Displaying similar documents to “Numerical approaches to rate-independent processes and applications in inelasticity”

A finite element scheme for the evolution of orientational order in fluid membranes

Sören Bartels, Georg Dolzmann, Ricardo H. Nochetto (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We investigate the evolution of an almost flat membrane driven by competition of the homogeneous, Frank, and bending energies as well as the coupling of the local order of the constituent molecules of the membrane to its curvature. We propose an alternative to the model in [J.B. Fournier and P. Galatoa, (1997) 1509–1520; N. Uchida, (2002) 040902] which replaces a Ginzburg-Landau penalization for the length of the order parameter by a rigid constraint. We...

Convergence of a fully discrete finite element method for a degenerate parabolic system modelling nematic liquid crystals with variable degree of orientation

John W. Barrett, Xiaobing Feng, Andreas Prohl (2006)

ESAIM: Mathematical Modelling and Numerical Analysis

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We consider a degenerate parabolic system which models the evolution of nematic liquid crystal with variable degree of orientation. The system is a slight modification to that proposed in [Calderer , (2002) 1033–1047], which is a special case of Ericksen's general continuum model in [Ericksen, (1991) 97–120]. We prove the global existence of weak solutions by passing to the limit in a regularized system. Moreover, we propose a practical fully discrete...

On the numerical modeling of deformations of pressurized martensitic thin films

Pavel Bělík, Timothy Brule, Mitchell Luskin (2001)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We propose, analyze, and compare several numerical methods for the computation of the deformation of a pressurized martensitic thin film. Numerical results have been obtained for the hysteresis of the deformation as the film transforms reversibly from austenite to martensite.

A class of minimum principles for characterizing the trajectories and the relaxation of dissipative systems

Michael Ortiz, Alexander Mielke (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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This work is concerned with the reformulation of evolutionary problems in a weak form enabling consideration of solutions that may exhibit evolving microstructures. This reformulation is accomplished by expressing the evolutionary problem in variational form, i.e., by identifying a functional whose minimizers represent entire trajectories of the system. The particular class of functionals under consideration is derived by first defining a sequence of time-discretized minimum problems...