Implicit non-ordinary state-based peridynamics model for linear piezoelectricity

Vieira, Francisco S.; Araújo, Aurélio L.

doi:10.1080/15376494.2021.1995798

Cited by 11 publications

(2 citation statements)

References 64 publications

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“…This is the case of thermomechanical coupling where both the thermal and mechanical field interact and have a high influence in the crack near-fields [40][41][42]. Another example is electromechanical coupling where interactions between electrical and mechanical fields have huge influence both in crack propagation direction and in fracture loads [43,44]. Fluid structure interaction has also been subject of study, where material failure can be accounted for in the simulations [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

Vieira,

Pagaimo,

Magalhães

et al. 2023

Multibody Syst Dyn

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The classical theory of continuum mechanics is formulated using partial differential equations (PDEs) that fail to describe structural discontinuities, such as cracks. This limitation motivated the development of peridynamics, reformulating the classical PDEs into integral-differential equations. In this theory, each material point interacts with its neighbours inside a characteristic length-scale through bond-interaction forces. However, while peridynamics can simulate complex multi-physics phenomena, its integration in the study of mechanical systems is still limited. This work presents a methodology that incorporates a peridynamics formulation into a planar multibody dynamics (MBD) formulation to allow the integration of flexible structures described by peridynamics into mechanical systems. A flexible body is described by a collection of point masses, in analogy with the meshless collocation scheme commonly used for peridynamics discretisations. Each point mass interacts with other point masses through nonlinear forces governed by a bond-based peridynamics (BBPD) formulation. The virtual bodies methodology enables the definition of kinematic joints connecting the flexible body with the neighbouring bodies. The implementation of the methodology proposed is illustrated using various mechanisms with different levels of complexity. Notched plates subjected to different loading conditions are compared with the results presented in the literature of the peridynamics field. The deformations of a flexible slider-crank mechanism compare well with the results obtained using a classical flexible MBD formulation. Additionally, three scenarios involving a rotating pendulum illustrate how the methodology proposed allows simulating impact scenarios. The results demonstrate how this methodology is capable to successfully simulate highly nonlinear phenomena, including crack propagation, in a multibody framework.

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Section: Introductionmentioning

confidence: 99%

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

Vieira,

Pagaimo,

Magalhães

et al. 2023

Multibody Syst Dyn

Self Cite

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“…Due to their large compliance, piezoelectric polymers provide high sensitivity to external mechanical stimuli. Such structures have been extensively analyzed using numerical approaches for both static and dynamic regimes by Chanda and Sahoo (2021); Vieira and Araújo (2021); Cinefra et al (2015a).…”

Section: Introductionmentioning

confidence: 99%

Electromechanical response of poly(vinylidenefluoride) thin films under acoustic stimuli

Viola

Chang

Steckler

et al. 2022

Mechanics of Advanced Materials and Structures

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Understanding and controlling the vibration of piezoelectric components induced by oscillating external stimuli is essential to develop smart sensing and energy harvesting devices that convert mechanical energy into electricity. Piezoelectric polymers based on Poly(vinylidenefluoride) (PVDF) thin films are amongst the most widely studied materials for flexible sensors and harvesters. Despite the large amount of research on these materials, their electromechanical response under acoustic sound stimuli has not yet been studied in detail. In this work, a thorough investigation on the mechanical vibrations and electrical response of PVDF circular plates of different diameters in response to multiple sound wave frequencies (100Hz-10kHz) has been carried out to gain further understanding of the resonance behaviour and acousto-electric conversion mechanisms of vibrating PVDF thin films. The work is based on experimental data generated using an integrated piezo-acoustic laser vibrometry system and on a theoretical framework based on the continuum theory of thin plates. The developed model enables the prediction of the resonance frequencies in dependence of the plates' diameter, and suggests that the electrical voltage generated during vibrations is not solely originating from the piezoelectric properties of the films, but might be affected by additional factors, including the triboelectric effect. The results of this study are expected to have a strong impact on the investigation of piezoelectric vibrating plates and on the development of different types of transducers and energy harvesting devices.

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An improved peridynamics topology optimization formulation for compliance minimization

Vieira,

Araújo

2024

Struct Multidisc Optim

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This work proposes an improved peridynamics density-based topology optimization framework for compliance minimization. One of the main advantages of using a peridynamics discretization relies in the fact that it provides a consistent regularization of classical continuum mechanics into a nonlocal continuum, thus containing an inherent length scale called the horizon. Furthermore, this reformulation allows for discontinuities and is highly suitable for treating fracture and crack propagation. Partial differential equations are rewritten as integrodifferential equations and its numerical implementation can be straightforwardly done using meshfree collocation, inheriting its advantages. In the optimization formulation, Solid Isotropic Material with Penalization (SIMP) is used as interpolation for the design variables. To improve the peridynamic formulation and to evaluate the objective function in a energetically consistent manner, surface correction is implemented. Moreover, a detailed sensitivity analysis reveals an analytical expression for the objective function derivatives, different from an expression commonly used in the literature, providing an important basis for gradient-based topology optimization with peridynamics. The proposed implementation is studied with two examples illustrating different characteristics of this framework. The analytical expression for the sensitivities is validated against a reference solution, providing an improvement over the referred expression in the literature. Also, the effect of using the surface correction is evidenced. An extensive analysis of the horizon size and sensitivity filter radius indicates that the current method is mesh-independent, i.e. a sensitivity filter is redundant since peridynamics intrinsically filters length scales with the horizon. Different optimization methods are also tested for uncracked and cracked structures, demonstrating the capabilities and robustness of the proposed framework.

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Implicit non-ordinary state-based peridynamics model for linear piezoelectricity

Cited by 11 publications

References 64 publications

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

A peridynamics approach to flexible multibody dynamics for fracture analysis of mechanical systems

Electromechanical response of poly(vinylidenefluoride) thin films under acoustic stimuli

An improved peridynamics topology optimization formulation for compliance minimization

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