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Non-classical continuum theories for solid and fluent continua and some applications

International Journal of smart and Nano Materials 2019年第1期10卷 28-89,I0003页

作者： k.s.surana D.Mysore J.N.Reddy Mechanical Engineering University of KansasLawrenceKSUSA Mechanical Engineering Texas A&M UniversityCollege StationTXUSA

This paper presents two specific thermodynamically consistent nonclassical continuum theories for solid and fluent *** 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 *** second non-classical continuum theory for solid continua considers Jacobian of deformation in its entirety as well as the Cosserat rotations in the conservation and balance laws as well as the constitutive *** first non-classical continuum theory for fluent continua presented here considers velocity gradient tensor in its *** second non-classical continuum theory for fluent continua considers velocity gradient tensor in its entirety as well as Cosserat rotation rates in the derivation of the conservation and balance laws and the constitutive *** the non-classical continuum theories for solid and fluent continua considered here incorporate additional physics of deformation due to rotations and rotation rates compared to classical continuum mechanics,the conservation and balance laws of classical continuum mechanics are shown to require modification as well as a new balance law balance of moment of moments is required to accommodate the new physics due to rotations and rotation ***’s micropolar,micromorphic and microstretch theories,couple stress theories and nonlocal theories are also discussed within the context of the non-classical theories presented here for solid and fluent *** applications of these theories are also discussed.

关键词： Non-classical continuum theories micropolar Jacobian of deformation internal rotations Cosserat rotations Cosserat rotation rates

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Finite Deformation, Finite strain Nonlinear Dynamics and Dynamic Bifurcation in TVE solids with Rheology

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Applied Mathematics 2024年第1期15卷 108-168页

作者： karan s. surana sri sai Charan Mathi Department of Mechanical Engineering University of Kansas Lawrence US

This paper presents a mathematical model consisting of conservation and balance laws (CBL) of classical continuum mechanics (CCM) and ordered rate constitutive theories in Lagrangian description derived using entropy inequality and the representation theorem for thermoviscoelastic solids (TVEs) with rheology. The CBL and the constitutive theories take into account finite deformation and finite strain deformation physics and are based on contravariant deviatoric second Piola-kirchhoff stress tensor and its work conjugate covariant Green’s strain tensor and their material derivatives of up to order m and n respectively. All published works on nonlinear dynamics of TVEs with rheology are mostly based on phenomenological mathematical models. In rare instances, some aspects of CBL are used but are incorrectly altered to obtain mass, stiffness and damping matrices using space-time decoupled approaches. In the work presented in this paper, we show that this is not possible using CBL of CCM for TVEs with rheology. Thus, the mathematical models used currently in the published works are not the correct description of the physics of nonlinear dynamics of TVEs with rheology. The mathematical model used in the present work is strictly based on the CBL of CCM and is thermodynamically and mathematically consistent and the space-time coupled finite element methodology used in this work is unconditionally stable and provides solutions with desired accuracy and is ideally suited for nonlinear dynamics of TVEs with memory. The work in this paper is the first presentation of a mathematical model strictly based on CBL of CCM and the solution of the mathematical model is obtained using unconditionally stable space-time coupled computational methodology that provides control over the errors in the evolution. Both space-time coupled and space-time decoupled finite element formulations are considered for obtaining solutions of the IVPs described by the mathematical model and are presented i

关键词： Thermoviscoelasticity Rheology Memory Finite strain Finite Deformation Nonlinear Dynamics Dynamic Bifurcation Ordered Rate Theories

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spectroscopic investigations and luminescence spectra of sm3+ doped soda lime silicate glasses

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Journal of Rare Earths 2009年第5期27卷 773-780页

