
A Unified Peridynamics for Solids and Fluids: Coupled Total- and Semi-Lagrangian formulation
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Peridynamics (PD), introduced by Silling [1] and Silling et al. [2], is a relatively new Lagrangian method based on the concept of particle interactions. While it is well-known for its capability to handle discontinuities in solid mechanics [3-4], there is a scarcity of literature addressing fluid flow using PD. This paper aims to establish a unified PD framework that encompasses both solids and fluids. We employ the total-Lagrangian formulation to represent the behavior of brittle solids which is consistent with traditional PD theory, while integrating the semi-Lagrangian formulation and non-local operators [5] to manage large deformations and solve the non-local Navier-Stokes equations for fluids [6]. The framework is further extended to include coupled thermo-hydrodynamic-mechanical conditions by incorporating the energy equation in both solid and fluid models [7-8]. A novel multi-horizon approach is introduced, utilizing distinct horizons for the thermal field, mechanical field, and flow field. This approach effectively addresses numerical challenges associated with non-local operators, particularly the non-unique mapping of neighboring particles to a master particle. The effectiveness of this computational framework is demonstrated through various numerical examples spanning both solid and fluid mechanics, including scenarios such as thermally induced fracturing in solids, natural and mixed convection, and quenching processes. This work represents a unified PD framework for comprehensive multi-physics analysis, capable of modeling complex evolving discontinuities and moving interfaces.