Total Lagrangian smoothed particle hydrodynamics for large-strain elastoplasticity with particle resolution refinement using an anisotropic Lagrangian kernel

Abstract

Key features for the versatile industrial applications of smoothed particle hydrodynamics (SPH) are numerical accuracy and stability, computational efficiency, and ease of implementation. To meet these requirements, this study presents a straightforward algorithm to treat large-strain elastoplasticity within Total Lagrangian SPH (TLSPH) framework. In terms of accuracy and stability, the total Lagrangian formulation in SPH completely eliminates tensile instability related to the use of Eulerian kernel functions. This study adopts a multiplicative hyperelastic-based plasticity model, enabling the model to treat from purely elastic to elastoplastic structural deformations. A common strategy of efficient simulations in structural analysis is utilizing predefined local resolution refinement with non-uniform particle spacing. However, within TLSPH framework, numerical accuracy and efficiency of this strategy were not investigated sufficiently. To maintain a proper number of neighboring particles in the presence of non-uniform spacing, an anisotropic kernel and its derivatives are incorporated in SPH approximations. Beyond its inherent stability, TLSPH can offer great convenience for the multi-resolution implementation with minimized computational load, as repeated kernel computations at each time advancement are not required. Several benchmark tests are conducted to validate the proposed TLSPH model with various initial particle distributions, demonstrating good accuracy and robustness while lowering computational load.