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Variational Continuum Multiphase Poroelasticity - Theory and Applications (Hardcover, 1st ed. 2017)
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Variational Continuum Multiphase Poroelasticity - Theory and Applications (Hardcover, 1st ed. 2017)
Series: Advanced Structured Materials, 67
Expected to ship within 12 - 17 working days
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This book collects the theoretical derivation of a recently
presented general variational macroscopic continuum theory of
multiphase poroelasticity (VMTPM), together with its applications
to consolidation and stress partitioning problems of interest in
several applicative engineering contexts, such as in geomechanics
and biomechanics. The theory is derived based on a
purely-variational deduction, rooted in the least-Action principle,
by considering a minimal set of kinematic descriptors. The
treatment herein considered keeps a specific focus on the
derivation of most general medium-independent governing equations.
It is shown that VMTPM recovers paradigms of consolidated use in
multiphase poroelasticity such as Terzaghi's stress partitioning
principle and Biot's equations for wave propagation. In particular,
the variational treatment permits the derivation of a general
medium-independent stress partitioning law, and the proposed
variational theory predicts that the external stress, the fluid
pressure, and the stress tensor work-associated with the
macroscopic strain of the solid phase are partitioned according to
a relation which, from a formal point of view, turns out to be
strictly compliant with Terzaghi's law, irrespective of the
microstructural and constitutive features of a given medium.
Moreover, it is shown that some experimental observations on
saturated sandstones, generally considered as proof of deviations
from Terzaghi's law, are ordinarily predicted by VMTPM. As a
peculiar prediction of VMTPM, the book shows that the phenomenon of
compression-induced liquefaction experimentally observed in
cohesionless mixtures can be obtained as a natural implication of
this theory by a purely rational deduction. A characterization of
the phenomenon of crack closure in fractured media is also inferred
in terms of macroscopic strain and stress paths. Altogether the
results reported in this monograph exemplify the capability of
VMTPM to describe and predict a large class of linear and nonlinear
mechanical behaviors observed in two-phase saturated materials.
General
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