18
1 Introduction
The alternative formulation of visco-plasticity, based on convex analysis in the spirit
of the ‘closest-point-projection’, is advocated by Duvant and Lions [65]. In the realm
of fluid mechanics, Huilgol [66] considers fluids exhibiting a yield stress.
Only few problems of continuum mechanics are amenable to analytical solutions, thus emphatically asking for Computational Continuum Mechanics. Bonet
and Wood [67] present a bespoke combination of non-linear continuum mechanics
and the finite element method. An examination of non-linear continuum mechanics
in concert with the finite element method is offered by Ibrahimbegovic [68]. The
early treatise by Oden [69] develops an amazing integration of non-linear continuum mechanics and the finite element method. Algorithmic illustrations of computational inelasticity are the topic of the contribution by Kojic and Bathe [70]. Shabana
[71] attempts a state-of-the-art coverage of computational continuum mechanics. Le
Tallec [72] provides an in-depth compilation of non-linear computational elasticity. A computational guide to visco-elasticity is given by Marques and Creus [73].
Computational elasticity and plasticity characterise the book by Anandarajah [74].
Borja [75] gives a narrative coverage of theoretical and computational plasticity.
Dunne and Petrinic [76] strive for an engineering tutorial to computational plasticity.
Advanced computational methods in plasticity are contained in De Souza Neto, Peric
and Owen [77]. The comprehensive monograph by Hashiguchi [78] outlines theoretical and computational plasticity. Probably the key references to computational
plasticity are the expositions by Simo and Hughes [79], that contains most influential
computational approaches towards inelasticity, and by Simo [80], that focusses on
the algorithmically-driven analysis and computation of plasticity.
Continuum mechanics and material modelling are also underlying Structural
Modelling. One example is the monograph by Jirasek and Bazant [81] that gives a
systematic presentation of inelastic structural analysis. Chen and Han [82] provide
an application-driven account on engineering plasticity, and Krenk [83] focusses on
the combination of solid and structural mechanics from an engineering viewpoint.
Furthermore, many aspects of Biomechanics are attacked by tools from non-linear
continuum mechanics and the corresponding material modelling. A few examples
are the book by Epstein [84], that takes a differential geometry view on continuum
biomechanics, and the comprehensive exposition on mathematical and mechanical
formulations of biological growth by Goriely [85].
Oftentimes, combinations of continuum mechanics with other areas of continuum
physics, so-called Coupled Problems, are of considerable interest. A non-exhaustive
list comprise the account by Coussy [86] on the mechanics of porous solids, the
landmark tracts on continuum electrodynamics by Eringen and Maugin [87, 88],
and the state-of-the-art treatment of electro- and magneto-elasticity by Dorfmann
and Ogden [89].
Finally, various problems involving defects such as inclusions, vacancies and
interfaces as well as singularities at crack tips, wedges and in dislocation cores can
be approached within the unifying framework of Configurational Mechanics. Here
the main protagonists are the milestone publications on material forces by Maugin
[90, 91], the engineering presentation of mechanics in material space by Kienzler
and Hermann [92], and the views on configurational forces expressed by Gurtin [93].
1 Introduction
The alternative formulation of visco-plasticity, based on convex analysis in the spirit
of the ‘closest-point-projection’, is advocated by Duvant and Lions [65]. In the realm
of fluid mechanics, Huilgol [66] considers fluids exhibiting a yield stress.
Only few problems of continuum mechanics are amenable to analytical solutions, thus emphatically asking for Computational Continuum Mechanics. Bonet
and Wood [67] present a bespoke combination of non-linear continuum mechanics
and the finite element method. An examination of non-linear continuum mechanics
in concert with the finite element method is offered by Ibrahimbegovic [68]. The
early treatise by Oden [69] develops an amazing integration of non-linear continuum mechanics and the finite element method. Algorithmic illustrations of computational inelasticity are the topic of the contribution by Kojic and Bathe [70]. Shabana
[71] attempts a state-of-the-art coverage of computational continuum mechanics. Le
Tallec [72] provides an in-depth compilation of non-linear computational elasticity. A computational guide to visco-elasticity is given by Marques and Creus [73].
Computational elasticity and plasticity characterise the book by Anandarajah [74].
Borja [75] gives a narrative coverage of theoretical and computational plasticity.
Dunne and Petrinic [76] strive for an engineering tutorial to computational plasticity.
Advanced computational methods in plasticity are contained in De Souza Neto, Peric
and Owen [77]. The comprehensive monograph by Hashiguchi [78] outlines theoretical and computational plasticity. Probably the key references to computational
plasticity are the expositions by Simo and Hughes [79], that contains most influential
computational approaches towards inelasticity, and by Simo [80], that focusses on
the algorithmically-driven analysis and computation of plasticity.
Continuum mechanics and material modelling are also underlying Structural
Modelling. One example is the monograph by Jirasek and Bazant [81] that gives a
systematic presentation of inelastic structural analysis. Chen and Han [82] provide
an application-driven account on engineering plasticity, and Krenk [83] focusses on
the combination of solid and structural mechanics from an engineering viewpoint.
Furthermore, many aspects of Biomechanics are attacked by tools from non-linear
continuum mechanics and the corresponding material modelling. A few examples
are the book by Epstein [84], that takes a differential geometry view on continuum
biomechanics, and the comprehensive exposition on mathematical and mechanical
formulations of biological growth by Goriely [85].
Oftentimes, combinations of continuum mechanics with other areas of continuum
physics, so-called Coupled Problems, are of considerable interest. A non-exhaustive
list comprise the account by Coussy [86] on the mechanics of porous solids, the
landmark tracts on continuum electrodynamics by Eringen and Maugin [87, 88],
and the state-of-the-art treatment of electro- and magneto-elasticity by Dorfmann
and Ogden [89].
Finally, various problems involving defects such as inclusions, vacancies and
interfaces as well as singularities at crack tips, wedges and in dislocation cores can
be approached within the unifying framework of Configurational Mechanics. Here
the main protagonists are the milestone publications on material forces by Maugin
[90, 91], the engineering presentation of mechanics in material space by Kienzler
and Hermann [92], and the views on configurational forces expressed by Gurtin [93].