2006
DOI: 10.1016/j.jmps.2005.08.010
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A variational formulation of the coupled thermo-mechanical boundary-value problem for general dissipative solids

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Cited by 183 publications
(226 citation statements)
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References 40 publications
(52 reference statements)
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“…In this manner, meanfield models become controlled approximation schemes resulting in convergent sequences of approximations. Likewise, the variational structure of the theory provides a basis for variational time discretization cf., e. g., Ortiz and Stainier (1999); Yang et al (2006)) and for spatial coarsegraining, e. g., by recourse to the quasi-continuum method (Tadmor et al, 1996;Knap and Ortiz, 2001;Kulkarni et al, 2008;Ariza et al, 2012). These and other extensions suggest worthwhile avenues for further work.…”
Section: Summary and Concluding Remarksmentioning
confidence: 99%
See 1 more Smart Citation
“…In this manner, meanfield models become controlled approximation schemes resulting in convergent sequences of approximations. Likewise, the variational structure of the theory provides a basis for variational time discretization cf., e. g., Ortiz and Stainier (1999); Yang et al (2006)) and for spatial coarsegraining, e. g., by recourse to the quasi-continuum method (Tadmor et al, 1996;Knap and Ortiz, 2001;Kulkarni et al, 2008;Ariza et al, 2012). These and other extensions suggest worthwhile avenues for further work.…”
Section: Summary and Concluding Remarksmentioning
confidence: 99%
“…A powerful connection between variational meanfield theory and variational time-integrators (Ortiz and Stainier, 1999) may be forged by recourse to time discretization (Yang et al, 2006;Kulkarni et al, 2008;Ponga et al, 2012). It is indeed possible to formulate time-discretized minimum principles that fold in both the time-discretization and meanfield approximations into a single functional whose stationarity yields consistent time-discretizations of all governing equations.…”
Section: Proof We Havementioning
confidence: 99%
“…and the flow rules (0.13),(0.14) (Yang et al, 2006;Weinberg et al, 2006;Ortiz and Stainier, 1999;Fancello et al, 2006) that the Euler-Lagrange equations corresponding to the minimization problem (0.25) are the equations of motion…”
Section: M) and The Directions Of Plastic And Viscous Flowsmentioning
confidence: 99%
“…More precisely, the update is performed pointwise at the integration points. Similar numerical procedure and further elaborations can be found, for instance, in [16][17][18][19]. For models based on linearized kinematics, the reader is referred to [20].…”
Section: Introductionmentioning
confidence: 98%
“…In the present paper, an enhanced constitutive update for so-called standard dissipative solids obeying the postulate of maximum dissipation, in line with [13,14,16,20,[17][18][19], is elaborated. In contrast to the algorithms discussed in the cited works, the advocated novel scheme does not rely on any material symmetry and therefore, it can be applied to a broad range of different plasticity theories.…”
Section: Introductionmentioning
confidence: 99%