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Existence theory for the equations of inelastic material behavior of metals - Transformation of interior variables and energy estimates

100%

Alber H.-D., Chełmiński K.

Mathematica Applicanda

1996

tom 25

nr 39

The system of equations, which we study, consists of linear partial differential equations and of nonlinear ordinary differential equations for internal variables. The existence theory for such systems was studied first by the french mathematicians G. Duvaut and J.L. Lions [1]. Next we can find in the literature a work of C. Johnson [2] on a quasi-static problem for a special model. Then in the nineties we can find more works in the domain. 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.

Coercive limits for a subclass of monotonne constitutive equations in the theory of inelastic material behaviour of metals

80%

Chełmiński K.

Mathematica Applicanda

1997

tom 26

nr 40

We prove existence and uniqueness of strong global in tme solution 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.

Ograniczanie wyników

2 Mathematica Applicanda

2 Chełmiński K.

1 Alber H.-D.

1 1997

1 1996

Wyniki wyszukiwania

Existence theory for the equations of inelastic material behavior of metals - Transformation of interior variables and energy estimates

Coercive limits for a subclass of monotonne constitutive equations in the theory of inelastic material behaviour of metals