On the role of bond-associated stabilization and discretization on deformation and fracture in non-ordinary state-based peridynamics

Vieira, Francisco S.; Araújo, Aurélio L.

doi:10.1016/j.engfracmech.2022.108557

Cited by 10 publications

(2 citation statements)

References 69 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…To assess the numerical accuracy of the formulation, Fig. 9 shows the load-displacement curve of the MBD-PD numerical dynamic simulation and a comparison with quasi-static results from the literature [63][64][65][66]. As can be observed, the result obtained in the present work is in good agreement with the references.…”

Section: Plate Subject To Traction Loadingsupporting

confidence: 78%

See 1 more Smart Citation

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

Vieira,

Pagaimo,

Magalhães

et al. 2023

Multibody Syst Dyn

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Plate Subject To Traction Loadingsupporting

confidence: 78%

“…In the computational fracture mechanics literature, the single-edge notched test is a commonly used benchmark where a square plate is subjected to tension and shear in-plane loads [63][64][65][66]. Figure 7 shows a simple setup with general boundary conditions and associated virtual bodies and kinematic joints.…”

Section: Plate With Different In-plane Loadingsmentioning

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

View full text Add to dashboard Cite

show abstract

An improved peridynamics topology optimization formulation for compliance minimization

Vieira,

Araújo

2024

Struct Multidisc Optim

View full text Add to dashboard Cite

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.

show abstract

Quantifying Post-peak Behavior of Rocks with Type-I, Type-II, and Mixed Fractures by Developing a Quasi-State-Based Peridynamics

Tian,

Liu,

Zhou

et al. 2024

Rock Mech Rock Eng

View full text Add to dashboard Cite

On the role of bond-associated stabilization and discretization on deformation and fracture in non-ordinary state-based peridynamics

Cited by 10 publications

References 69 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

An improved peridynamics topology optimization formulation for compliance minimization

Quantifying Post-peak Behavior of Rocks with Type-I, Type-II, and Mixed Fractures by Developing a Quasi-State-Based Peridynamics

Contact Info

Product

Resources

About