A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics

TL;DR

This paper introduces a versatile, rotation-free Kirchhoff-Love shell formulation within peridynamics, capable of modeling large deformations, fracture, and plasticity in thin-walled structures using meshfree methods and local surface parameterization.

Contribution

It develops a novel, comprehensive peridynamic shell model that is rotation-free, meshfree, and capable of simulating complex behaviors including fracture and plasticity, with convergence to classical models.

Findings

Accurately models large elasto-plastic deformations and fracture.

Demonstrates convergence to classical Kirchhoff-Love shell solutions.

Validates robustness through diverse numerical examples.

Abstract

We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formulation for peridynamics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need for a predefined global parametric domain, Principal Component Analysis is employed in a meshfree setting to develop a local parameterization of the shell midsurface. The KL shell kinematics is utilized to develop a correspondence-based PD formulation. A bond-stabilization technique is employed to naturally achieve stability of the discrete solution. Only the mid-surface velocity degrees of freedom are used in the governing thin-shell equations. 3D rate-form material models are employed to enable simulating a wide range of material behavior. A bond-associative damage correspondence modeling approach is adopted to use classical failure criteria at the bond level, which readily enables the simulation of brittle and ductile fracture. \NAT{Discretizing the model with asymptotically compatible meshfree approximation provides a scheme which converges to the classical KL shell model while providing an accurate and flexible framework for treating fracture.} A wide range of numerical examples, ranging from elastostatics to problems involving plasticity, fracture, and fragmentation, are conducted to validate the accuracy, convergence, and robustness of the developed PD thin-shell formulation. It is also worth noting that the present method naturally enables the discretization of a shell theory requiring higher-order smoothness on a completely unstructured surface mesh.