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Spatial and Material Forces in Nonlinear Continuum Mechanics - A Dissipation-Consistent Approach (Hardcover, 1st ed. 2022)
Loot Price: R5,322
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Spatial and Material Forces in Nonlinear Continuum Mechanics - A Dissipation-Consistent Approach (Hardcover, 1st ed. 2022)
Series: Solid Mechanics and Its Applications, 272
Expected to ship within 10 - 15 working days
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This monograph details spatial and material vistas on non-linear
continuum mechanics in a dissipation-consistent approach. Thereby,
the spatial vista renders the common approach to nonlinear
continuum mechanics and corresponding spatial forces, whereas the
material vista elaborates on configurational mechanics and
corresponding material or rather configurational forces.
Fundamental to configurational mechanics is the concept of force.
In analytical mechanics, force is a derived object that is power
conjugate to changes of generalised coordinates. For a continuum
body, these are typically the spatial positions of its continuum
points. However, if in agreement with the second law, continuum
points, e.g. on the boundary, may also change their material
positions. Configurational forces are then power conjugate to these
configurational changes. A paradigm is a crack tip, i.e. a singular
part of the boundary changing its position during crack
propagation, with the related configurational force, typically the
J-integral, driving its evolution, thereby consuming power,
typically expressed as the energy release rate. Taken together,
configurational mechanics is an unconventional branch of continuum
physics rationalising and unifying the tendency of a continuum body
to change its material configuration. It is thus the ideal
formulation to tackle sophisticated problems in continuum defect
mechanics. Configurational mechanics is entirely free of
restrictions regarding geometrical and constitutive nonlinearities
and offers an accompanying versatile computational approach to
continuum defect mechanics. In this monograph, I present a detailed
summary account of my approach towards configurational mechanics,
thereby fostering my view that configurational forces are indeed
dissipation-consistent to configurational changes.
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