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020 _a9783030890704
024 7 _a10.1007/978-3-030-89070-4
_2doi
040 _aTR-AnTOB
_beng
_cTR-AnTOB
_erda
041 _aeng
050 4 _aQA808.2
072 7 _aTGMD
_2bicssc
072 7 _aSCI096000
_2bisacsh
072 7 _aTGMD
_2thema
090 _aQA808.2EBK
100 1 _aSteinmann, Paul.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
245 1 0 _aSpatial and Material Forces in Nonlinear Continuum Mechanics
_h[electronic resource] :
_bA Dissipation-Consistent Approach /
_cby Paul Steinmann.
250 _a1st ed. 2022.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2022.
300 _a1 online resource
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aSolid Mechanics and Its Applications,
_x2214-7764 ;
_v272
505 0 _a1 Introduction -- 2 Kinematics in Bulk Volumes -- 3 Kinematics on Dimensionally Reduced Smooth Manifolds -- 4 Kinematics at Singular Sets -- 5 Generic Balances -- 6 Kinematical 'Balances'* -- 7 Mechanical Balances -- 8 Consequences of Mechanical Balances -- 9 Virtual Work -- 10 Variational Setting -- 11 Thermo-Dynamical Balances -- 12 Consequences of Thermo-Dynamical Balances -- 13 Computational Setting.
520 _aThis 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.
650 0 _aMechanics, Applied.
650 0 _aSolids.
650 0 _aContinuum mechanics.
650 1 4 _aSolid Mechanics.
650 2 4 _aContinuum Mechanics.
710 2 _aSpringerLink (Online service)
830 0 _aSolid Mechanics and Its Applications,
_x2214-7764 ;
_v272
856 4 0 _uhttps://doi.org/10.1007/978-3-030-89070-4
_3Springer eBooks
_zOnline access link to the resource
942 _2lcc
_cEBK