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Rosati, Luciano

doi:10.1023/a:1007663620943

Cited by 30 publications

(3 citation statements)

References 24 publications

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“…Many works have devoted to give an expression of the derivative of the right stretch tensor U with respect to the deformation gradient F, ∂U/∂F, as one can see in [1][2][3][4][5][6][7] Chen and Wheeler (1993), Rosati (1999), Padovani (2000), Itskvov (2002), Carrol (2004), Jog (2006) and Wheeler and Casey (2011).…”

Section: Introductionmentioning

confidence: 99%

Alternative approach to obtain the derivative of the right stretch tensor with respect to the deformation gradient

Vasconcellos,

Greco

2023

Preprint

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Section: Introductionmentioning

confidence: 99%

Alternative approach to obtain the derivative of the right stretch tensor with respect to the deformation gradient

Vasconcellos,

Greco

2023

Preprint

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“…Such an approach was developed by the Cosserat brothers [23,36]. In the non-linear settings as in this paper, the time evolution for R can be obtained [21,93] and R can be considered as a natural choice of the state variable to represent the internal rotations. However, in the context of multiphysics modeling and development of efficient computational methods this choice is not that obvious.…”

Section: Introductionmentioning

confidence: 99%

Continuum mechanics with torsion

Peshkov

Romenski

Dumbser

2019

Continuum Mech. Thermodyn.

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This paper is an attempt to introduce methods and concepts of the Riemann-Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics, etc. to fluid dynamics in general and to studying and modeling turbulence in particular. Thus, in order to account for the rotational degrees of freedom of the irregular dynamics of small scale vortexes, we further generalize our unified first-order hyperbolic formulation of continuum fluid and solid mechanics which treats the flowing medium as a Riemann-Cartan manifold with zero curvature but non-vanishing torsion. We associate the rotational degrees of freedom of the main field of our theory, the distortion field, to the dynamics of microscopic (unresolved) vortexes. The distortion field characterizes the deformation and rotation of the material elements and can be viewed as anholonomic basis triad with non-vanishing torsion. The torsion tensor is then used to characterize distortion's spin and is treated as an independent field with its own time evolution equation. This new governing equation has essentially the structure of the non-linear electrodynamics in a moving medium and can be viewed as a Yang-Mills-type gauge theory. The system is closed by providing an example of the total energy potential. The extended system describes not only irreversible dynamics (which raises the entropy) due to the viscosity or plasticity effect but it also has dispersive features which are due to the reversible energy exchange (which conserves the entropy) between micro and macro scales. Both the irreversible and dispersive processes are represented by relaxation-type algebraic source terms so that the overall system remains first-order hyperbolic. The turbulent state is then treated as an excitation of the equilibrium laminar state due to the non-linear interplay between dissipation and dispersion.

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“…A number of papers on the derivatives of wider classes of tensor-valued functions of a tensor were published during the past decade. Often, these investigations were motivated in the field of continuum mechanics [Rosati 1999;Itskov 2002;Jog 2008] and in the modeling of nonlinear elastoplastic constitutive laws [de Souza Neto 2001]. Most papers concern the representation and the derivatives of isotropic tensor functions of either a symmetrical or a generally unsymmetrical tensor [Ortiz et al 2001;de Souza Neto 2001;Itskov and Aksel 2002;Itskov 2003;Fung 2004;Lu 2004;Dui et al 2006;Wang and Dui 2007;Jog 2008].…”

Section: Introductionmentioning

confidence: 99%

On successive differentiations of the rotation tensor: An application to nonlinear beam elements

Merlini¹,

Morandini²

2013

J. Mech. Mater. Struct.

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Successive differentiations of the rotation tensor are characterized by successive differential rotation vectors. Useful expressions of the differential rotation vectors for differentiations up to third order are derived. In the context of the exponential parameterization, explicit expressions for the differential maps (the maps providing the differential rotation vectors from the differentials of the parameters chosen) are obtained by resorting to an original infinite family of recursive subexponential maps. Useful properties of the mapping tensors are discussed. The formulation is appropriate for nonlinear problems of computational solid mechanics, when spatial, incremental, and virtual variations of particle orientations must be dealt with together. As an application, the classical problem of modeling space-curved slender beams by finite elements is considered. The variational formulation and the nonlinear interpolation of the orientations, together with the relevant linearizations, consistently exploit the proposed differentiations and lead to an objective beam element. Two test cases are discussed.

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Untitled

Cited by 30 publications

References 24 publications

Alternative approach to obtain the derivative of the right stretch tensor with respect to the deformation gradient

Alternative approach to obtain the derivative of the right stretch tensor with respect to the deformation gradient

Continuum mechanics with torsion

On successive differentiations of the rotation tensor: An application to nonlinear beam elements

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