Quasistatic nonlinear viscoelasticity and gradient flows

Name: Quasistatic nonlinear viscoelasticity and gradient flows
Author: Ball, J. M., Şengül, Yasemin

İsim	Quasistatic nonlinear viscoelasticity and gradient flows
Yazar	Ball, J. M., Şengül, Yasemin
Basım Tarihi:	2014
Basım Yeri	- Springer Science+Business Media
Konu	Viscoelasticity, Gradient flows, Nonlinear partial differential equations, Infinite-dimensional dynamical systems
Tür	Süreli Yayın
Dil	İngilizce
Dijital	Evet
Yazma	Hayır
Kütüphane:	Özyeğin Üniversitesi
Demirbaş Numarası	1572-9222
Kayıt Numarası	a8140187-8c0b-4667-9cfb-5a2538f46981
Lokasyon	Natural and Mathematical Sciences
Tarih	2014
Notlar	Oxford Centre for Nonlinear PDE ; European Commission ; TÜBİTAK
Örnek Metin	We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is λ-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the deformation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium state as time t→∞ and prove convergence to equilibrium under a nondegeneracy condition. We show that this condition is satisfied in particular for any real analytic cubic-like stress-strain function.
DOI	10.1007/s10884-014-9410-1

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Quasistatic nonlinear viscoelasticity and gradient flows

Yazar Ball, J. M., Şengül, Yasemin

Basım Tarihi 2014

Basım Yeri - Springer Science+Business Media

Konu Viscoelasticity, Gradient flows, Nonlinear partial differential equations, Infinite-dimensional dynamical systems

Tür Süreli Yayın

Dil İngilizce

Dijital Evet

Yazma Hayır

Kütüphane Özyeğin Üniversitesi

Demirbaş Numarası 1572-9222

Kayıt Numarası a8140187-8c0b-4667-9cfb-5a2538f46981

Lokasyon Natural and Mathematical Sciences

Tarih 2014

Notlar Oxford Centre for Nonlinear PDE ; European Commission ; TÜBİTAK

Örnek Metin We consider the equation of motion for one-dimensional nonlinear viscoelasticity of strain-rate type under the assumption that the stored-energy function is λ-convex, which allows for solid phase transformations. We formulate this problem as a gradient flow, leading to existence and uniqueness of solutions. By approximating general initial data by those in which the deformation gradient takes only finitely many values, we show that under suitable hypotheses on the stored-energy function the deformation gradient is instantaneously bounded and bounded away from zero. Finally, we discuss the open problem of showing that every solution converges to an equilibrium state as time t→∞ and prove convergence to equilibrium under a nondegeneracy condition. We show that this condition is satisfied in particular for any real analytic cubic-like stress-strain function.

DOI 10.1007/s10884-014-9410-1