Periodic solutions of non-linear kinematic hardening models

Kunze, Markus

doi:10.1002/(sici)1099-1476(199904)22:6<515::aid-mma48>3.0.co;2-s

Cited by 9 publications

(5 citation statements)

References 8 publications

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“…and f : R × R n × R → R n (see [15,29,23,18]). The unboundedness of the right-hand-sides in (1) makes the classical theory of differential inclusions (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Global stability of almost periodic solutions to monotone sweeping processes and their response to non-monotone perturbations

Kamenskiĭ

Makarenkov

Wadippuli

et al. 2018

Nonlinear Analysis: Hybrid Systems

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We develop a theory which allows making qualitative conclusions about the dynamics of both monotone and non-monotone Moreau sweeping processes. Specifically, we first prove that any sweeping processes with almost periodic monotone right-hand-sides admits a globally exponentially stable almost periodic solution. And then we describe the extent to which such a globally stable solution persists under non-monotone perturbations.

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“…and f : R × R n × R → R n (see [15,29,23,18]). The unboundedness of the right-hand-sides in (1) makes the classical theory of differential inclusions (see e.g.…”

Section: Introductionmentioning

confidence: 99%

Global stability of almost periodic solutions to monotone sweeping processes and their response to non-monotone perturbations

Kamenskiĭ

Makarenkov

Wadippuli

et al. 2018

Nonlinear Analysis: Hybrid Systems

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“…From [9] it is known that for each admissible periodic input there exists a periodic solution of (1) - (3). We give here a partial answer to the 2 Stress-controlled Armstrong -Frederick model 2…”

Section: Introductionmentioning

confidence: 93%

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

Brokate

Рачинский

2006

Nonlinear differ. equ. appl.

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The paper is concerned with the study of plasticity models described by differential equations with stop and play operators. We suggest sufficient conditions for the global stability of a unique periodic solution for the scalar models and for the vector models with biaxial inputs of a particular form, namely the sum of a uniaxial function and a constant term. For another class of simple biaxial inputs, we present an example of the existence of unstable periodic solutions.2000 Mathematics Subject Classification: 47J40, 74C05

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“…To prove the convergence of {x n k (t, q n k , λ n k )} k∈N we will now extend the discrete map (18) to such an operator F n : C([0, T ], E) → C([0, T ], E) whose fixed point is exactly t → x n (t, q n , λ n ). The convergence of x n k will then follow from the continuity of F n in n at n = ∞.…”

Section: Convergence Of the Catching-up Algorithmmentioning

confidence: 99%

“…Motivated by applications to elastoplastic models with hardening and softening (see e.g. Gilles-Ulisse [12], Kunze [18]), the present paper investigates the initial-value and periodic problems to the following state-dependent version of (3):…”

Section: Introductionmentioning

confidence: 99%

A continuation principle for periodic BV-continuous state-dependent sweeping processes

Kamenskiĭ¹,

Makarenkov²,

Wadippuli³

2018

Preprint

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We consider a Caratheodory differential equation with a state-dependent convex constraint that changes BV-continuously in time (a perturbed BVcontinuous state-dependent sweeping processes). By setting up an appropriate catching-up algorithm we prove solvability of the initial value problem. Then, for sweeping processes with T -periodic right-hand-sides, we prove the existence of at least one T -periodic solution. Finally, we further consider a T -periodic sweeping process which is close to an autonomous sweeping process with a constant constraint and prove the existence of a T -periodic solution specifically located near the boundary switched equilibrium of the autonomous sweeping process.

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Periodic solutions of non-linear kinematic hardening models

Cited by 9 publications

References 8 publications

Global stability of almost periodic solutions to monotone sweeping processes and their response to non-monotone perturbations

Global stability of almost periodic solutions to monotone sweeping processes and their response to non-monotone perturbations

Global stability of the Armstrong-Frederick model with periodic biaxial inputs

A continuation principle for periodic BV-continuous state-dependent sweeping processes

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