Coordinate-independent representation of spins in continuum mechanics

Reinhardt, Wolf; Dubey, R. N.

doi:10.1007/bf00040957

Cited by 51 publications

(12 citation statements)

References 13 publications

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“…Also, Ω E represents spin of the Eulerian triad which is called the Eulerian spin. The logarithmic spin has a specific property such that its corresponding corotational rate of lnV results in the rate of deformation tensor D. This spin has been introduced seperately by Lehman et al [15], Reinhardt and Dubey [21,22] and Xiao et al [28,29]. Some useful details on this issue are given in [30].…”

Section: Preliminariesmentioning

confidence: 97%

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On The Objective Corotational Rates of Eulerian Strain Measures

Asghari

Naghdabadi

2008

J Elasticity

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Section: Preliminariesmentioning

confidence: 97%

“…of e ( f ) should be determined by use of (63), (21) and (22). With α f 1 ; α f 2 in hand, tensor K is adjusted to the appropriate one.…”

Section: Basis-free Expression In the Case Of Distinct Principal Strementioning

confidence: 99%

On The Objective Corotational Rates of Eulerian Strain Measures

Asghari

Naghdabadi

2008

J Elasticity

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“…Here, e 8 Log is the logarithmic rate of the strain tensor e as specified in Equation (16). From the symmetry requirement of t and e, and the objectivity of t and _ w w, it is concluded that the extended work conjugacy relation (27) holds only for objective corotational rates e 8 * [11].…”

Section: Work Conjugacy and Work Conjugated Stressmentioning

confidence: 97%

An Eulerian Model for Pseudoelastic Shape Memory Alloys

Müller

Bruhns

2004

Materialwissenschaft Werkst

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. BruhnsA thermodynamic model describing pseudoelasticity is proposed. The kinematics are based on a self-consistent Eulerian theory of finite deformations using the logarithmic rate. The thermomechanical state of the material is described by means of the mass fraction of martensite as internal state variable. From the Helmholtz free energy of the two-phase solid, a kinetic law for the evolution of martensite is derived, taking into account the heat generated during phase transition. The material model is implemented into a finite element code in an updated Lagrangian scheme. Its parameters are calibrated to experimental data. The characteristics of the model are illustrated by simulations under different loading conditions.

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“…Later, Eq. (71) was also rediscovered by Reinhardt and Dubey [74,75]. This relationship was derived in the general sense of studying Eq.…”

Section: The Logarithmic Rate and Related Propertiesmentioning

confidence: 99%

The Prandtl‐Reuss equations revisited

Bruhns

2013

Z Angew Math Mech

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At the beginning of the last century two different types of constitutive relations to describe the complex behavior of elastoplastic material were presented. These were the deformation theory originally developed by Hencky and the Prandtl-Reuss theory. Whereas the former provides a direct solid-like relation of stress as function of strain, the latter has been based on an additive composition of elastic and plastic parts of the increments of strains. These in turn were taken as a solid-and fluid-like combination of the de Saint-Venant/Lévy theory with an incremental form of Hookes law.Even nowadays this Prandtl-Reuss theory is still accepted within the restriction of small elastic deformations, i.e. it is generally stated in most textbooks on plasticity that this theory due to a number of defects can not be applied to large deformations. In the present article it is shown that this restrictive statement may be no longer true. Introducing a specific objective time derivative it could be shown that these defects disappear.

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Coordinate-independent representation of spins in continuum mechanics

Cited by 51 publications

References 13 publications

On The Objective Corotational Rates of Eulerian Strain Measures

On The Objective Corotational Rates of Eulerian Strain Measures

An Eulerian Model for Pseudoelastic Shape Memory Alloys

The Prandtl‐Reuss equations revisited

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