作者： Y.k. sharma s.s.L. surana R.k. singh Department of Physics Govt. Post Graduate College Rudrapur 263153 (U S Nagar) India Department of Physics J. N. V. University Jodhpur-342001 India Department of Physics Govt. Post Graduate College Rudrapur 263153 (U S Nagar) India

sm3+ doped soda lime silicate glasses co-doped with As2O3 were prepared and characterised by measuring their absorption spectra in UV-VIs/NIR regions and luminescence spectra in the visible region. Judd-Ofelt intensity parameters, Ωλ, were evaluated from the measured intensities of the various absorption bands. Ωλ parameters of these glasses were compared with the Ωλ parameters of other reported sm3+ glasses to study the bonding environment surrounding the sm3+ in the present glasses. Presence of [AsO4]3– tetrahedra in the second coordination sphere around the central sm3+ ion made these glasses less covalent as compared to other oxide glasses but the ratio Ω4/Ω6 of the 1.83 indicated them to be fairly stable. With the help of Ωλ parameters and luminescence data for various emission lines, radiative properties for different emission lines were calculated. The values of radiative properties indicated that 4G5/2→6H7/2 and 4G5/2→6H9/2 transitions responsible for orange luminescence might be used in the development of materials for LED's and other optical devices in the visible region.

关键词： rare earth glasses Judd-Ofelt theory absorption spectroscopy luminescence

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NCCT for Micropolar solid and Fluid Media Based on Internal Rotations and Rotation Rates with Rotational Inertial Physics: Model Problem studies

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Applied Mathematics 2023年第9期14卷 612-651页

作者： karan s. surana Jacob k. kendall school of Mechanical Engineering University of Kansas Lawrence Kansas USA

This paper presents model problem studies for micropolar thermoviscoelastic solids without memory and micropolar thermoviscous fluid using micropolar non-classical continuum theories (NCCT) based on internal rotations and rotation rates in which rotational inertial physics is considered in the derivation of the conservation and balance laws (CBL). The dissipation mechanism is due to strain rates as well as rotation rates. Model problems are designed to demonstrate and illustrate various significant aspects of the micropolar NCCT with rotational inertial physics considered in this paper. In case of micropolar solids, the translational and rotational waves are shown to coexist. In the absence of microconstituents (classical continuum theory, CCT) the internal rotations are a free field, hence have no influence on CCT. Absence of gradients of displacements and strains in micropolar thermoviscous fluid medium prohibits existence of translational waves as well as rotational waves even though the appearance of the mathematical model is analogous to the solids, but in terms of strain rates. It is shown that in case of micropolar thermoviscous fluids the BAM behaves more like time dependent diffusion equation i.e., like heat conduction equation in Lagrangian description. The influence of rotational inertial physics is demonstrated using BLM as well as BAM in the model problem studies.

关键词： Micropolar Internal Rotations Internal Rotation Rates Translational Waves Rotational Waves Dissipation Thermoviscous Rotational Inertial Physics

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Rotational Inertial Physics in Non-Classical Thermoviscous Fluent Continua Incorporating Internal Rotation Rates

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Applied Mathematics 2022年第6期13卷 453-487页

作者： k. s. surana J. k. kendall school of Mechanical Engineering University of Kansas Lawrence Kansas USA

In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, sLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integ

关键词： Non-Classical Continuum Mechanics Internal Rotation Rates Angular Velocities Angular Accelerations Rotational Inertia Balance of Moment of Moments Thermoviscous Fluent Continua

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Flor Revisited(Again):eQTL and Mutational Analysis of NB-LRR Mediated Immunity to Powdery Mildew in Barley

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Journal of Integrative Agriculture 2014年第2期13卷 237-243页

作者： Roger Wise Priyanka surana Greg Fuerst Ruo Xu Divya Mistry Julie Dickerson Dan Nettleton Corn Insects and Crop Genetics Research Unit U.S.Department of Agriculture-Agricultural Research ServiceIowa State UniversityAmesIowa 50011USA Department of Plant Pathology & Microbiology Center for Plant Responses to Environmental StressesIowa State UniversityAmesIowa 50011USA Bioinformatics and Computational Biology Graduate Program Iowa State UniversityAmesIowa 50011USA Department of statistics Iowa State UniversityAmesIowa 50011USA Department of Electrical and Computer Engineering Iowa State UniversityAmesIowa 50011USA

