Quasistatic Problems in Viscoplasticity Theory I: Models with Linear Hardening

Alber, Hans-Dieter; Chełmiński, Krzysztof

doi:10.1007/978-3-0348-7926-2_22

Cited by 31 publications

(70 citation statements)

References 6 publications

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“…This is essentially the way chosen in Reference [3,4] to prove existence and uniqueness for the Norton-Ho model and the special models with kinematic hardening. The reader is referred to References [3,4] for details. This approach has many disadvantages, since it leads only to partial results.…”

Section: What Are the Right Spaces?mentioning

confidence: 99%

“…The extension of the results of the papers [3,4] is not the only reason to write this paper. There are moreover two other purposes.…”

Section: Introductionmentioning

confidence: 94%

“…In case of the model with kinematic hardening the existence was obtained only in a special case, namely ¿r. Below we sketch brie y the method used in References [3,4]. Later in the paper we prove (in a di erent way) existence and uniqueness of a solution to the kinematic hardening model for any constants r; ¿1, but only in the autonomous case, i.e.…”

Section: Introductionmentioning

confidence: 95%

“…The existence of solutions to both the Norton-Ho model and the model with kinematic hardening of power law type in the quasistatic case was studied recently in References [3,4]. In case of the model with kinematic hardening the existence was obtained only in a special case, namely ¿r.…”

Section: Introductionmentioning

confidence: 97%

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Quasistatic and dynamic problems in viscoplasticity theory—non‐linearities with power growth

Pompe

2004

Math Methods in App Sciences

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SUMMARYWe ÿnd a common abstract formulation of the quasistatic and dynamic problems from viscoplasticity theory. Based on this formulation we show existence and uniqueness of the solution to this abstract problem by choosing appropriate spaces and by reducing the problem to an evolution equation, which can be treated by the general theory of monotone operators in Hilbert space. Our proof is valid for non-linearities in the constitutive equation with power law growth.

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Section: What Are the Right Spaces?mentioning

confidence: 99%

“…The extension of the results of the papers [3,4] is not the only reason to write this paper. There are moreover two other purposes.…”

Section: Introductionmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 97%

See 2 more Smart Citations

Quasistatic and dynamic problems in viscoplasticity theory—non‐linearities with power growth

Pompe

2004

Math Methods in App Sciences

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“…There is a well developed existence theory to a wide range of problems in plasticity. Some results can be found in [1], [2], [6], [10]. But in the piezoelectric models the electric and mechanical properties of materials are coupled.…”

Section: Introductionmentioning

confidence: 98%

Existence results for a nonlinear evolution equation containing a composition of two monotone operators

Kraynyukova

2011

GAMM-Mitteilungen

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We present an existence result for an evolution equation with a nonlinear operator, which is a composition of two monotone mappings. The first monotone mapping is a subdifferential of the indicator function of some convex set while the other is constructed as the Nemyckii operator of a monotone function. Such equations arise from the mathematical models, which describe piezoelectric material behavior. Under some additional assumptions we prove the existence and uniqueness of the strong solution for the case, when the operator generated by the monotone function is a Lipschitz continuous mapping. In the case of a nonlinear growth of the monotone function we prove the existence of the strong solution.

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Existence of solution for a nonlinear model of thermo‐visco‐plasticity

Bartczak

Owczarek

2018

Math Methods in App Sciences

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a visco-plastic metal subjected to temperature changes. We complete the model with the mixed boundary condition on displacement and stress and Neumann-type condition for temperature. The main result is an existence of solutions. KEYWORDScontinuum mechanics, heat conduction, thermo-visco-plasticity, viscoplastic deformation t l (t, x) =Λ ( (t, x), (t, x)), u(t, x))) · ( t u(t, x)). (TP)Math Meth Appl Sci. 2018;41:3533-3546. wileyonlinelibrary.com/journal/mma

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Quasistatic Problems in Viscoplasticity Theory I: Models with Linear Hardening

Cited by 31 publications

References 6 publications

Quasistatic and dynamic problems in viscoplasticity theory—non‐linearities with power growth

Quasistatic and dynamic problems in viscoplasticity theory—non‐linearities with power growth

Existence results for a nonlinear evolution equation containing a composition of two monotone operators

Existence of solution for a nonlinear model of thermo‐visco‐plasticity

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