media of an interactio...

The rate constitutive equations based on upper convected, lower convected, Jaumann, Truesdell and Green–Naghdi stress rates, etc. [1, 2, 3, 4, 5, 6, 7, 8, 9, 10] have been used for the solid matter and polymeric liquids when the mathematical models are derived employing conservation laws in the Eulerian description. The rate constitutive equations...

In this research, the rate constitutive theories for ordered thermoviscous fluids, ordered thermoelastic solids and ordered thermoviscoelastic polymeric fluids in contra- and co-variant bases are developed. Such theories are necessitated when the mathematical models of the deforming matter are derived using the Eulerian description. In each case, t...

This paper presents numerical solutions of boundary value problems (BVPs) for 1-D and 2-D polymer flows using the Giesekus constitutive model in the hpk mathematical and finite element (FE) computational framework utilizing variationally consistent (VC) integral forms. In the mathematical framework used here, h , the characteristic length, p , the...