## 1 Introduction  
Finite element analysis (FEA) is the only available method allowing the individual study (both qualitatively and quantitatively) of each dental tissue's component, and it has been introduced in dentistry over the last decade [1]. Being a mathematical algorithm-based method that subdivides a larger structure into smaller and simpler parts called finite elements, it is widely used in the engineering field due to its high accuracy [2]. Nevertheless, its accuracy depends on the accuracy of the input data (i.e., complex geometry, dissimilar material properties, local effects), all acknowledged and known in the engineering field [1]. FEA dental studies [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19], despite their considerable number, supply various results that differ from one study to another and sometimes contradict clinical data [6; 7; 8; 20]. If the engineering field benefits from long-established knowledge of materials' physical properties and behavioral types, the dental field does not [1]. FEA begins with the selection of the proper failure criteria (a mathematical algorithm describing the material's behavior as brittle, ductile, or liquid/gas). Ductile materials have a variable ability to deform and recover when subjected to a load, while brittle materials deform little, usually do not recover from deformations, and suffer from cracks and destruction. Dental tissues are considered to be ductile resemblance materials (with a certain brittle flow mode) [1; 21; 22; 23; 24; 25]. The ductile materials' failure criteria are Tresca (T, maximum shear stress) and Von Mises (VM, maximum overall stress); the brittle criteria are S1 (maximum principal stress) and S3 (minimum principal stress); for liquids, hydrostatic pressure is mandatory [21; 22]. In each of these criteria, the variable boundary conditions are the initial parameters that help solve the differential equations and study the biomechanical behavior under specific physical properties (linear elasticity, homogeneity and isotropy vs. non-linear elasticity, non-homogeneity, and anisotropy). The results are also significantly influenced by the analyzed 3D structural model (i.e., anatomical accuracy), obtained either by CBCT's anatomical reconstruction (high accuracy) or artificially created based on anatomical data (low accuracy) [2; 4; 6; 7; 8; 9; 10; 11; 12; 14; 15; 16; 18; 19]. The periodontal ligament (PDL) is the most FEA-studied dental tissue component, employing a variety of failure criteria, boundary conditions, and loads, displaying various contradicting results (since none of the above-mentioned issues were thoroughly addressed) [3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19]. Anatomically, the PDL's internal micro-architecture consists of collagen fibers displayed as variously orientated dense fiber bundles filling a 0.4-1.5 mm space [22; 26], which is of extreme importance for addressing the above issues. The PDL, along with the neurovascular bundle (NVB), are the most sensitive dental tissues to circulatory disturbances due to well-represented vascular support: apical vessels, perforating vessels, and gingival vessels. Outward-facing blood vessels take part in biomechanical suspension and an absorption-dissipation ability, while those that are inward-facing take part in nutritional metabolism [22; 26]. Anatomically and biomechanically, dental tissues are non-homogenous, anisotropic, and do not show linear elasticity [23]. However, all dental studies (PDL included) have neglected these issues, assuming linear elasticity, homogeneity, and isotropy (as boundary conditions assumptions), obeying [PERSON]'s law due to its easier mathematical equations and a lack of awareness. Nevertheless, from a mechanical point of view (common engineering knowledge), up to a 1 N load and due to small deformations and displacements, all tissues assume linear elasticity and isotropy [13; 21; 22; 23; 24]. However, for more than 1 N, there are no available data regarding the linear elasticity and isotropy assumptions.