## 1 Introduction
[14] simulated a mandibular arch model with three teeth subjected to orthodontic movements reporting unnatural and clinically incorrect qualitative stress displays, due to the high element size and reduced number of elements-nodes of the analyzed model. To have a correct anatomical model, it needs to be based on CBCT images of in vivo tissues, recorded with at least a 0.075 mm voxel size, but that implies restraining the recorded field. Moreover, a model with a single anatomically accurate tooth (i.e., an extremely small global element size and a high number of elements and nodes) needs extremely high amounts of computation power [1; 21; 22; 23; 24; 25]. Another issue is related to the fact that there are no algorithms to test the complex tissular biomechanics. In the current dental research flow, there are FEA studies employed for the PDL study S1 [2; 3; 4; 18], S3 [2; 4], VM [2; 5; 13; 14; 15; 16; 17; 18; 19], and the hydrostatic pressure [6; 7; 8; 9; 10; 11; 12] criterion, with various amounts of loads applied over molar and incisor intact periodonotin models, with homogeneity, isotropy, and linear elasticity as boundary conditions, and reporting contradictory results [20; 36]. No Tresca studies were available except ours. A small minority of these studies assumed the PDL's non-linearity but used a brittle materials or liquids criterion, with debatable results. Some of these studies reported a 20-50% difference between non-linearity and linearity for less than 1 N loads but employed S1-S3 brittle failure criteria for the PDL (ductile like) [3; 4]. Other studies assumed non-linearity/linearity by employing the hydrostatic pressure criterion (with no shear stress) and the Ogden hyper-elastic model for the PDL (despite the internal micro-architectural anatomical reality), with contradictory results from one study to another [3; 4; 6; 7; 8; 9; 10; 14], and firmly reporting that only the hydrostatic pressure can be used in the FEA studies [5]. All these studies proved a lack of awareness about the requirements of the FEA method applied in dentistry, not addressing the above-mentioned issues. Only by correctly identifying and employing the boundary conditions and the proper failure criterion, can a FEA dental study become as reliable and correct as those in the engineering field [21; 22]. In previous comparative studies, our team proved that dental tissues have ductile-like resemblances and that only VM and T criteria supply accurate results [1; 21; 22; 23; 24; 25]. Only one other older FEA-based study approached the issue of the proper failure criteria, but for brittle-like root canal filling, correlating the failure criterion with the analyzed material type (which is mandatory in the engineering field) [2]. No other FEA studies approached these extremely critical issues for FEA accuracy. Herein, the aims were (a) to qualitatively and quantitatively assess the differences between T (non-homogenous) and VM (homogenous) failure criterion by simulating 0-8 mm periodontal breakdown under five orthodontic movements (extrusion, intrusion, rotation, tipping and translation) and three loads (0.6, 1.2 and 2.4 N) in PDL; (b) to verify the use of linear elasticity, isotropy, and homogeneity/non-homogeneity as boundary conditions assumptions for more than 1 N loads for PDL; and (c) to correlate the quantitative results with MHP and available clinical knowledge, evaluating the ischemic and resorptive risks for more than 1 N orthodontic loads in PDL.