Pulmonary hypertension (PH) is one of the least understood and highly elusive cardiovascular conditions associated with elevated pulmonary arterial pressure. Although the disease mechanisms are not completely understood, evidence has accumulated from human and animal studies that irreversible processes of pulmonary arterial wall damage, compensated by stress-mediated growth, play critical roles in eliciting the mechanisms of disease progression. The aim of this study is to develop a thermodynamic modeling structure of the pulmonary artery to consider coupled plastic-degradation-growth irreversible processes to investigate the mechanical roles of the dissipative phenomena in the disease progression. The proposed model performs a model parameter study of plastic deformation and degradation processes coupled with dissipative growth subjected to elevated pulmonary arterial pressure and computationally generates in silico simulations of PH progression using the clinical features of PH, found in human morphological and mechanical data. The results show that considering plastic deformation can provide a much better fitting of the ex vivo inflation tests than a widely used pure hyperelastic model in higher pressure conditions. In addition, the parameter sensitivity study illustrates that arterial damage and growth cause the increased stiffness, and the full simulation (combining elastic-plastic-degradation-growth models) reveals a key postpathological recovery process of compensating vessel damage by vascular adaptation by reducing the rate of vessel dilation and mediating vascular wall stress. Finally, the simulation results of luminal enlargement, arterial thickening, and arterial stiffness for an anisotropic growth are found to be close to the values from the literature.