Incremental constitutive models for elastoplastic materials undergoing finite deformations by using a four-dimensional formalism

Abstract : When constructing incremental constitutive models of elastoplasticity for materials undergoing finite deformations, the tensors and their rates should respect the principle of frame-indifference. Instead of classical 3D approaches in which different objective transports may be arbitrarily used in the constitutive equations, we propose to model the constitutive equations using the four-dimensional formalism of the theory of Relativity. This formalism ensures that any 4D tensor is frame-indifferent thanks to the principle of covariance. It is further possible to define 4D rate operators that are all, by construction, frame-indifferent. Among these covariant rates, the 4D Lie derivative is chosen to construct incremental constitutive relations because it is invariant to the superposition of rigid body motion. A 4D rate type model of elastoplasticity with isotropic hardening is thus developed and compared with existing classical 3D constitutive models of elastoplasticity established in the context of finite deformations.
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https://hal-utt.archives-ouvertes.fr/hal-02278312
Contributor : Jean-Baptiste Vu Van <>
Submitted on : Wednesday, September 4, 2019 - 12:08:26 PM
Last modification on : Monday, September 16, 2019 - 4:35:40 PM

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Mingchuan Wang, Benoît Panicaud, Emmanuelle Rouhaud, Richard Kerner, Arjen Roos. Incremental constitutive models for elastoplastic materials undergoing finite deformations by using a four-dimensional formalism. International Journal of Engineering Science, Elsevier, 2016, 106, pp.199-219. ⟨10.1016/j.ijengsci.2016.06.006⟩. ⟨hal-02278312⟩

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