Global in time existence of solutions to the
constitutive model of
Bodner -- Partom with isotropic hardeningDem. Math. v. 28 pp. 667-688, 1995
Abstract:
We study a system of equations modelling the nonelastic deformation of metals. This system has been proposed by R.S. Bodner and Y. Partom. We show that in the one-dimensional case the initial boundary-value problem generated by this system has global in time solutions to all sufficiently small initial data.
On large solutions for the quasistatic problem in
nonlinear viscoelasticity with the constitutive
equations of Bodner-PartomMath. Meth. in App. Sci. v. 19 pp. 933-942, 1996
Abstract:
This work proves global in time existence of large solutions for a quasistatic problem in nonlinear viscoelasticity in the three-dimensional case. The basic idea is to apply the energy method for local in time solutions.
Energy estimates and global in time results for
a problem from nonlinear viscoelasticity Bull. of Pol. Acad. of Sci.: Math. v. 44 pp. 465-477, 1996
Abstract:
This paper proves global in time existence to large solutions for a problem in nonlinear viscoelasticity in the three--dimensional dynamical case with a bounded constitutive function. The idea of the proof is to show energy estimates for a Faedo--Galerkin sequence of approximate solutions.
Existence theory for the equations of inelastic material
behaviour of metals -- Transformation of interior variables
and energy estimates(with H.-D. Alber) Roczniki PTM: App. Math. v.39 pp 1-15, 1996
Abstract:
This work consists of two parts. In the first part we will classify constitutive equations and therefore we define constitutive equations of monotone type. Moreover by transformation of internal variables we will enlarge the class of constitutive equations, for which we can prove a global in time existence theorem for large initial data. But there exist models, which are not of monotone type and which we can not transform to monotone type. Therefore we must study such models with other methods. This is the second part of the work. We write about the energy method for the model of Bodner-Partom.
Stress $L^{\infty}$-- estimates and the uniqueness
problem for the quasistatic equations
to the model of Bodner--PartomMath. Meth. in App. Sci. v.20 pp.1127-1134 (1997)
Abstract:
This paper proves the uniqueness result for global in time large solutions of quasistatic equations to an inelastic model of material behaviour of metals, provided that an apriori L^{\infty}--estimation for the Cauchy stress tensor holds.
Stress $L^{\infty}$-- estimates and the uniqueness
problem for the equations
to the model of Bodner--Partom
in the two dimensional caseaccepted for publication in Math. Meth. in App. Sci. (1997)
Abstract:
This paper is a continuation of the previous work. We prove the uniqueness result for global in time large solutions of dynamic equations to an inelastic model of material behaviour of metals in the two dimensional case, provided a higher regularity of the solutions. Moreover the L^p-stability for p<2 of the solutions in the case of homogeneous boundary data is established.
On initial-boundary value problems for the inelastic material
behaviour of metalsGAMM'97-proceeding, ZAMM v.78 suppl.3 pp. 873-876 (1998)
Abstract:
We prove existence of strong solutions for a subclass of noncoercive, monotone constitutive equations in the theory of inelastic material behaviour of metals.
On the Model of Bodner-Partom with Nonhomogeneous
Boundary Data(with P. Gwiazda) submitted to Mathematische Nachrichten (1997)
Abstract:
In the present paper we study existence and the uniqueness of global in time, strong, large solutions to the inelastic model of Bodner--Partom with nonhomogeneous boundary data, and with the perturbation term A((y-y_2)/y_1)^r in the equation for the isotropic hardening function y. Moreover we consider the limit case A -> 0^+ and prove the convergence result in a suitable topology to the unperturbed problem.
Coercive limits for a subclass of monotone constitutive equations
in the theory of inelastic material behaviour of metalsRoczniki PTM: App. Math. v.40 pp. 41-81 (1997)
Abstract:
We prove existence and uniqueness of strong global in time solutions for a subclass of monotone constitutive equations in the theory of inelastic material behaviour of metals without the coercivity assumption for the free energy function. We approximate noncoercive models by a sequence of coercive problems and prove the convergence result.
Monotonicity of Operators of Viscoplastic Response:
Application to the Model of Bodner-Partom
(with P. Gwiazda) Preprint No. 1949 in FB Math. TU Darmstadt and submitted to Bull. of Pol. Acad. of Sci.: Tech. Sci. (1997)
Abstract:
We study monotone lipschitz perturbations of the class of monotone constitutive equations. Moreover, using the idea of coercive limits, we obtain existence of large, global in time, strong solutions for the system of equations modelling the nonelastic material behavior of a metal with the constitutive equations proposed by S.R. Bodner and Y. Partom.
On self-controlling models in the theory of inelastic
material behavior of metals Continuum Mechanics and Thermodynamics v.10 pp. 121-133 (1998)
Abstract:
We discuss here solvability of systems modelling the nonelastic material behavior of metals under the assumption of monotonicity of the constitutive function and of the self-controlling property of the model under consideration. The main idea is to use the conception of coercive limits and to prove a suitable convergence result. Examples of self-controlling models are presented at the end of the article.
On monotone plastic constitutive equations with
polynomial growth conditionsubmitted to Math. Meth. in App. Sci. (1998)