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A platform for research: civil engineering, architecture and urbanism
A Well‐posed Hypoelastic Model Derived From a Hyperelastic One
In the literature, two classes of models for the high‐strain dynamics of solids can be found: hypoelastic and hyperelastic ones. Hypoelastic models are widely used in industrial and military numerical codes. For this class of models, an empirical partial differential equation for the deviatoric part of the stress tensor is formulated to close the governing equations. The deviatoric stress rate depends on the choice of a so‐called objective derivative. Hyperelastic models, where the stress tensor is obtained by the variation of the stored energy, have been intensively studied in the last decades. This chapter proposes a link between hypoelastic and hyperelastic models. This link is in some sense obvious and related to the problem of inversion of stress‐strain relation. The chapter presents the governing equations for hyperelastic materials. It also presents the derivation of the hypoelastic model for neo‐Hookean solids.
A Well‐posed Hypoelastic Model Derived From a Hyperelastic One
In the literature, two classes of models for the high‐strain dynamics of solids can be found: hypoelastic and hyperelastic ones. Hypoelastic models are widely used in industrial and military numerical codes. For this class of models, an empirical partial differential equation for the deviatoric part of the stress tensor is formulated to close the governing equations. The deviatoric stress rate depends on the choice of a so‐called objective derivative. Hyperelastic models, where the stress tensor is obtained by the variation of the stored energy, have been intensively studied in the last decades. This chapter proposes a link between hypoelastic and hyperelastic models. This link is in some sense obvious and related to the problem of inversion of stress‐strain relation. The chapter presents the governing equations for hyperelastic materials. It also presents the derivation of the hypoelastic model for neo‐Hookean solids.
A Well‐posed Hypoelastic Model Derived From a Hyperelastic One
Lambert, David Edward (editor) / Pasiliao, Crystal L. (editor) / Erzar, Benjamin (editor) / Revil‐Baudard, Benoit (editor) / Cazacu, Oana (editor)
Dynamic Damage and Fragmentation ; 417-427
2018-12-31
11 pages
Article/Chapter (Book)
Electronic Resource
English
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