In the present contribution a novel model for the description of the dynamic response of biphasic media at finite deformations is illustrated. The model is formulated by means of eight kinematic scalar fields: the displacement field of the solid phase, the velocity of the fluid, the density of fluid and an additional scalar field associated with the microscopic volumetric deformation of the solid phase. In order to overcome the limits imposed by hypoelastic models, the present formulation is completely developed in the context of finite deformations and, in analogy with a model recently developed by Li et al., all balance equations are expressed in the reference configuration of the solid phase. Unlike the latter model, the present formulation is suitable for describing also the response of biphasic media for which the ratio between volumetric jacketed and unjacketed compressibility is different from zero, a feature shared also by Biot and Willis seminal work, while retaining distinct constitutive relations for the solid and the fluid phases. The governing equations are derived in terms of macroscopic balance laws and the relation with other biphasic theories is discussed with particular attention to the general case of a highly compressible gas and to the limit case of a solid phase constituted by a volumetrically incompressible material.

A Finite Deformation Model for the Dynamic Behaviour of Fluid saturated Porous Biphasic Media

SERPIERI R;
2009

Abstract

In the present contribution a novel model for the description of the dynamic response of biphasic media at finite deformations is illustrated. The model is formulated by means of eight kinematic scalar fields: the displacement field of the solid phase, the velocity of the fluid, the density of fluid and an additional scalar field associated with the microscopic volumetric deformation of the solid phase. In order to overcome the limits imposed by hypoelastic models, the present formulation is completely developed in the context of finite deformations and, in analogy with a model recently developed by Li et al., all balance equations are expressed in the reference configuration of the solid phase. Unlike the latter model, the present formulation is suitable for describing also the response of biphasic media for which the ratio between volumetric jacketed and unjacketed compressibility is different from zero, a feature shared also by Biot and Willis seminal work, while retaining distinct constitutive relations for the solid and the fluid phases. The governing equations are derived in terms of macroscopic balance laws and the relation with other biphasic theories is discussed with particular attention to the general case of a highly compressible gas and to the limit case of a solid phase constituted by a volumetrically incompressible material.
978-989-96264-2-3
Biphasic porous media; Finite deformations; Dynamics
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12070/11906
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