# Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics

ESAIM: Control, Optimisation and Calculus of Variations (2014)

- Volume: 20, Issue: 4, page 983-1008
- ISSN: 1292-8119

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topNegri, Matteo. "Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics." ESAIM: Control, Optimisation and Calculus of Variations 20.4 (2014): 983-1008. <http://eudml.org/doc/272770>.

@article{Negri2014,

abstract = {We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class C1 in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence of functionals ℱn and its Γ-limit ℱ we provide, under suitable assumptions, a convergence result for the associated quasi-static evolutions. Finally, we apply this approach to a phase field model in brittle fracture.},

author = {Negri, Matteo},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {quasi-static evolutions; phase-field; quasi-static rate-independent evolutions; graph parametrization; reflexive separable Banach spaces; -limit; brittle fracture},

language = {eng},

number = {4},

pages = {983-1008},

publisher = {EDP-Sciences},

title = {Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics},

url = {http://eudml.org/doc/272770},

volume = {20},

year = {2014},

}

TY - JOUR

AU - Negri, Matteo

TI - Quasi-static rate-independent evolutions: characterization, existence, approximation and application to fracture mechanics

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2014

PB - EDP-Sciences

VL - 20

IS - 4

SP - 983

EP - 1008

AB - We characterize quasi-static rate-independent evolutions, by means of their graph parametrization, in terms of a couple of equations: the first gives stationarity while the second provides the energy balance. An abstract existence result is given for functionals ℱ of class C1 in reflexive separable Banach spaces. We provide a couple of constructive proofs of existence which share common features with the theory of minimizing movements for gradient flows. Moreover, considering a sequence of functionals ℱn and its Γ-limit ℱ we provide, under suitable assumptions, a convergence result for the associated quasi-static evolutions. Finally, we apply this approach to a phase field model in brittle fracture.

LA - eng

KW - quasi-static evolutions; phase-field; quasi-static rate-independent evolutions; graph parametrization; reflexive separable Banach spaces; -limit; brittle fracture

UR - http://eudml.org/doc/272770

ER -

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