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020 _a9783319406824
_9978-3-319-40682-4
024 7 _a10.1007/978-3-319-40682-4
_2doi
050 4 _aTA349-359
072 7 _aTGMD
_2bicssc
072 7 _aSCI096000
_2bisacsh
072 7 _aTGMD
_2thema
082 0 4 _a620.105
_223
100 1 _aFrémond, Michel.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_959401
245 1 0 _aVirtual Work and Shape Change in Solid Mechanics
_h[electronic resource] /
_cby Michel Frémond.
250 _a1st ed. 2017.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2017.
300 _aXVII, 371 p. 17 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSpringer Series in Solid and Structural Mechanics,
_x2195-352X ;
_v7
505 0 _aIntroduction -- The System -- The Principle of Virtual Work -- What We See: the Velocities -- The Actions which are Applied to the System: the Work of the External Forces -- What We See: the Velocities of Deformation -- The Work to Change the Shape of the System -- The Work to Change the Velocities of the System -- The Principle of Virtual Work and the Equations of Motion -- Summary of the Abstract Setting to get the Equations of Motion -- Two Points on a Line -- Three Disks in a Plane -- Three Balls on a Plane -- A Deformable Solid -- Two Deformable Solids -- At a Distance Interactions: Continuum Reinforced by Fibers -- At a Distance Interactions: Continuum Reinforced by Beams -- At a Distance Interactions: Continuum Reinforced by Plates -- Damage of a Connection -- Damage of a Rod Glued on a Rigid Surface -- Damage of a Beam Glued on a Rigid Surface -- A Damageable Solid -- Two Damageable Solids -- Porous Solids -- Discontinuum Mechanics: Collisions and Fractures in Solids -- There is neither Flattening nor Self-contact or Contact with an Obstacle. Smooth Evolution -- There is neither Flattening nor Self-contact or Contact with an Obstacle. Non Smooth Evolution -- There is no Flattening. There is Self-contact and Contact with an Obstacle. Smooth Evolution -- There is no Flattening. There is Self-contact and Contact with an Obstacle. Non Smooth Evolution. Flattening. Smooth and Non Smooth Evolutions -- Conclusions.
520 _aThis book provides novel insights into two basic subjects in solid mechanics: virtual work and shape change. When we move a solid, the work we expend in moving it is used to modify both its shape and its velocity. This observation leads to the Principle of Virtual Work. Virtual work depends linearly on virtual velocities, which are velocities we may think of. The virtual work of the internal forces accounts for the changes in shape. Engineering provides innumerable examples of shape changes, i.e., deformations, and of velocities of deformation. This book presents examples of usual and unusual shape changes, providing with the Principle of Virtual Work various and sometimes new equations of motion for smooth and non-smooth (i.e., with collisions) motions: systems of disks, systems of balls, classical and non-classical small deformation theories, systems involving volume and surface damage, systems with interactions at a distance (e.g., solids reinforced by fibers), systems involving porosity, beams with third gradient theory, collisions, and fracturing of solids. The final example of shape change focuses on the motion of solids with large deformations. The stretch matrix and the rotation matrix of the polar decomposition are chosen to describe the shape change. Observation shows that a third gradient theory is needed to sustain the usual external loads. The new equations of motion are complemented with constitutive laws. Assuming a viscoelastic behavior, a mathematically coherent new predictive theory of motion is derived. The results are extended to motion with smooth and non-smooth self-contact, collision with an obstacle, incompressibility, and plasticity. Extreme behaviors are sufficiently numerous to consider the parti pris that a material may flatten into a surface (e.g., flattening of a structure by a power hammer) or a curve (e.g., transformation of an ingot into a wire in an extruder). Flattening is an example of the importance of the spatial variation of the rotation matrix when investigating the motion of a solid.
650 0 _aMechanics, Applied.
_93253
650 0 _aSolids.
_93750
650 0 _aMechanics.
_98758
650 0 _aEngineering design.
_93802
650 1 4 _aSolid Mechanics.
_931612
650 2 4 _aClassical Mechanics.
_931661
650 2 4 _aEngineering Design.
_93802
710 2 _aSpringerLink (Online service)
_959402
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783319406817
776 0 8 _iPrinted edition:
_z9783319406831
776 0 8 _iPrinted edition:
_z9783319821535
830 0 _aSpringer Series in Solid and Structural Mechanics,
_x2195-352X ;
_v7
_959403
856 4 0 _uhttps://doi.org/10.1007/978-3-319-40682-4
912 _aZDB-2-ENG
912 _aZDB-2-SXE
942 _cEBK
999 _c80340
_d80340