LEADER 04136nam 22005775 450 001 9910556897103321 005 20251113180219.0 010 $a3-030-89070-8 024 7 $a10.1007/978-3-030-89070-4 035 $a(MiAaPQ)EBC6941399 035 $a(Au-PeEL)EBL6941399 035 $a(CKB)21435611200041 035 $a(PPN)261518364 035 $a(OCoLC)1312170023 035 $a(DE-He213)978-3-030-89070-4 035 $a(EXLCZ)9921435611200041 100 $a20220328d2022 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aSpatial and Material Forces in Nonlinear Continuum Mechanics $eA Dissipation-Consistent Approach /$fby Paul Steinmann 205 $a1st ed. 2022. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2022. 215 $a1 online resource (418 pages) 225 1 $aSolid Mechanics and Its Applications,$x2214-7764 ;$v272 311 08$aPrint version: Steinmann, Paul Spatial and Material Forces in Nonlinear Continuum Mechanics Cham : Springer International Publishing AG,c2022 9783030890698 327 $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. 330 $aThis monograph details spatial and material vistas on non-linear continuum mechanics in a dissipation-consistent approach. Thereby, the spatial vista renders the common approach to nonlinear continuum mechanics and corresponding spatial forces, whereas the material vista elaborates on configurational mechanics and corresponding material or rather configurational forces. Fundamental to configurational mechanics is the concept of force. In analytical mechanics, force is a derived object that is power conjugate to changes of generalised coordinates. For a continuum body, these are typically the spatial positions of its continuum points. However, if in agreement with the second law, continuum points, e.g. on the boundary, may also change their material positions. Configurational forces are then power conjugate to these configurational changes. A paradigm is a crack tip, i.e. a singular part of the boundary changing its position during crack propagation, with the related configurational force, typically the J-integral, driving its evolution, thereby consuming power, typically expressed as the energy release rate. Taken together, configurational mechanics is an unconventional branch of continuum physics rationalising and unifying the tendency of a continuum body to change its material configuration. It is thus the ideal formulation to tackle sophisticated problems in continuum defect mechanics. Configurational mechanics is entirely free of restrictions regarding geometrical and constitutive nonlinearities and offers an accompanying versatile computational approach to continuum defect mechanics. In this monograph, I present a detailed summary account of my approach towards configurational mechanics, thereby fostering my view that configurational forces are indeed dissipation-consistent to configurational changes. 410 0$aSolid Mechanics and Its Applications,$x2214-7764 ;$v272 606 $aMechanics, Applied 606 $aSolids 606 $aContinuum mechanics 606 $aSolid Mechanics 606 $aContinuum Mechanics 615 0$aMechanics, Applied. 615 0$aSolids. 615 0$aContinuum mechanics. 615 14$aSolid Mechanics. 615 24$aContinuum Mechanics. 676 $a531 676 $a531.7 700 $aSteinmann$b Paul$0739814 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910556897103321 996 $aSpatial and Material Forces in Nonlinear Continuum Mechanics$94462757 997 $aUNINA