Abstract
The review paper covers an overview of the early and current research related to models for both solid and damage mechanics. It addresses the most well-known phenomenological metal plasticity and ductile fracture models in these fields for monotonic loading conditions. The paper commences with a comprehensive literature review outlining the history and current state of the art of the plasticity and ductile fracture models. Then, the paper explains the principal stresses, showing how they represent a metal yield surface. Because most yield functions involve the stress invariant, an extended explanation of stress invariants' space is extensively described. Moreover, a list of coupled and non-coupled plasticity models and ductile fracture criteria are thoroughly explained chronologically to show the emerging of stress triaxiality and Lode angle in models for solid and damage mechanics. The models presented in this paper assume the material's isotropy, homogeneity, and elastic-plastic behavior. Finally, two comparison tables demonstrating the most well-known phenomenal plasticity and fracture models for continuum mechanics are chronologically listed.