Mathematical Modeling of Bio-Compounds from Experimental Data

This thesis is concerned with the mathematical modeling of bioplastic compoundswith fillers of agri-food origin (brewery waste) in the context of the mechanics ofsolids. The modeling will be carried out on the basis of original experimental laboratorydata produced by using materials and equipments belonging to the Polymer,Biopolymers and Composites laboratory and to the Mechanical Treatment Prototype laboratoryof the Department of Engineering of the University of Messina in collaborationswith the Advanced Social District of Messina, with "Crossing" (spin-off of theDepartment of Molecular Sciences and Nanosystems of the Ca’ Foscari Universityof Venice and other partners of the LIFE RESTART project. The thesis is part of acollaborative perspective between experimental disciplines (Chemistry and MaterialsEngineering) and theoretical disciplines (Mathematical Physics), and it is consistentwith the increasingly widespread need to implement development policiesaccording to the paradigm of the circular economy, with attention to environmentalprotection and sustainable use of resources.The plan of the thesis is the following.In Chapter 1, some general qualitative and quantitative considerations about thepollution problems, determined by the dispersion of a huge amount of fossil–basedplastics in the environment, are given; consequently, it is stressed the importancethat bio-based plastics may have. The higher cost of the bioplastics, compared withthe one of fossil-based plastics, can be significantly reduced by the production ofcompounds where the biopolymer is mixed with some agricultural waste. This processis within the framework of the new paradigma of circular economy which triesto minimize waste and optimize the use of resources.Chapter 2 briefly reviews the very basic elements of continuous solid mechanics,whereas in Chapter 3, the laboratory production process of the mixture of bioplastics(Polybutylene Succinate, PBS) and brewer spent grains (BSG), together with theexperimental setup for carrying out the mechanical tests, are described. The experimentaldata in Chapter 3 are then fitted in order to characterize the relations betweensome relevant mechanical parameters of the bio-compound and the filler concentration.Chapter 4 is devoted to the description of the experimental data for a newbio-compound where an additive has been mixed to PBS and BSG to increase thephysical and chemical affinity of the two components. The experimental data, representedby stress–strain curves, show that the Young’s modulus and the ultimatetensile strength of dog-bone samples are linearly related to the filler concentration.Finally, in Chapter 5, the mathematical modelization of the bio-compounds studiedin Chapter 4 is numerically developed along with the Finite Element Method using COMSOL Multiphysics software; the two theoretical models that have been investigatedare the Maxwell model and the Burgers model.