Genes encoding early signaling events in pathogen defense often are identified only by their phenotype. such genes involved in barley-powdery mildew interactions include Mla, specifying race-specific resistance; Rarl （Required for Mla12-specified resistance1）, and Roml （Restoration of Mla-specified resistancel）. The HsP90-sGT1-RAR1 complex appears to function as chaperone in MLA-specified resistance, however, much remains to be discovered regarding the precise signaling underlying plant immunity. Genetic analyses of fast-neutron mutants derived from CI 16151 （Mla6） uncovered a novel locus, designated Rar3 （R_equired for Mla6-specified resitance3）. Rar3 segregates independent of Mla6 and Rarl, and rar3 mutants are susceptible to Blumeria graminis f. sp. hordei （Bgh） isolate 5874 （A VRar）, whereas, wild-type progenitor plants are resistant. Comparative expression analyses of the rar3 mutant vs. its wild-type progenitor were conducted via Barleyl GeneChip and GAIIx paired-end RNA-seq. Whereas Rarl affects transcription of relatively few genes; Rar3 appears to influence thousands, notably in genes controlling ATP binding, catalytic activity, transcription, and phosphorylation; possibly membrane bound or in the nucleus, eQTL analysis of a segregating doubled haploid population identified over two-thousand genes as being regulated by Mla （q value/FDR=0.00001）, a subset of which are significant in Rar3 interactions. The intersection of datasets derived from mla-loss-of-function mutants, Mla-associated eQTL, and rar3-mediated transcriptome reprogramming are narrowing the focus on essential genes required for Mla-specified immunity.

关键词： eQTL transcript profiling immunity resistance signaling barley Blumeria graminis

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Formation, Propagation and Reflection of 1D Normal shocks in Riemann shock Tube

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Applied Mathematics 2022年第3期13卷 295-323页

作者： karan s. surana Jacob k. kendall Celso H. Carranza Mechanical Engineering University of Kansas Lawrence USA

The purpose of this paper is to consider 1D Riemann shock tube to investigate the formation and propagation of compression waves leading to formation, propagation and reflection of 1D normal shocks using simplified mathematical models commonly used in the published work as well as using complete mathematical models based on Conservation and Balance Laws (CBL) of classical continuum mechanics and constitutive theories for compressible viscous medium derived using entropy inequality and representation theorem. This work is aimed at resolving compression waves, the shock structure, shock formation, propagation and reflection of fully formed shocks. Evolutions obtained from the mathematical models always satisfy differentiability requirements in space and time dictated by the highest order of the derivatives of the dependent variables in the mathematical models investigated. All solutions reported in this paper including boundary conditions and initial conditions are always analytic. solutions of the mathematical models are obtained using the space-time finite element method in which the space-time integral forms are space-time variationally consistent ensuring unconditionally stable computations during the entire evolution. solution for a space-time strip or slab is calculated and is time marched upon convergence to obtain complete evolution for the desired space-time domain, thus ensuring time accurate evolutions. The space-time local approximation over a space-time element of a space-time strip or slab is p-version hierarchical with higher-order global differentiability in space and time, i.e., we consider scalar product approximation spaces in which k = (ksub>1sub>, ksub>2sub>) are the order of the space in space and time and p = (psub>1sub>, psub>2sub>) are p-levels of the approximations in space and time. Model problem studies are presented for different mathematical models and are compared with solutions obtained from the complete mathematical model b

关键词： Compression Wave 1D Normal shock Riemann shock Tube space-Time

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Methods of Approximation in hpk Framework for ODEs in Time Resulting from Decoupling of space and Time in IVPs

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American Journal of Computational Mathematics 2011年第2期1卷 83-103页

作者： k.s. surana L. Euler J.N. Reddy A. Romkes University of kansas Mechanical Engineering Department Lawrence KS 66045

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 element approximations in time. A correspondence is established between these integral forms and the elements of the calculus of variations: 1) to determine which methods of approximation yield unconditionally stable (variationally consistent integral forms, VC ) computational processes for which types of operators and, 2) to establish which integral forms do not yield unconditionally stable computations (variationally inconsistent integral forms, VIC ). It is shown that variationally consistent time integral forms in hpk framework yield computational processes for ODEs in time that are unconditionally stable, provide a mechanism of higher order global differentiability approximations as well as higher degree local approximations in time, provide control over approximation error when used as a time marching process and can indeed yield time accurate solutions of the evolution. Numerical studies are presented using standard model problems from the literature and the results are compared with Wilson’s θ method as well as Newmark method to demonstrate highly meritorious features of the proposed methodology.

