Thermodynamic consistency of beam theories in the context of classical and non-classical continuum mechanics and a thermodynamically consistent new formulation

Surana, Karan S.; Mysore, D.; Reddy, J. N.

doi:10.1007/s00161-019-00744-8

Cited by 9 publications

(6 citation statements)

References 34 publications

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“…Величина прогибов и критические условия потери устойчивости стержня зависят от всех параметров модели. Заметим, что подобные задачи вызывают интерес в совершенно разных приложениях [1][2][3] и др.…”

Section: институт физики прочности и материаловедения со ран томскunclassified

Нелинейные Колебания Стержня С Нелокальной Диффузией, Сопровождаемой Фазообразованием

2021

Международная Конференция "Физическая Мезомеханика. Материалы С Многоуровневой Иерархически Организованной Структурой И Интелле

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Section: институт физики прочности и материаловедения со ран томскunclassified

Нелинейные Колебания Стержня С Нелокальной Диффузией, Сопровождаемой Фазообразованием

2021

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“…erences [22] [23] [24] [25]. In a recent paper, Surana et al [26] investigated thermodynamic consistency of the currently used beam mathematical models that are based on kinematic assumptions and are derived either using energy methods or using the principle of virtual work. The authors concluded that the currently used beam models cannot be derived using the conservation and balance laws of CCM or NCCM.…”

Section: ( )mentioning

confidence: 99%

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

Surana¹,

Mathi²

2020

AJCM

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Inclusion of dissipation and memory mechanisms, non-classical elasticity and thermal effects in the currently used plate/shell mathematical models require that we establish if these mathematical models can be derived using the conservation and balance laws of continuum mechanics in conjunction with the corresponding kinematic assumptions. This is referred to as thermodynamic consistency of the mathematical models. Thermodynamic consistency ensures thermodynamic equilibrium during the evolution of the deformation. When the mathematical models are thermodynamically consistent, the second law of thermodynamics facilitates consistent derivations of constitutive theories in the presence of dissipation and memory mechanisms. This is the main motivation for the work presented in this paper. In the currently used mathematical models for plates/shells based on the assumed kinematic relations, energy functional is constructed over the volume consisting of kinetic energy, strain energy and the potential energy of the loads. The Euler's equations derived from the first variation of the energy functional for arbitrary length when set to zero yield the mathematical model(s) for the deforming plates/shells. Alternatively, principle of virtual work can also be used to derive the same mathematical model(s). For linear elastic reversible deformation physics with small deformation and small strain, these two approaches, based on energy functional and the principle of virtual work, yield the same mathematical models. These mathematical models hold for reversible mechanical deformation. In this paper, we examine whether the currently used plate/shell mathematical models with the corresponding kinematic as

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“…In a recent paper Surana et al [40] showed that all currently used beam mathematical models for isotropic and homogeneous matter are thermodynamically inconsistent. That is, these mathematical models can neither be derived using the conservation and balance laws of classical continuum mechanics (CCM) nor non-classical continuum mechanics (NCCM).…”

Section: Literature Reviewmentioning

confidence: 99%

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

Surana¹,

Alverio²

2020

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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 con-How to cite this paper: Surana, K.S. and Alverio, E.N. (2020) 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

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Thermodynamic consistency of beam theories in the context of classical and non-classical continuum mechanics and a thermodynamically consistent new formulation

Cited by 9 publications

References 34 publications

Нелинейные Колебания Стержня С Нелокальной Диффузией, Сопровождаемой Фазообразованием

Нелинейные Колебания Стержня С Нелокальной Диффузией, Сопровождаемой Фазообразованием

Thermodynamic Consistency of Plate and Shell Mathematical Models in the Context of Classical and Non-Classical Continuum Mechanics and a Thermodynamically Consistent New Thermoelastic Formulation

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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