Experimental nanoindentation tests on dental resins: an in-silico replica based on visco-elastic modelling

In the biomedical field, cements are fundamental biomaterials due to their several uses and functions, such as cement pastes used in dentistry or as bone fillers in prosthesis placement.Cements exhibit a viscoelastic-plastic behavior and one of the possible experimental methodologies to investigate their mechanical response is nanoindentation.The obtained experimental data can then be used to fix existing mechanical constitutive models, which could be employed in Finite Element (FE) analyses. Being able to determine a computational mechanical model that best represents the cement’s behavior would open up many avenues in the field of simulations. Depending on the type of material used, different cases of its attitude can be hypothesized. In this thesis, dental cements, known as composite materials, have been investigated in a coupled experimental-computational analysis. This study has taken advantage of nanoindentation experimental tests previously performed at the PolitoBIOMed Lab at Polytechnic University of Turin.The researcher, after careful preparation of cement called HARVAD, conducted different nanoindentation tests with the Nanoindenter XP with the diamond indenter tip. The tests were performed on different areas of the specimen considering four strain rates of 0.1,1,5 and, 10 s-1. The Burger model (viscoelastic component) in series with a friction element (plastic component) was chosen as adequate to model the mechanical behavior of cement. After, the experimental data were used to identify the constitutive parameters using genetic algorithm. This process has allowed the development of this work by creating a symmetrical 2D FE model to reproduce the experimental tests and to assess the adequacy of the model in reproducing the experimental mechanical response.The FE software used to recreate the nanoindentation process was Abaqus. As the cement mechanical model was very complex, only the viscoelastic component was implemented in FE model.Because Burger model cannot be directly implemented in Abaqus, Prony series was adopted. Prony series parameters were extracted through specific mathematical formulations from Burger model parameters. To identify the best set for each set saved, Thompson's function was used to delete the outliers and a further check was performed by calculating the Prony series values for each set. Sets that returned complex Prony series values were removed. To reproduce the experimental conditions, the FE model was fixed both at specimen base and along the axis of symmetry. The loading condition was defined by applying the experimental displacement on indenter tip. The total experimental displacement values together with the test run time were used to set the load. After the simulations were carried out, the results obtained from the force-displacement curves obtained from Abaqus were compared with the viscoelastic analytical model results. A good match between the two curves was obtained when the shear modulus values were the same unit of magnitude, whereas when the shear modulus associated with the spring in series was larger, a high difference between the two curves was observed. As for both the viscoelastic analytical and numerical curves, a higher maximum force was recorded compared to the experimental force-displacement curve. This result supports the thesis that a non-negligible error is made ignoring the plastic component. A future step could be the implementation of the complete constitutive law of the cement through the UMAT subroutine in Abaqus.