On the Lagrangian formulation of continuum mechanics

Golebiewska-Herrmann, A.

doi:10.1016/0378-4371(83)90196-6

Cited by 11 publications

(16 citation statements)

References 8 publications

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“…In the spirit of several prior investigators [2,[11][12][13][14][15][25][26][27], we subject the action (1) to a set of transformations of both independent and dependent fields:…”

Section: Balance Lawsmentioning

confidence: 99%

“…Because Eqs. (24)(25)(26) arise from a continuous shift in material coordinates made possible by a continuum description of a body, they have no analogue in a discrete set of particles [11,13].…”

Section: Simple Elastic Solidmentioning

confidence: 99%

“…Rogula later revisited material forces and corresponding balance laws in the presence of localized inhomogeneities [10]. In a series of papers, A. Golebiewska Herrmann presented a unified Lagrangian treatment of continuum mechanics for systems that admit an action principle, deriving a complete set of dynamic balance laws [11][12][13]. She showed that while conservation of momentum follows from homogeneity of the ambient space, conservation of material momentum implies a homogeneous material "space".…”

Section: Introductionmentioning

confidence: 99%

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Pseudomomentum: origins and consequences

Singh

Hanna

2021

Z. Angew. Math. Phys.

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The balance of pseudomomentum is discussed and applied to simple elasticity, ideal fluids, and the mechanics of inextensible rods and sheets. A general framework is presented in which the simultaneous variation of an action with respect to position, time, and material labels yields bulk balance laws and jump conditions for momentum, energy, and pseudomomentum. The example of simple elasticity of space-filling solids is treated at length. The pseudomomentum balance in ideal fluids is shown to imply conservation of vorticity, circulation, and helicity, and a mathematical similarity is noted between the evaluation of circulation along a material loop and the J-integral of fracture mechanics. Integration of the pseudomomentum balance, making use of a prescription for singular sources derived by analogy with the continuous form of the balance, directly provides the propulsive force driving passive reconfiguration or locomotion of confined, inhomogeneous elastic rods. The conserved angular momentum and pseudomomentum are identified in the classification of conical sheets with rotational inertia or bending energy.

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“…In the spirit of several prior investigators [2,[11][12][13][14][15][25][26][27], we subject the action (1) to a set of transformations of both independent and dependent fields:…”

Section: Balance Lawsmentioning

confidence: 99%

Section: Simple Elastic Solidmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Pseudomomentum: origins and consequences

Singh

Hanna

2021

Z. Angew. Math. Phys.

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“…The differential operator (d/dt) denotes the total time derivative at fixed X. By following the treatment of Golebiewska and Herrmann [21], evaluate the total gradient of L and write…”

Section: Dynamicsmentioning

confidence: 99%

“…This tensor was named the Maxwell tensor of elasticity by Eshelby in 1951, in the context of linear elasticity [18]. In the literature that is concerned with the configurational material forces, b is currently known as the Eshelby tensor [4][5][6][7][8][19][20][21].…”

Section: Elasticitymentioning

confidence: 99%

Material electromagnetic fields and material forces

Trimarco

2006

Arch Appl Mech

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Electromagnetic fields address configurational forces in a natural way through an energy-stress tensor, which reduces to the Maxwell tensor in the simplest case. This tensor is related to physical forces and to the Cauchy traction in a continuum. Material forces, as opposed to physical forces, are of a different nature as they act upon a site of a continuum where the possible material inhomogeneity is located. A material energy-stress tensor, which is reminiscent of the Maxwell stress, is associated with these forces. Through appropriate balance laws, a material momentum is also associated with material forces. The material momentum is of particular interest in electromagnetic materials as it is intimately related to the pseudomomentum of light

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Introduction

Steinmann

2022

Solid Mechanics and Its Applications

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On the Lagrangian formulation of continuum mechanics

Cited by 11 publications

References 8 publications

Pseudomomentum: origins and consequences

Pseudomomentum: origins and consequences

Material electromagnetic fields and material forces

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