1,721,037 research outputs found
A Simple Way to Couple Peridynamic Grids to FEM Meshes for the Solution of Static Problems
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An adaptive mesh-free approach for dynamic failure analysis
No full textIn this paper a novel mesh-free method by a simple coupling between the finite point method (FPM) and a mesh-free Peridynamic method is introduced. In this method, the solution domain is mainly discretized by FPM points at the beginning of the analysis; FPM produces results with lower computational cost compared to a Peridynamic-only model. Then as the analysis progresses in time, FPM points can change to Peridynamic points in the parts where there is a possibility of crack nucleation or propagation. In this way, the approach benefits from the full advantages of both methods by using an adaptive partitioning of the solution domain, and it restricts the Peridynamic solution only to necessary parts
Accurate computation of partial volumes in 3D peridynamics
Full text linkThe 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
A New Surface Node Method to Accurately Model the Mechanical Behavior of the Boundary in 3D State-Based Peridynamics
Full text linkSulla determinazione del carico su un attuatore piezoelettrico tramite la misura della corrente di alimentazione
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A general ordinary state-based peridynamic formulation for anisotropic materials
Full text linkA general ordinary state -based peridynamic formulation to model anisotropic materials in 2D and 3D is proposed. The new peridynamic constitutive model introduces two bond stiffness functions depending on the bond orientations. These functions are defined such that the components of the elasticity tensor evaluated by using the new formulation exactly reproduce those of classical continuum mechanics in the case of homogeneous deformation. Several numerical examples in 2D and 3D illustrate the validity of the proposed formulation for fully anisotropic materials. This formulation is also suitable to model monoclinic, orthotropic, transversely isotropic, and isotropic materials
A peridynamic approach to simulating fatigue crack propagation in composite materials
Full text linkIn this article, a numerical tool is proposed in the framework of bond-based peridynamics to simulate fatigue crack propagation in composite materials and structures. The cycle-dependent damage-cumulative model derived from Peerlings' law and applied to a bilinear constitutive law is used to evaluate the fatigue degradation of the bond stiffness. Several benchmark cases are studied to validate the proposed approach. Finally, static and fatigue crack propagations in composite systems with single or multi-inclusions are simulated to illustrate the capabilities and characteristics of the developed approach.This article is part of the theme issue 'Ageing and durability of composite materials'
A novel and effective way to impose boundary conditions and to mitigate the surface effect in state-based Peridynamics
Full text linkPeridynamics is a nonlocal continuum theory capable of modeling effectively crack initiation and propagation in solid bodies. However, the nonlocal nature of this theory is the cause of two main problems near the boundary of the body: an undesired stiffness fluctuation, the so-called surface effect, and the difficulty of defining a rational method to properly impose the boundary conditions. The surface effect is analyzed analytically and numerically in the present paper in a state-based peridynamic model. The authors propose a modified fictitious node method based on an extrapolation with a truncated Taylor series expansion. Furthermore, a rational procedure to impose the boundary conditions is defined with the aid of the fictitious nodes. In particular, Neumann boundary conditions are implemented via the peridynamic concept of force flux. The accuracy of the proposed method is assessed by means of several numerical examples for a state-based peridynamic model: with respect to the peridynamic model adopting no corrections, the results are significantly improved even if low values of the truncation order for the Taylor expansion are chosen
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