An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures

Tupek, Michael R.; Radovitzky, Raúl

doi:10.1016/j.jmps.2013.12.012

Cited by 138 publications

(59 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the standard peridynamic constitutive formulation used in this work, unphysical deformation modes allowing matter interpenetration are permitted[27]. This is different from constitutive theory in classical elasticity where interpenetration costs an infinite amount of strain energy.…”

Section: Methodsmentioning

confidence: 99%

Peridynamic Modeling of Ruptures in Biomembranes

et al. 2016

View full text Add to dashboard Cite

We simulate the formation of spontaneous ruptures in supported phospholipid double bilayer membranes, using peridynamic modeling. Experiments performed on spreading double bilayers typically show two distinct kinds of ruptures, floral and fractal, which form spontaneously in the distal (upper) bilayer at late stages of double bilayer formation on high energy substrates. It is, however, currently unresolved which factors govern the occurrence of either rupture type. Variations in the distance between the two bilayers, and the occurrence of interconnections (“pinning sites”) are suspected of contributing to the process. Our new simulations indicate that the pinned regions which form, presumably due to Ca2+ ions serving as bridging agent between the distal and the proximal bilayer, act as nucleation sites for the ruptures. Moreover, assuming that the pinning sites cause a non-zero shear modulus, our simulations also show that they change the rupture mode from floral to fractal. At zero shear modulus the pores appear to be circular, subsequently evolving into floral pores. With increasing shear modulus the pore edges start to branch, favoring fractal morphologies. We conclude that the pinning sites may indirectly determine the rupture morphology by contributing to shear stress in the distal membrane.

show abstract

Section: Methodsmentioning

confidence: 99%

Peridynamic Modeling of Ruptures in Biomembranes

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Although the state-based peridynamics is very promising, it has been observed in numerical simulations that certain nonphysical deformation modes may happen, which can lead to particle interpenetrations [19,20]. This issue is extremely prominent for large deformation problems that have high strain rates resulting from explosive load.…”

Section: State-based Peridynamicsmentioning

confidence: 99%

A hybrid peridynamics–SPH simulation of soil fragmentation by blast loads of buried explosive

Fan

Bergel

2016

International Journal of Impact Engineering

113

View full text Add to dashboard Cite

A B S T R A C TIn this work, we employ both the state-based peridynamics and the smoothed particle hydrodynamics (SPH) to simulate soil fragmentation/ejection induced by the blast of buried explosives. We use peridynamics representation to model soil medium, and we use SPH representation to model explosive gas. The key of the simulation is the coupling of the two. In the peridynamics-SPH computational domain, there is an interphase zone, in which a peridynamic particle can have SPH particles within its own horizon, while an SPH particle can have peridynamic particles within its supporting domain. The interactions of the peridynamic and SPH particles in this interphase zone are discussed. By assuming the equivalence of the two methods in the current configuration, we study how to choose simulation parameters that can seamlessly couple the two methods. A Drucker-Prager plasticity soil model at finite strain is used for soil medium and a charge model of equation of state is used to model the buried explosive. Numerical examples are carried out to simulate soil fragmentation/ejection induced by the shock waves from the buried explosive. It is shown that the numerical results are in general agreement with that of the experiment.

show abstract

“…Non‐ordinary correspondence peridynamics is characterized by a formulation similar to that of other meshfree methods: for uniform grids, the discretizations for the element‐free Galerkin method , the reproducing kernel particle method , and smoothed‐particle hydrodynamics are equivalent to that of the correspondence model . Because all these methods suffer from the zero‐energy mode problem, several techniques to control or minimize it have been proposed in and, in particular, in for the correspondence formulation, but the problem has not yet been completely solved .…”

Section: Introductionmentioning

confidence: 99%

Linearized state‐based peridynamics for 2‐D problems

Sarego

Bobaru

et al. 2016

Numerical Meth Engineering

109

View full text Add to dashboard Cite

Summary In this work, the authors formulate a 2‐D linearized ordinary state‐based peridynamic model of elastic deformations and compute the stiffness matrix for 2‐D plane stress/strain conditions. This model is then verified by testing the recovery of elastic properties for given Poisson's ratios in the range 0.1–0.45. The convergence behavior of peridynamic solutions in terms of the size of the nonlocal region by comparison with the classical (local) mechanics model is also discussed. The degree to which the peridynamic surface effect influences the recovery of elastic properties is examined, and stress/strain recovery values are found to have a definite influence on the results. The technique used here can provide the basis for applying 2‐D peridynamic models to the study of fatigue failure and quasi‐static fracture problems. Copyright © 2016 John Wiley & Sons, Ltd.

show abstract

An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures

Cited by 138 publications

References 25 publications

Peridynamic Modeling of Ruptures in Biomembranes

Peridynamic Modeling of Ruptures in Biomembranes

A hybrid peridynamics–SPH simulation of soil fragmentation by blast loads of buried explosive

Linearized state‐based peridynamics for 2‐D problems

Contact Info

Product

Resources

About