A General-Purpose, Inelastic, Rotation-Free Kirchhoff-Love Shell Formulation for Peridynamics
arXiv:2107.13062 · doi:10.1016/j.cma.2021.114422
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.
References in corpus (11)
- A new rotation-free isogeometric thin shell formulation and a corresponding continuity constraint for patch boundaries
- Meshfree Methods on Manifolds for Hydrodynamic Flows on Curved Surfaces: A Generalized Moving Least-Squares (GMLS) Approach
- Mesh-free Semi-Lagrangian Methods for Transport on a Sphere Using Radial Basis Functions
- A Fully Lagrangian Meshfree Framework for PDEs on Evolving Surfaces
- RBF-LOI: Augmenting Radial Basis Functions (RBFs) with Least Orthogonal Interpolation (LOI) for Solving PDEs on Surfaces
- On the stability of the generalized, finite deformation correspondence model of peridynamics
- Approximation of tensor fields on surfaces of arbitrary topology based on local Monge parametrizations
- A Meshfree Lagrangian Method for Flow on Manifolds
- From fracture to fragmentation: discrete element modeling -- Complexity of crackling noise and fragmentation phenomena revealed by discrete element simulations
- Asymptotically compatible reproducing kernel collocation and meshfree integration for the peridynamic Navier equation
- Generalized moving least squares and moving kriging least squares approximations for solving the transport equation on the sphere