Prediction of ductile fracture is vital to numerous industries. Peridynamics (PD) is a nonlocal reformulation of continuum mechanics which uses integrals instead of derivatives in its governing equations. This makes PD models very suitable of simulating the nucleation and propagation of discontinuities such as cracks. PD has been mostly used to predict brittle fracture, but more recently several authors have introduced PD models for simulating ductile fracture and failure [1,2,3]. PD models for ductile fracture usually use correspondence models, which enables the use of classical constitutive models in a PD framework.&nbsp; These approaches also open the path for using classical continuum damage models (e.g., models based on a tearing parameter [2], the classical Johnson-Cook approach [3]) within the PD framework.In this study, we employ the two-dimensional (2D) PD elastoplastic deformation model introduced in [4], to demonstrate its ability to simulate strain localization and fracture under plane stress conditions. For this purpose, we utilize the simplest damage model based on critical bond strain. The intention is to show the potential of the model introduced, while being aware of the limitations of the simple damage model. We qualitatively compare our results with a thin dog-bone shaped aluminum specimen which is under tenson. Although our model, in its current version, is limited to small strains (it can handle large rotations), perfect plasticity, and uses a simple failure criterion, its ability to capture the experimentally observed rupturing behavior in thin dog-bone specimens is remarkable. For a quantitative validation of the elastoplastic fracture model, an elastoplastic deformation model capable of handling large deformations is needed. There are two ways for deriving an elastoplastic model for large deformations: (1) using the native elastoplastic PD model (where the constitutive relationship between the PD force and extension states are directly defined in the nonlocal setting without passing through the classical/local theory) capable of modeling large deformations, and (2) using the PD correspondence models [1,2]. While native PD models are costly when compared to solving a model based on the classical/local theory, the correspondence approaches are even more expensive. Recently, an efficient computational method for peridynamics was introduced [5]. The fast convolution-based method (FCBM) uses FFT-accelerated quadrature and a Fourier-compatible approach to apply boundary conditions. In this study we use the FCBM to discretize a class of PD correspondence models that allows us to benefit from the classical plasticity models, and at the same time provide significant efficiency gains compared with previous discretization methods.References:[1] Tupek, M.R., Radovitzky, R., 2014. An extended constitutive correspondence formulation of &nbsp;&nbsp;&nbsp;&nbsp;peridynamics based on nonlinear bond-strain measures. J. Mech. Phys. Solids 65, 82–92.[2] Behzadinasab, M., Foster, J.T., 2020. Revisiting the third Sandia Fracture Challenge: a bond associated, semi-Lagrangian peridynamic approach to modeling large deformation and ductile fracture. Int. J. Fract. 224, 261–267.[3] Behzadinasab, M., Foster, J.T., 2020. A semi-Lagrangian constitutive correspondence framework for peridynamics. J. Mech. Phys. Solids 137, 103862.[4] Mousavi, F., Jafarzadeh, S., &amp; Bobaru, F. (2021). An ordinary state-based peridynamic elastoplastic 2D model consistent with J2 plasticity.&nbsp;International Journal of Solids and Structures, 111146.[5] Jafarzadeh, S., Mousavi, F., Larios, A., &amp; Bobaru, F. (2021). A general and fast convolution-based method for peridynamics: applications to elasticity and brittle fracture.&nbsp;(in review),arXiv preprint arXiv:2105.06055.

Recent Progress in Modeling Plasticity and Ductile Fracture With Peridynamics

Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2021/volume/85543

ASME 2021 International Mechanical Engineering Congress and Exposition (IMECE2021)

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