A damage constitutive model of layered slate under the action of triaxial compression and water environment erosion.

Based on the macroscopic structure control theory, The slate with a significant bedding plane is a composite rock mass composed of rock blocks containing microscopic defects, joint surface closure elements, and shear deformation elements. Considering the coupling damage effect of water erosion and triaxial compressive load on bedding structure plane, the transversely isotropic damage constitutive model of slate under triaxial compressive load is derived with the dip angle of bedding and confining pressure as the variable. Firstly, based on the statistical theory of continuous damage mechanics and the maximum tensile strain criterion, the transversely isotropic deformation constitutive model of rock block with micro-defects is given; Secondly, based on the phenomenological theory of closed deformation and shear-slip deformation mechanism of layered structural plane under the coupling action of water erosion and triaxial compression load, the calculation formula of axial deformation of layered structural plane under the coupling action is given; Finally, to verify the accuracy of the established constitutive model, triaxial compression tests are carried out to study the influence of dip angle and confining pressure on the macroscopic mechanical properties and mechanism of slate. The results show that: the established triaxial compression damage constitutive model of bedding slate can accurately describe the stress-strain relationship of bedding slate after water environment erosion. With the increase of bedding dip angle, the strength and deformation capacity of the bedding slate first decreases and then increases, showing a U-shaped distribution as a whole. There are three main types of failure: tension shear composite failure, shear slip failure, and splitting tension failure.

On the uncertainty quantification of the active uterine contraction during the second stage of labor simulation.

Uterine contractions in the myometrium occur at multiple scales, spanning both organ and cellular levels. This complex biological process plays an essential role in the fetus delivery during the second stage of labor. Several finite element models of active uterine contractions have already been developed to simulate the descent of the fetus through the birth canal. However, the developed models suffer severe reliability issues due to the uncertain parameters. In this context, the present study aimed to perform the uncertainty quantification (UQ) of the active uterine contraction simulation to advance our understanding of pregnancy mechanisms with more reliable indicators. A uterus model with and without fetus was developed integrating a transversely isotropic Mooney-Rivlin material with two distinct fiber orientation architectures. Different contraction patterns with complex boundary conditions were designed and applied. A global sensitivity study was performed to select the most valuable parameters for the uncertainty quantification (UQ) process using a copula-based Monte Carlo method. As results, four critical material parameters ( C 1 , C 2 , K , Ca 0 ) of the active uterine contraction model were identified and used for the UQ process. The stress distribution on the uterus during the fetus descent, considering first and second fiber orientation families, ranged from 0.144 to 1.234 MPa and 0.044 to 1.619 MPa, respectively. The simulation outcomes revealed also the segment-specific contraction pattern of the uterus tissue. The present study quantified, for the first time, the effect of uncertain parameters of the complex constitutive model of the active uterine contraction on the fetus descent process. As perspectives, a full maternal pelvis model will be coupled with reinforcement learning to automatically identify the delivery mechanism behind the cardinal movements of the fetus during the active expulsion process.

A Review of Mechanical Properties and Rockburst Investigation of Transversely Isotropic Rocks by Experimental Technique.

Under complex geostress caused by long-term geological evolution, approximately parallel bedding structures are normally created in rocks due to sedimentation or metamorphism. This type of rock is known as transversely isotropic rock (TIR). Due to the existence of bedding planes, the mechanical properties of TIR are quite different from those of relatively homogeneous rocks. The purpose of this review is to discuss the research progress into the mechanical properties and failure characteristics of TIR and to explore the influence of the bedding structure on the rockburst characteristics of the surrounding rocks. First, the P-wave velocity characteristics of the TIR is summarized, followed by the mechanical properties (e.g., the uniaxial compressive strength, the triaxial compressive strength, and tensile strength) and the related failure characteristics of the TIR. The strength criteria of the TIR under triaxial compression are also summarized in this section. Second, the research progress of the rockburst tests on the TIR is reviewed. Finally, six prospects for the study of the transversely isotropic rock are presented: (1) measuring the Brazilian tensile strength of the TIR; (2) establishing the strength criteria for the TIR; (3) revealing the influence mechanism of the mineral particles between the bedding planes on rock failure from the microscopic point of view; (4) investigating the mechanical properties of the TIR in complex environments; (5) experimentally investigating the rockburst of the TIR under the stress path of "the three-dimensional high stress + internal unloading + dynamic disturbance"; and (6) studying the influence of the bedding angle, thickness, and number on the rockburst proneness of the TIR. Finally, some conclusions are summarized.

Design of protective and high sensitivity encapsulation layers in wearable devices.

Elastomeric encapsulation layers are widely used in soft, wearable devices to physically isolate rigid electronic components from external environmental stimuli (e.g., stress) and facilitate device sterilization for reusability. In devices experiencing large deformations, the stress-isolation effect of the top encapsulation layer can eliminate the damage to the electronic components caused by external forces. However, for health monitoring and sensing applications, the strain-isolation effect of the bottom encapsulation layer can partially block the physiological signals of interest and degrade the measurement accuracy. Here, an analytic model is developed for the strain- and stress-isolation effects present in wearable devices with elastomeric encapsulation layers. The soft, elastomeric encapsulation layers and main electronic components layer are modeled as transversely isotropic-elastic mediums and the strain- and stress-isolation effects are described using isolation indexes. The analysis and results show that the isolation effects strongly depend on the thickness, density, and elastic modulus of both the elastomeric encapsulation layers and the main electronic component layer. These findings, combined with the flexible mechanics design strategies of wearable devices, provide new design guidelines for future wearable devices to protect them from external forces while capturing the relevant physiological signals underneath the skin. Electronic Supplementary Material: Supplementary material is available in the online version of this article at 10.1007/s11431-022-2034-y.

