Session: 12-08-01: Peridynamic Modeling of Materials’ Behavior

Paper Number: 100166

100166 - Plasticity and Ductile Failure Using the Fast Convolution-Based Method for Peridynamic Formulations 

Prediction of ductile failure is critical in many industries. Classical models of ductile failure have certain limitations, and numerical methods used to approximate solutions to such models introduce extra constraints. This often leads to solutions that do not represent well the experimentally observed behavior. To address issues related to complex fracture situations, in which multiple cracks may interact with one another, microcracks may form and influence the evolution of the main crack front, etc. peridynamics (PD) has been introduced in 2000 by Silling [1]. PD is a nonlocal reformulation of continuum mechanics in which spatial derivatives are no longer used in its governing equations. This makes PD models naturally suitable for simulating the nucleation and propagation of discontinuities such as cracks. PD has been mostly used to predict brittle fracture, but recently several authors have proposed PD models for simulating ductile fracture and failure [2,3,4]. PD models for ductile fracture usually use correspondence models, which enables the use of classical constitutive models in a PD framework.  These approaches also open the path for using classical continuum damage models (e.g. models based on a tearing parameter [3], the classical Johnson-Cook approach [4]) within the PD framework.

In PD, two ways can be used to derive an elastoplastic model for large deformations: (1) using the native elastoplastic PD model (in which the constitutive relationship between the PD force and extension states is directly defined in the nonlocal setting without passing through the classical/local theory), and (2) using the PD correspondence models [2,3]. While native PD models are costly compared to solving a classical/local model, the correspondence approaches are even more expensive because they require back-and-forth “translations” between forces/displacements and stresses/strains representations. Recently, an efficient computational method for peridynamic formulations of diffusion [5], and of elasticity and brittle fracture [6] was introduced. The fast convolution-based method (FCBM) uses FFT-accelerated quadrature and a Fourier-compatible approach to apply the boundary conditions. In this talk, we first review PD models for elasticity and brittle fracture (bond-based, state-based, and correspondence models) and their discretization using FCBM. We then show how one can extend the PD-correspondence model to plasticity and ductile fracture. This allows us to use existing constitutive models from classical plasticity and damage while resulting in significant efficiency gains compared with 

previous discretization methods. We use the Johnson-Cook damage model to capture ductile failure in 3D samples with different geometries and compare our results with those from the experimental literature [7].

Acknowledgments: This work has been supported in part by the US National Science Foundation Grant No. 1953346. This work was completed utilizing the Holland Computing Center of the University of Nebraska, which receives support from the Nebraska Research Initiative.

References:

[1] Silling, S. A. (2000). J. Mech. Phys. Solids, 48(1), 175-209.

[2] Tupek, M.R., Radovitzky, R., 2014. J. Mech. Phys. Solids 65, 82–92.

[3] Behzadinasab, M., Foster, J.T., 2020. Int. J. Fract. 224, 261–267.

[4] Behzadinasab, M., Foster, J.T., 2020. J. Mech. Phys. Solids 137, 103862.

[5] Jafarzadeh, S., Wang, L., Larios, A., & Bobaru, F. (2021). Comput Methods Appl Mech Eng , 375, 113633.

[6] Jafarzadeh, S., Mousavi, F., Larios, A., & Bobaru, F. (2022). Comput Methods Appl Mech Eng , 392, 114666.

[7] Bao, Y. (2003).  Doctoral dissertation, Massachusetts Institute of Technology.

Presenting Author: Farzaneh Mousavi University of Nebrask-Lincoln

Presenting Author Biography: My name is Farzaneh Mousavi, A PhD candidate at university of Nebraska-Lincoln. I am working on modeling platicity and ductile failure using Peridynamics.

Authors:

Farzaneh Mousavi University of Nebrask-Lincoln
Siavash Jafarzadeh The Pennsylvania State University
Florin Bobaru University of Nebraska-Lincoln