# Mathematical Papers

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Global in time existence of solutions to the
constitutive model of
Bodner -- Partom with isotropic hardening

*Dem. 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-Partom

*Math. 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--Partom

*Math. 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 case

* accepted 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 metals

*GAMM'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 metals

* Roczniki 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 condition

*submitted to Math. Meth. in App. Sci. (1998)*

### Abstract:

In the theory of inelastic behaviour of metals we study an example
of a monotone plastic constitutive equation, which does not belong to the
class of the self-controlling models. Existence and uniqueness
of solutions for this model is obtained in Orlicz spaces using the external
coercive approximation and the Minty-Browder method.

Please note that these files are for personal use only (consider copyright
restrictions by journals).

Last updated on October 6, 1998