Peridynamic modeling of inelastic materials for aerospace applications

Study of the mechanical behavior of ductile materials is essential in engineering and materials science due to the widespread use of these materials in industry. Ductile materials are known for their ability to deform significantly before fracture, and this has contributed to their extensive adoption in many industrial sectors such as aerospace, automotive, and structural engineering. Ductile materials undergo elastoplastic deformation prior to fracture. This process reduces the stiffness of the material before failure. When a material is loaded, it initially exhibits elastic behavior. A surface in the stress space known as the yield surface controls the initiation of the plastic deformation. Plastic deformation occurs when the stress in the material remains on the yield surface throughout the loading process. Furthermore, to reflect the real behavior observed in most ductile materials, the size of the yield surface is controlled by adding a hardening/softening assumption to the formulation. The linear elastic fracture mechanics (LEFM) approach, which neglects yielding at the crack front, is not reliable for simulating the mechanical behavior of ductile materials that undergo significant deformation under service loads. In contrast, the elasto-plastic fracture mechanics (EPFM) approach considers the impact of yielding at crack tips and characterizes the plastic behavior of the material. Consequently, it is appropriate for analysing ductile materials. Moreover, the deformation of all metals is, to some extent, time-dependent. This behavior can be effectively characterized by elasto-viscoplasticity. This framework accounts for the time-dependent inelastic strains observed in solids. The Perzyna constitutive law, with its simple formulation, accurately simulates the evolution of viscous effects and is thus widely employed in engineering applications. Classical continuum mechanics is a theory that establishes the mathematical foundation for the study of the mechanical behavior of ductile materials. However, fracture analysis is challenging, especially when it is approached within the framework of the classical mechanics theory because this theory uses partial derivatives in the equation of motion, which require continuity of the displacement field. This assumption becomes problematic when dealing with discontinuities such as cracks. Peridynamics is a nonlocal theory of solid mechanics designed for discontinuous problems. It is well suited to failure analysis because it uses integral equations rather than partial differential equations. It redefines the equation of motion and improves its suitability for solving problems involving cracks. However, since it is a recently introduced theory, Peridynamics is not equipped with all constitutive laws normally available for classical continuum mechanics. Therefore, it is reasonable to develop a peridynamic elastoplastic model for the study of the mechanical behaviour of ductile materials. The main purpose of this dissertation is to develop peridynamic approaches to simulate both elastoplastic materials and elasto-viscoplastic materials with strain hardening. The elastoplastic model is based on the classical theory of plasticity. The model is capable of simulating the elastoplastic behavior of materials with isotropic, kinematic and combined hardening. The elasto-viscoplastic peridynamic model is based on the Perzyna constitutive law. For materials with hardening, the yield surface changes with any change in plastic strain, a behavior observed in most materials. This effect is duly taken into account in the proposed models. We shall briefly show that the proposed approaches are well suited for fracture analysis of ductile materials. Several examples, including 2D plane stress and plane strain, and 3D cases, are performed to demonstrate the capabilities of the proposed approaches.