Beyond classical dynamic structural plasticity using mesh-free modelling techniques

• Parkes cantilever problem is revisited via a novel mesh-free approach.
• Contains treatment of plastic shearing and shear strain variation.
• Employs a pseudo-spring model to simulate damage in SPH framework.
• Captures arbitrary crack orientation without continuous tracking.

The problem of modelling the transient response of an elastic-perfectly-plastic cantilever beam, carrying an impulsively loaded tip mass, is often referred to as the Parkes cantilever problem [25]; The permanent deformation of a cantilever struck transversely at its tip, Proc. R. Soc. A., 288, pp. 462). This paradigm for classical modelling of projectile impact on structures is re-visited and updated using the mesh-free method, smoothed particle hydrodynamics (SPH). The purpose of this study is to investigate further the behaviour of cantilever beams subjected to projectile impact at its tip, by considering especially physically real effects such as plastic shearing close to the projectile, shear deformation, and the variation of the shear strain along the length and across the thickness of the beam. Finally, going beyond macroscopic structural plasticity, a strategy to incorporate physical discontinuity (due to crack formation) in SPH discretization is discussed and explored in the context of tip-severance of the cantilever beam. Consequently, the proposed scheme illustrates the potency for a more refined treatment of penetration mechanics, paramount in the exploration of structural response under ballistic loading. The objective is to contribute to formulating a computational modelling framework within which transient dynamic plasticity and even penetration/failure phenomena for a range of materials, structures and impact conditions can be explored ab initio, this being essential for arriving at suitable tools for the design of armour systems.