General particle dynamics: On the correlation of nonlocal and local theories for large deformation problems.

• General particle dynamics is proposed to address the large deformation mechanics. • GPD for nonlinear elastic and plastic constitutive model is established. • Relationships between GPD and other mechanical theories are discussed. • Numerical examples verify GPD's ability in large deformation and fracture problems. This paper presents a detailed investigation on the General Particle Dynamics (GPD) method and its implications for addressing challenges in large deformation mechanics and fracture modeling. The GPD method integrates nonlocal interactions and nonlocal differential operators to overcome limitations of classical continuum mechanics in capturing long-range interactions and material behaviors under extreme deformation conditions. Through a systematic examination of the physical and mathematical foundations of GPD, including its governing equations and constitutive relations, we elucidate the robust and applicability of the proposed method in simulating complex deformation phenomena. Furthermore, the relationships among GPD, conventional mechanical theories (Smoothed Particle Hydrodynamics), nonlocal theory (Peridynamics) and Molecular Dynamic theories are discussed. Numerical examples related to large deformation and fracture problems are tested to verify the ability of the proposed method. The numerical results show that GPD inherits the advantages of the classical method and also has its unique properties in solid fracture mechanics and large deformation problems, making it a promising approach in computational mechanics. [ABSTRACT FROM AUTHOR]