Peridynamic‐based modeling of elastoplasticity and fracture dynamics

• Published in: Computer animation and virtual worlds Vol. 35; no. 4
• Main Authors: Wang, Haoping, Wang, Xiaokun, Xu, Yanrui, Zhang, Yalan, Yao, Chao, Guo, Yu, Ban, Xiaojuan
• Format: Journal Article
• Language: English
• Published: Chichester Wiley Subscription Services, Inc 01.07.2024
• Subjects: Constitutive models; Constraints; Density; Elastic deformation; elastoplastic simulation; Elastoplasticity; Finite element method; fracture; Fractures; Fracturing; Mathematical models; Modelling; peridynamic; Plastic deformation; Smooth particle hydrodynamics; Stability criteria; Yield criteria
• ISSN: 1546-4261; 1546-427X
• DOI: 10.1002/cav.2242

This paper introduces a particle‐based framework for simulating the behavior of elastoplastic materials and the formation of fractures, grounded in Peridynamic theory. Traditional approaches, such as the Finite Element Method (FEM) and Smoothed Particle Hydrodynamics (SPH), to modeling elastic materials have primarily relied on discretization techniques and continuous constitutive model. However, accurately capturing fracture and crack development in elastoplastic materials poses significant challenges for these conventional models. Our approach integrates a Peridynamic‐based elastic model with a density constraint, enhancing stability and realism. We adopt the Von Mises yield criterion and a bond stretch criterion to simulate plastic deformation and fracture formation, respectively. The proposed method stabilizes the elastic model through a density‐based position constraint, while plasticity is modeled using the Von Mises yield criterion within the bond of particle paris. Fracturing and the generation of fine fragments are facilitated by the fracture criterion and the application of complementarity operations to the inter‐particle connections. Our experimental results demonstrate the efficacy of our framework in realistically depicting a wide range of material behaviors, including elasticity, plasticity, and fracturing, across various scenarios. An experiment on the elasticity, plasticity and cutting of an elastoplastic dough. The dough is made to drop onto a wooden board, and collide with the rolling pin and the metal blade to exhibit the rendering effects of elasticity, plasticity and fracture within our particle framework.