Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase field fracture by nonlocal operator method

Ren, Huilong; Zhuang, Xiaoying; Öterkuş, Erkan; Zhu, Hehua; Rabczuk, Timon

doi:10.48550/arxiv.2103.08696

Cited by 2 publications

(2 citation statements)

References 71 publications

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“…Subsequently, state-based peridynamics was developed [2], introducing the possibility of varying the Poisson's ratio. In the literature, there are many examples of applications [3,4], ranging from complex crack patterns, such as spontaneous branching [5], to multi-physics problems involving fracture [6,7].…”

Section: Introductionmentioning

confidence: 99%

Accurate computation of partial volumes in 3D peridynamics

Scabbia

Zaccariotto

Galvanetto

2022

Engineering with Computers

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The peridynamic theory is a nonlocal formulation of continuum mechanics based on integro-differential equations, devised to deal with fracture in solid bodies. In particular, the forces acting on each material point are evaluated as the integral of the nonlocal interactions with all the neighboring points within a spherical region, called “neighborhood”. Peridynamic bodies are commonly discretized by means of a meshfree method into a uniform grid of cubic cells. The numerical integration of the nonlocal interactions over the neighborhood strongly affects the accuracy and the convergence behavior of the results. However, near the boundary of the neighborhood, some cells are only partially within the sphere. Therefore, the quadrature weights related to those cells are computed as the fraction of cell volume which actually lies inside the neighborhood. This leads to the complex computation of the volume of several cube–sphere intersections for different positions of the cells. We developed an innovative algorithm able to accurately compute the quadrature weights in 3D peridynamics for any value of the grid spacing (when considering fixed the radius of the neighborhood). Several examples have been presented to show the capabilities of the proposed algorithm. With respect to the most common algorithm to date, the new algorithm provides an evident improvement in the accuracy of the results and a smoother convergence behavior as the grid spacing decreases.

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Section: Introductionmentioning

confidence: 99%

Accurate computation of partial volumes in 3D peridynamics

Scabbia

Zaccariotto

Galvanetto

2022

Engineering with Computers

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“…In these methods, such as the gradient-enhanced damage model and its variants [8,51,52,61], and the phase-field model (PFM) [3,21,44], a sharp crack is approximated by a diffuse damage band thanks to introducing a length-scale parameter that controls interactions between material points. Generalizing Griffith's theory, PFMs have emerged as variational fracture models to adequately predict the crack initiation, propagation, and branching [1,2,54,65,67]. In these models, a fracture can be revisited as the minimization of the potential energy consisting of the stored bulk energy, the work of external forces, and the surface energy.…”

Section: Introductionmentioning

confidence: 99%

Effect of moisture on the nonlinear viscoelastic fracture behavior of polymer nanocompsites: a finite deformation phase-field model

Arash

Exner

Rolfes

2022

Engineering with Computers

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The mechanisms underlying damage in high-performance polymer nanocomposites are remarkably affected by hygrothermal conditions. In this study, we develop a phase-field formulation to investigate the influence of hygrothermal conditions on the nonlinear viscoelastic fracture behavior of epoxy resins and their nanocomposites at finite deformation. For this, the Helmholtz free energy, capturing the effect of temperature and moisture and nanoparticle contents, is defined based on an additive decomposition of the energy into an equilibrium, a non-equilibrium, and a volumetric contribution with different definitions under tensile and compressive loading. The coupled displacement phase-field problem is solved using a quasi-Newton monolithic algorithm and a staggered solution scheme. Numerical examples show that the monolithic algorithm is more efficient. Simulations are performed to investigate the effect of temperature, deformation rate, and moisture content on the force–displacement response of boehmite nanoparticle/epoxy samples in benchmark numerical problems. Comparing numerical predictions and experimental data for compact-tension tests shows good agreement at different nanoparticle contents. Also, the model’s capability to predict fracture patterns is evaluated using simulations of single-edge notched nanocomposite plates under tensile and shear loading.

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Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase field fracture by nonlocal operator method

Cited by 2 publications

References 71 publications

Accurate computation of partial volumes in 3D peridynamics

Accurate computation of partial volumes in 3D peridynamics

Effect of moisture on the nonlinear viscoelastic fracture behavior of polymer nanocompsites: a finite deformation phase-field model

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