TITLE

Quasistatic evolution for Cam-Clay plasticity: a weak formulation via viscoplastic regularization and time rescaling

AUTHOR(S)
Dal Maso, Gianni; DeSimone, Antonio; Solombrino, Francesco
PUB. DATE
January 2011
SOURCE
Calculus of Variations & Partial Differential Equations;Jan2011, Vol. 40 Issue 1/2, p125
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Cam-Clay nonassociative plasticity exhibits both hardening and softening behaviour, depending on the loading. For many initial data the classical formulation of the quasistatic evolution problem has no smooth solution. We propose here a notion of generalized solution, based on a viscoplastic approximation. To study the limit of the viscoplastic evolutions we rescale time, in such a way that the plastic strain is uniformly Lipschitz with respect to the rescaled time. The limit of these rescaled solutions, as the viscosity parameter tends to zero, is characterized through an energy-dissipation balance, that can be written in a natural way using the rescaled time. As shown in Dal Maso and DeSimone (Math Models Methods Appl Sci 19:1-69, 2009) and Dal Maso and Solombrino (Netw Heterog Media 5:97-132, 2010), the proposed solution may be discontinuous with respect to the original time. Our formulation allows us to compute the amount of viscous dissipation occurring instantaneously at each discontinuity time.
ACCESSION #
55471501

 

Related Articles

  • On Some Properties of Szasz-Mirakyan Operators in H�lder Spaces. Rempulska, L.; Walczak, Z. // Turkish Journal of Mathematics;2003, Vol. 27 Issue 3, p435 

    Examines some properties of Szasz-Mirakyan operators in H�lder spaces. Presentation of basic formula on examining approximation properties of Szasz-Mirakyan operators; Theorems on the degree of approximation of functions by these operators.

  • Upper Subderivatives and Generalized Gradients of the Marginal Function of a Non-Lipschitzian Program. Ward, D. E.; Lee, G. M. // Annals of Operations Research;2001, Vol. 101 Issue 1-4, p299 

    We obtain an upper bound for the upper subderivative of the marginal function of an abstract parametric optimization problem when the objective function is lower semicontinuous. Moreover, we apply the result to a nonlinear program with right-hand side perturbations. As a result, we obtain an...

  • Approximate Regulator for Evolutionary Inclusions Subdifferential Type. Kapustyan, O. A.; Yasinsky, V. V. // Naukovi visti NTUU - KPI;2012, Vol. 81 Issue 1, p64 

    The article considers the problem of optimal stabilization for an evolution inclusion of subdifferential type with non-Lipschitz multi-valued interaction function of ε ⋅ F(y), where ε > 0 -- small parameter. Provided that ε = 0 problem allows an optimal regulator u [y], we prove...

  • The Steiner Formula and the Polar Moment of Inertia for the Closed Planar Homothetic Motions in Complex Plane. Tutar, Ayhan; Sener, Onder // Advances in Mathematical Physics;9/1/2015, Vol. 2015, p1 

    The Steiner area formula and the polar moment of inertia were expressed during one-parameter closed planar homothetic motions in complex plane. The Steiner point or Steiner normal concepts were described according to whether rotation number was different from zero or equal to zero, respectively....

  • Bruck formula for a perturbed Lipschitzian iteration of Lipschitz pseudocontractive maps. Kumar, Krishna; Sharma, B. // Applied Mathematics & Mechanics;Nov2005, Vol. 26 Issue 11, p1427 

    The solution to evolution equations has developed an independent theory within nonlinear analysis dealing with the existence and approximation of such solution (fixed point) of pseudocontractive operators and its variants. The object is to introduce a perturbed iteration method for proving the...

  • Consolidation by Prefabricated Vertical Drains with a Threshold Gradient. Xiao Guo; Kang-He Xie; Yue-Bao Deng // Mathematical Problems in Engineering;2014, p1 

    This paper shows the development of an approximate analytical solution of radial consolidation by prefabricated vertical drains with a threshold gradient. To understand the effect of the threshold gradient on consolidation, a parametric analysis was performed using the present solution. The...

  • The issue of forecasting and control of the knowledge evolution in complex training systems. Yasinsky, V. V. // Naukovi visti NTUU - KPI;2011, Vol. 2011 Issue 6, p79 

    Relying on studies of systematic approach, we investigate the issue of forecasting and control for the model describing the knowledge evolution in complex training systems. We obtain the substantial mathematical results for the proposed nonlinear evolution equation. These results depend on...

  • Stochastic dynamo in critical situations. Klyatskin, V. // Theoretical & Mathematical Physics;Sep2012, Vol. 172 Issue 3, p1243 

    Based on the functional method of consecutive approximations, we consider the problem of magnetic field excitation (stochastic dynamo) by a random velocity field with a finite temporal correlation radius. In critical situations, in the first (diffusion) approximation, the Lyapunov characteristic...

  • Well-Posedness of the Ericksen—Leslie System. Wang, Wei; Zhang, Pingwen; Zhang, Zhifei // Archive for Rational Mechanics & Analysis;Dec2013, Vol. 210 Issue 3, p837 

    We prove the local well-posedness of the Ericksen–Leslie system, and the global well-posedness for small initial data under a physical constraint condition on the Leslie coefficients, which ensures that the energy of the system is dissipated. Instead of the Ginzburg–Landau...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics