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The configuration space and principle of virtual power for rough bodies

Abstract : In the setting of an n-dimensional Euclidean space, the duality between velocity fields on the class of admissible bodies and Cauchy fluxes is studied using tools from geometric measure theory. A generalized Cauchy flux theory is obtained for sets whose measure theoretic boundaries may be as irregular as flat (n−1)-chains. Initially, bodies are modeled as normal n-currents induced by sets of finite perimeter. A configuration space comprising Lipschitz embeddings induces virtual velocities given by locally Lipschitz mappings. A Cauchy flux is defined as a real valued function on the Cartesian product of (n−1)-currents and locally Lipschitz mappings. A version of Cauchy's postulates implies that a Cauchy flux may be uniquely extended to an n-tuple of flat (n−1)-cochains. Thus, the class of admissible bodies is extended to include flat n-chains and a generalized form of the principle of virtual power is presented. Wolfe's representation theorem for flat cochains enables the identification of stress as an n-tuple of flat (n−1)-forms.
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https://hal.archives-ouvertes.fr/hal-01060951
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Submitted on : Thursday, September 4, 2014 - 4:19:48 PM
Last modification on : Monday, July 22, 2019 - 11:46:01 AM
Long-term archiving on: : Friday, December 5, 2014 - 10:39:35 AM

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  • HAL Id : hal-01060951, version 1

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Lior Falach, Reuven Segev. The configuration space and principle of virtual power for rough bodies. 2014. ⟨hal-01060951⟩

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