关键词： Finite Element Approximations Numerical studies Time Approximation Variationally Consis- tent Integral Forms

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Consistency and Validity of the Mathematical Models and the solution Methods for BVPs and IVPs Based on Energy Methods and Principle of Virtual Work for Homogeneous Isotropic and Non-Homogeneous Non-Isotropic solid Continua

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Applied Mathematics 2020年第7期11卷 546-578页

作者： karan s. surana Emilio N. Alverio Mechanical Engineering University of Kansas Lawrence KS USA

Energy methods and the principle of virtual work are commonly used for obtaining solutions of boundary value problems (BVPs) and initial value problems (IVPs) associated with homogeneous, isotropic and non-homogeneous, non-isotropic matter without using (or in the absence of) the mathematical models of the BVPs and the IVPs. These methods are also used for deriving mathematical models for BVPs and IVPs associated with isotropic, homogeneous as well as non-homogeneous, non-isotropic continuous matter. In energy methods when applied to IVPs, one constructs energy functional (I) consisting of kinetic energy, strain energy and the potential energy of loads. The first variation of this energy functional (δI) set to zero is a necessary condition for an extremum of I. In this approach one could use δI = 0 directly in constructing computational processes such as the finite element method or could derive Euler’s equations (differential or partial differential equations) from δI = 0, which is also satisfied by a solution obtained from δI = 0. The Euler’s equations obtained from δI = 0 indeed are the mathematical model associated with the energy functional I. In case of BVPs we follow the same approach except in this case, the energy functional I consists of strain energy and the potential energy of loads. In using the principle of virtual work for BVPs and the IVPs, we can also accomplish the same as described above using energy methods. In this paper we investigate consistency and validity of the mathematical models for isotropic, homogeneous and non-isotropic, non-homogeneous continuous matter for BVPs that are derived using energy functional consisting of strain energy and the potential energy of loads. similar investigation is also presented for IVPs using energy functional consisting of kinetic energy, strain energy and the potential energy of loads. The computational approaches for BVPs and the IVPs design

关键词： Energy Methods Principle of Virtual Work Calculus of Variations Euler’s Equation Mathematical Model Classical and Non-Classical Continuum Mechanics

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Nonlinear Waves in solid Continua with Finite Deformation

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American Journal of Computational Mathematics 2015年第3期5卷 345-386页

作者： k. s. surana J. knight J. N. Reddy Department of Mechanical Engineering University of Kansas Lawrence KS USA Department of Mechanical Engineering Texas A & M University College Station TX USA

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 second Piola-kirchoff stress tensor and Green’s strain tensor and their material derivatives [1]. Fourier heat conduction law with constant conductivity is used as the constitutive theory for heat vector. Numerical studies are performed using space-time variationally consistent finite element formulations derived using space-time residual functionals and the non-linear equations resulting from the first variation of the residual functional are solved using Newton’s Linear Method with line search. space-time local approximations are considered in higher order scalar product spaces that permit desired order of global differentiability in space and time. Computed results for non-linear wave propagation, reflection, and interaction are compared with linear wave propagation to demonstrate significant differences between the two, the importance of the nonlinear wave propagation over linear wave propagation as well as to illustrate the meritorious features of the mathematical models and the space-time variationally consistent space-time finite element process with time marching in obtaining the numerical solutions of the evolutions.

关键词： Linear and Nonlinear Waves second Piola-kirchoff stress Green's strain Constitutive Theories Dissipation Memory Rheology Finite strain

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