https://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1083&context=mechengfacpub

Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites

Non-ordinary state-based peridynamic analysis of stationary crack problems

In this paper we review the peridynamic model for brittle fracture and use it to investigate crack branching in brittle homogeneous and isotropic materials. The peridynamic simulations offer a possible explanation for the generation of dynamic instabilities in dynamic brittle crack growth and crack branching. We focus on two systems, glass and homalite, often used in crack branching experiments. After a brief review of theoretical and computational models on crack branching, we discuss the peridynamic model for dynamic fracture in linear elastic–brittle materials. Three loading types are used to investigate the role of stress waves interactions on crack propagation and branching. We analyze the influence of sample geometry on branching. Simulation results are compared with experimental ones in terms of crack patterns, propagation speed at branching and branching angles. The peridynamic results indicate that as stress intensity around the crack tip increases, stress waves pile-up against the material directly in front of the crack tip that moves against the advancing crack; this process “deflects” the strain energy away from the symmetry line and into the crack surfaces creating damage away from the crack line. This damage “migration”, seen as roughness on the crack surface in experiments, modifies, in turn, the strain energy landscape around the crack tip and leads to preferential crack growth directions that branch from the original crack line. We argue that nonlocality of damage growth is one key feature in modeling of the crack branching phenomenon in brittle fracture. The results show that, at least to first order, no ingredients beyond linear elasticity and a capable damage model are necessary to explain/predict crack branching in brittle homogeneous and isotropic materials.

Why do cracks branch? A peridynamic investigation of dynamic brittle fracture

This study presents the ordinary state-based peridynamic constitutive relations for plastic deformation based on von Mises yield criteria with isotropic hardening. The peridynamic force density–stretch relations concerning elastic deformation are augmented with increments of force density and stretch for plastic deformation. The expressions for the yield function and the rule of incremental plastic stretch are derived in terms of the horizon, force density, shear modulus, and hardening parameter of the material. The yield surface is constructed based on the relationship between the effective stress and equivalent plastic stretch. The validity of peridynamic predictions is established by considering benchmark solutions concerning a plate under tension, a plate with a hole and a crack also under tension.

Ordinary state-based peridynamics for plastic deformation according to von Mises yield criteria with isotropic hardening

Peridynamic models are derived by assuming that a material point is located in the bulk. Near a surface or boundary, material points do not have a full non-local neighborhood. This leads to effective material properties near the surface of a peridynamic model to be slightly different from those in the bulk. A number of methods/algorithms have been proposed recently for correcting this peridynamic surface effect. In this study, we investigate the efficacy and computational cost of peridynamic surface correction methods for elasticity and fracture. We provide practical suggestions for reducing the peridynamic surface effect.

Surface corrections for peridynamic models in elasticity and fracture

This note discusses the peridynamic horizon (the nonlocal region around a material point), its role, and practical use in modelling. The objective is to eliminate some misunderstandings and misconceptions regarding the peridynamic horizon. An example of crack branching in a nominally brittle material (homalite) is addressed and we show that crack branching takes place without wave interaction. We explain under what conditions the crack propagation speed depends on the horizon size and the role of incident stress waves on this speed.

/pdf/the-meaning-selection-and-use-of-the-peridynamic-horizon-and-31esk4bxh2.pdf

The Meaning, Selection, and Use of the Peridynamic Horizon and Its Relation to Crack Branching in Brittle Materials

We propose a peridynamic formulation for a unidirectional fiber-reinforced composite lamina based on homogenization and mapping between elastic and fracture parameters of the micro-scale peridynamic bonds and the macro-scale parameters of the composite. The model is then used to analyze the splitting mode (mode II) fracture in dynamic loading of a 0 ◦ lamina. Appropriate scaling factors are used in the model in order to have the elastic strain energy, for a fixed nonlocal interaction distance (the peridynamic horizon), match the classical one. No special criteria for splitting failure are required to capture this fracture mode in the lamina. Convergence studies under uniform grid refinement for a fixed horizon size (m-convergence) and under decreasing the peridynamic horizon ( -convergence) are performed. The computational results show that the splitting fracture mode obtained with peridynamics compares well with experimental observations. Moreover, in the limit of the horizon going to zero, the maximum crack propagation speed computed with peridynamics approaches the value obtained from an analytical classical formulation for the steady-state dynamic interface debonding found in the literature.

/pdf/modeling-dynamic-fracture-and-damage-in-a-fiber-reinforced-2atudyfphy.pdf

Modeling dynamic fracture and damage in a fiber-reinforced composite lamina with peridynamics

https://apps.dtic.mil/sti/pdfs/ADA606248.pdf

Impact damage on a thin glass plate with a thin polycarbonate backing

This work presents a rigorous derivation for the formulation of the J-integral in bond-based peridynamics using the crack infinitesimal virtual extension approach. We give a detailed description of an algorithm for computing this nonlocal version of the J-integral. We present convergence studies (m-convergence and δ-convergence) for two different geometries: a single edge-notch configuration and a double edge-notch sample. We compare the results with results based on the classical J-integral and obtained from FEM calculations that employ special elements near the crack tip. We identify the size of the nonlocal region for which the peridynamic J-integral value is near the classical FEM solutions. We discuss how the boundary conditions and the peridynamic “skin effect” may influence the peridynamic J-integral value. We also observe, computationally, the path-independence of the peridynamic J-integral.

/pdf/the-formulation-and-computation-of-the-nonlocal-j-integral-qwv2r9fw1j.pdf

Wenke Hu

Papers

Peridynamic model for dynamic fracture in unidirectional fiber-reinforced composites

The Meaning, Selection, and Use of the Peridynamic Horizon and Its Relation to Crack Branching in Brittle Materials

Modeling dynamic fracture and damage in a fiber-reinforced composite lamina with peridynamics

Impact damage on a thin glass plate with a thin polycarbonate backing

The formulation and computation of the nonlocal J-integral in bond-based peridynamics