Plasticity

Han, Weimin; Reddy, B. D.

doi:10.1007/978-1-4614-5940-8

Cited by 80 publications

(34 citation statements)

References 117 publications

(229 reference statements)

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“…Thus, one is left to prove the Γ-convergence of F δ + H(·−P old ) as δ → 0. The Γ-lim inf follows from the Γ-convergence of F δ in Theorem 3.11 as H is independent of δ and lower 15 semicontinuous. The existence of a recovery sequence follows by pointwise convergence: see Proposition 3.6.…”

Section: Proofmentioning

confidence: 96%

Quasistatic elastoplasticity via Peridynamics: existence and localization

Kružík

Mora-Corral

Stefanelli

2018

Continuum Mech. Thermodyn.

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Peridynamics is a nonlocal continuum-mechanical theory based on minimal regularity on the deformations. Its key trait is that of replacing local constitutive relations featuring spacial differential operators with integrals over differences of displacement fields over a suitable positive interaction range. The advantage of such perspective is that of directly including nonregular situations, in which discontinuities in the displacement field may occur. In the linearized elastic setting, the mechanical foundation of the theory and its mathematical amenability have been thoroughly analyzed in the last years.We present here the extension of Peridynamics to linearized elastoplasticity. This calls for considering the time evolution of elastic and plastic variables, as the effect of a combination of elastic energy storage and plastic energy dissipation mechanisms. The quasistatic evolution problem is variationally reformulated and solved by time discretization. In addition, by a rigorous evolutive Γ-convergence argument we prove that the nonlocal peridynamic model converges to classic local elastoplasticity as the interaction range goes to zero. 2

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Section: Proofmentioning

confidence: 96%

Quasistatic elastoplasticity via Peridynamics: existence and localization

Kružík

Mora-Corral

Stefanelli

2018

Continuum Mech. Thermodyn.

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“…As the dissipation is generally nonsmooth, the derivative is to be understood as the subgradient of ϕ, which represents a set. In what follows, we will regularize the dissipation function appropriately such that the subgradient reduces to the conventional derivative, see [9,24]. To a priori fulfill the Clausius-Duhem inequality of positive dissipation (46), which, in terms of the dissipation function, transforms into…”

Section: Dissipative Responsementioning

confidence: 99%

“…For the numerical analysis, we regularize the dissipation function such that its derivative always exists. In the context of plasticity, Han and Reddy [9] proposed and analyzed a regularization of the form…”

Section: Dissipative Responsementioning

confidence: 99%

Nonlinear electromechanical coupling in ferroelectric materials: large deformation and hysteresis

et al. 2020

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Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct and converse piezoelectric effects, for instance, is used for both actuation and sensing in diverse engineering applications. The response of ferroelectric materials depends on their state of remanent polarization and the presence of an external electric field. To extend the operational range of sensors and actuators, an accurate understanding of the evolution of the material's state of polarization is imperative, which requires both physical and geometric nonlinearities to be taken into account. Moreover, polymeric smart materials like PVDF allow significantly larger deformation as compared to conventional piezoelectric ceramics. The electromechanical coupling in piezoelectric materials manifests in ferroelectric and ferroelastic hystereses, which are related to both reversible and irreversible processes. Focusing on the latter, we transfer phenomenological models for domain switching in ferroelectric materials to the geometrically nonlinear regime. For this purpose, we follow related concepts of geometrically nonlinear elastoplasticity, where the concept of a multiplicative decomposition of the deformation gradient plays a key role. Accordingly, an additional deformation path that describes the evolution of the poled state from the unpoled referential configuration is introduced. The constitutive response of the material to mechanical and electrical loads is discussed, and dissipative internal forces that drive the evolution of the remanent polarization are derived within a thermodynamical framework and the principle of maximum dissipation.

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“…Our notation follows Han and Reddy [1999] for the forward problem. Since the presentation of optimality conditions relies on adjoint variables and Lagrange multipliers associated with inequality constraints, additional variables are needed.…”

Section: Notation and Standing Assumptionsmentioning

confidence: 99%

Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications

Herzog

Meyer

Wachsmuth

2014

International Series of Numerical Mathematics

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Abstract. An optimal control problem is considered for the variational inequality representing the stress-based (dual) formulation of static elastoplasticity. The linear kinematic hardening model and the von Mises yield condition are used. The forward system is reformulated such that it involves the plastic multiplier and a complementarity condition. In order to derive necessary optimality conditions, a family of regularized optimal control problems is analyzed. C-stationarity type conditions are obtained by passing to the limit with the regularization. Numerical results are presented.Mathematics Subject Classification (2010). Primary 49K20, 70Q05, 74C05; Secondary 90C33, 35R45.

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Plasticity

Cited by 80 publications

References 117 publications

Quasistatic elastoplasticity via Peridynamics: existence and localization

Quasistatic elastoplasticity via Peridynamics: existence and localization

Nonlinear electromechanical coupling in ferroelectric materials: large deformation and hysteresis

Optimal Control of Elastoplastic Processes: Analysis, Algorithms, Numerical Analysis and Applications

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