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Meccanica

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01.01.2014

Geometric continuum mechanics

verfasst von: Giovanni Romano, Raffaele Barretta, Marina Diaco

Erschienen in: Meccanica | Ausgabe 1/2014

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Abstract

Geometric Continuum Mechanics ( GCM) is a new formulation of Continuum Mechanics ( CM) based on the requirement of Geometric Naturality ( GN). According to GN, in introducing basic notions, governing principles and constitutive relations, the sole geometric entities of space-time to be involved are the metric field and the motion along the trajectory. The additional requirement that the theory should be applicable to bodies of any dimensionality, leads to the formulation of the Geometric Paradigm ( GP) stating that push-pull transformations are the natural comparison tools for material fields. This basic rule implies that rates of material tensors are Lie-derivatives and not derivatives by parallel transport. The impact of the GP on the present state of affairs in CM is decisive in resolving questions still debated in literature and in clarifying theoretical and computational issues. As a consequence, the notion of Material Frame Indifference ( MFI) is corrected to the new Constitutive Frame Invariance ( CFI) and reasons are adduced for the rejection of chain decompositions of finite elasto-plastic strains. Geometrically consistent notions of Rate Elasticity ( RE) and Rate Elasto-Visco-Plasticity ( REVP) are formulated and consistent relevant computational methods are designed.

Vorheriger Artikel A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation

Nächster Artikel Dynamics of a linear system with time-dependent mass and a coupled light mass with non-smooth potential

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In differential geometry these are respectively denoted by low and high asterisks _∗;^∗ [51]. This standard notation leads however to consider too many similar stars in the geometric sky, i.e. push, pull, duality, Hodge operator.

The time-function

https://static-content.springer.com/image/art%3A10.1007%2Fs11012-013-9777-9/MediaObjects/11012_2013_9777_IEq53_HTML.gif

is assumed to be a projection, i.e. surjective with a surjective tangent map.

An immersion is a injective map whose tangent map is injective too.

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CFI substitutes the notion of Material Frame Indifference stated in [54] by the equality

https://static-content.springer.com/image/art%3A10.1007%2Fs11012-013-9777-9/MediaObjects/11012_2013_9777_IEq211_HTML.gif

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Titel: Geometric continuum mechanics
verfasst von: Giovanni Romano
Raffaele Barretta
Marina Diaco
Publikationsdatum: 01.01.2014
Verlag: Springer Netherlands
Erschienen in: Meccanica / Ausgabe 1/2014
Print ISSN: 0025-6455
Elektronische ISSN: 1572-9648
DOI: https://doi.org/10.1007/s11012-013-9777-9

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