Advances in peridynamic modeling of environmentally- assisted cracking

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ADAPTIVE REFINEMENT AND MULTISCALE MODELING IN 2D PERIDYNAMICS

The original peridynamics formulation uses a constant nonlocal region, the horizon, over the entire domain. We propose here adaptive refinement algorithms for the bond-based peridynamic model for solving statics problems in two dimensions that involve a variable horizon size. Adaptive refinement is an essential ingredient in concurrent multiscale modeling, and in peridynamics changing the horizon is directly related to multiscale modeling. We do not use any special conditions for the “coupling” of the large and small horizon regions, in contrast with other multiscale coupling methods like atomistic-to-continuum coupling, which require special conditions at the interface to eliminate ghost forces in equilibrium problems. We formulate, and implement in two dimensions, the peridynamic theory with a variable horizon size and we show convergence results (to the solutions of problems solved via the classical partial differential equations theories of solid mechanics in the limit of the horizon going to zero) for a number of test cases. Our refinement is triggered by the value of the nonlocal strain energy density. We apply the boundary conditions in a manner similar to the way these conditions are enforced in, for example, the finite-element method, only on the nodes on the boundary. This, in addition to the peridynamic material being effectively “softer” near the boundary (the so-called “skin effect”) leads to strain energy concentration zones on the loaded boundaries. Because of this, refinement is also triggered around the loaded boundaries, in contrast to what happens in, for example, adaptive finite-element methods

ADAPTIVE REFINEMENT AND MULTISCALE MODELING IN 2D PERIDYNAMICS

The original peridynamics formulation uses a constant nonlocal region, the horizon, over the entire domain. We propose here adaptive refinement algorithms for the bond-based peridynamic model for solving statics problems in two dimensions that involve a variable horizon size. Adaptive refinement is an essential ingredient in concurrent multiscale modeling, and in peridynamics changing the horizon is directly related to multiscale modeling. We do not use any special conditions for the “coupling” of the large and small horizon regions, in contrast with other multiscale coupling methods like atomistic-to-continuum coupling, which require special conditions at the interface to eliminate ghost forces in equilibrium problems. We formulate, and implement in two dimensions, the peridynamic theory with a variable horizon size and we show convergence results (to the solutions of problems solved via the classical partial differential equations theories of solid mechanics in the limit of the horizon going to zero) for a number of test cases. Our refinement is triggered by the value of the nonlocal strain energy density. We apply the boundary conditions in a manner similar to the way these conditions are enforced in, for example, the finite-element method, only on the nodes on the boundary. This, in addition to the peridynamic material being effectively “softer” near the boundary (the so-called “skin effect”) leads to strain energy concentration zones on the loaded boundaries. Because of this, refinement is also triggered around the loaded boundaries, in contrast to what happens in, for example, adaptive finite-element methods

E(FG)\u3csup\u3e2\u3c/sup\u3e: A NEW FIXED-GRID SHAPE OPTIMIZATION METHOD

We propose a shape optimization method over a fixed grid. Nodes at the intersection with the fixed grid lines track the domain’s boundary. These “floating” boundary nodes are the only ones that can move/appear/disappear in the optimization process. The element-free Galerkin (EFG) method, used for the analysis problem, provides a simple way to create these nodes. The fixed grid (FG) defines integration cells for EFG method. We project the physical domain onto the FG and numerical integration is performed over partially cut cells. The integration procedure converges quadratically. The performance of the method is shown with examples from shape optimization of thermal systems involving large shape changes between iterations. The method is applicable, without change, to shape optimization problems in elasticity, etc. and appears to eliminate non-differentiability of the objective noticed in finite element method (FEM)-based fictitious domain shape optimization methods. We give arguments to support this statement. A mathematical proof is needed

Predictive Peridynamic 3D Models of Pitting Corrosion in Stainless Steel with Formation of Lacy Covers

In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits

Interfaces in Dynamic Brittle Fracture of PMMA: a peridynamic analysis

Recent experiments in bonded PMMA layers have shown dramatic changes in dynamic crack growth characteristics depending on the interface location and toughness. In this paper we present a peridynamic (PD) analysis of this phenomenon and determine three elements that are essential in a model reproducing the observed fracture behavior: (1) softening near the crack tip to account for changes in PMMA due to heat-generation induced by the high strain rates reached around the crack tip in dynamic fracture; (2) independent extension (mode I) and shear (mode II) modes of fracture; (3) a two-parameter fracture model, which matches both strength and fracture toughness for any horizon size. Once these elements are in place, the PD model captures the experimentally observed dynamic fracture characteristics in bilayer PMMA: crack branching or not at the interface, depending on the interface location; crack running along the interface for a while before punching through the second PMMA layer; slight crack path oscillations near the far end of the sample. The computed crack speed profiles are close to those measured experimentally. The model produces an enlargement of the fracture process zone when the crack running along the interface penetrates into the second PMMA layer, as observed in the experiments. This is where nonlocality of the PD model becomes relevant and critical

Predictive Peridynamic 3D Models of Pitting Corrosion in Stainless Steel with Formation of Lacy Covers

In this work, the peridynamic corrosion model is used for 3D simulation of pitting corrosion in stainless steel. Models for passivation and salt layer formation are employed to predict detailed characteristics of pit growth kinetic in stainless steels, such as lacy cover formation on top of the pit, and the diffusion-controlled regime at the pit bottom. The model is validated against an experimentally grown pit on 316L stainless steel in NaCl solution. Lacy covers in this model are formed autonomously during the simulation process. They are remarkably similar to the covers observed on top of the real pits

Construction of a peridynamic model for viscous flow

We derive the Eulerian formulation for a peridynamic (PD) model of Newtonian viscous flow starting from fundamental principles: conservation of mass and momentum. This formulation is different from models for viscous flow that utilize the so-called “peridynamic differential operator” with the classical Navier- Stokes equations. We show that the classical continuity equation is a limiting case of the PD one, assuming certain smoothness conditions. The PD model for viscous flow is calibrated to the classical Navier-Stokes equations by enforcing linear consistency for the viscous stress term. Couette and Poiseuille flows, and incompressible fluid flow past a regular lattice of cylinders are used to verify the new formulation, at least at low Reynolds numbers. The constructive approach in deriving the model allows for a seamless coupling with peridynamic models for corrosion or fracture for simulating complex fluid-structure interaction problems in which solid degradation takes place, such as in erosion-corrosion, hydraulic fracture, etc. Moreover, the new formulation sheds light on the relationships between local and nonlocal models

Intergranular corrosion and grain dissolution with peridynamics

In polycrystalline material, intergranular corrosion (IGC) is a major cause for failure initiation and leads to significant reduction in strength. The sharp and narrow defects along grain boundaries induced by the corrosion damage along grain boundaries act as stress concentration sites, from which cracks can easily develop. While progress has been made on certain aspects of modeling IGC damage, it can be said that a fully predictive model is no yet available. In this work, we introduce a peridynamic (PD) model (see [1] and [2]) for IGC damage ([3]). We use mixed potential theory and mass transfer in the electrolyte to model IGC. The model considers different dissolution rates for grains and grain boundaries based on their corresponding Tafel kinetics. We validate our model quantitatively against published experiments for IGC in a AA2024 foil immersed in NaCl solution. In addition, we show that new PD model can successfully capture the combination of grain boundary corrosion and grain dissolution at higher potential values (see Fig. 1), in agreement with experimental observations. We extend the model to treat general micro-galvanic corrosion and compare our results with experimental ones. Please click Additional Files below to see the full abstract