A novel knee joint model in FEBio with inhomogeneous fibril-reinforced biphasic cartilage simulating tissue mechanical responses during gait: data from the osteoarthritis initiative.

We developed a novel knee joint model in FEBio to simulate walking. Knee cartilage was modeled using a fibril-reinforced biphasic (FRB) formulation with depth-wise collagen architecture and split-lines to account for cartilage structure. Under axial compression, the knee model with FRB cartilage yielded contact pressures, similar to reported experimental data. Furthermore, gait analysis with FRB cartilage simulated spatial and temporal trends in cartilage fluid pressures, stresses, and strains, comparable to those of a fibril-reinforced poroviscoelastic (FRPVE) material in Abaqus. This knee joint model in FEBio could be used for further studies of knee disorders using physiologically relevant loading.

A Biomechanical Simulation of Forearm Flexion Using the Finite Element Approach.

Upper limb movement is vital in daily life. A biomechanical simulation of the forearm with consideration of the physiological characteristics of the muscles is instrumental in gaining deeper insights into the upper limb motion mechanisms. In this study, we established a finite element model of the forearm, including the radius, biceps brachii, and tendons. We simulated the motion of the forearm resulting from the contraction of the biceps brachii by using a Hill-type transversely isotropic hyperelastic muscle model. We adjusted the contraction velocity of the biceps brachii muscle in the simulation and found that a slower muscle contraction velocity facilitated forearm flexion. Then, we changed the percentage of fast-twitch fibers, the maximum muscle strength, and the neural excitation values of the biceps brachii muscle to investigate the forearm flexion of elderly individuals. Our results indicated that reduced fast-twitch fiber percentage, maximum muscle strength, and neural excitation contributed to the decline in forearm motion capability in elderly individuals. Additionally, there is a threshold for neural excitation, below which, motion capability sharply declines. Our model aids in understanding the role of the biceps brachii in forearm flexion and identifying the causes of upper limb movement disorders, which is able to provide guidance for enhancing upper limb performance.

Simplified FE model and experimental study on the tensile properties of the glass fiber reinforced polyester polymer.

This research aims to understand the simplified finite element (FE) model behavior for estimating the glass fiber reinforced polyester polymer (GFRP) structural response and studying its tensile properties. The simplified FE model has been developed using an equivalent single-ply transversely isotropic material model to estimate the multi-layer GFRP laminates tensile behavior. The linear elastic and a trilinear plasticity material formulation were adopted. The experimental study is conducted to determine the tensile properties of the equivalent single-ply model of the multi-layer laminates with the variation of layers number, stacking sequence, and fiber orientation. The tensile test specimen used E-glass fiber reinforcement and polyester resin (Yukalac 157 BQTN-EX) as the matrix. The hand layup method was used for the lamination procedure. The experimental results show that the nonlinearity might occur due to the imperfection and poor quality of the composite laminate. Therefore, the comparison of numerical simulation and the experimental results is conducted to understand the stress-strain behavior of the simplified FE model. Both models presented different characteristics and showed good agreement with the experimental results. The linear model can be adopted while the nonlinearity is not significantly identified. Furthermore, the plastic strain as a compensated constant should be defined thoroughly to conduct an accurate estimation using the trilinear plasticity model. However, neither model is suitable for predicting the composite laminate's initial failure point.

Effect of Transversely Isotropic Elasticity on Elastohydrodynamic Lubrication of Point Contacts.

Fiber-reinforced materials or 3D printed parts feature transversely isotropic elasticity. Although its influence on pressures, shapes, and sizes has been studied extensively for dry contacts, the transferability to lubricated contacts is fragmented. This numerical study investigates how the content and orientation of short fibers in fiber-reinforced polymers (FRP) affect elastohydrodynamic lubrication (EHL) of point contacts. Material properties are modeled with Tandon-Weng homogenization. For EHL modeling, a fully-coupled approach based on finite element discretization is used. Results on hydrodynamic pressure and film thickness as well as material stress distribution are analyzed and compared to common approximations using the effective contact moduli. It is shown that the combination of fiber content and orientation defines the effective contact stiffness that determines the contact shape, size, and film thickness. Furthermore, the contact regime can change if a contact-specific stiffness threshold is reached.

Numerical Simulation of the Bearing Capacity of Variotropic Short Concrete Beams Reinforced with Polymer Composite Reinforcing Bars.

One of the disadvantages of reinforced concrete is the large weight of structures due to the steel reinforcement. A way to overcome this issue and develop new types of reinforcing elements is by using polymer composite reinforcement, which can successfully compensate for the shortcomings of steel reinforcement. Additionally, a promising direction is the creation of variotropic (transversely isotropic) building elements. The purpose of this work was to numerically analyze improved short bending concrete elements with a variotropic structure reinforced with polymer composite rods and to determine the prospects for the further extension of the results obtained for long-span structures. Numerical models of beams of a transversally isotropic structure with various types of reinforcement have been developed in a spatially and physically nonlinear formulation in ANSYS software considering cracking and crashing. It is shown that, in combination with a stronger layer of the compressed zone of the beam, carbon composite reinforcement has advantages and provides a greater bearing capacity than glass or basalt composite. It has been proven that the use of the integral characteristics of concrete and the deflections of the elements are greater than those when using the differential characteristics of concrete along the height of the section (up to 5%). The zones of the initiation and propagation of cracks for different polymer composite reinforcements are determined. An assessment of the bearing capacity of the beam is given. A significant (up to 146%) increase in the forces in the reinforcing bars and a decrease in tensile stresses (up to 210-230%) were established during the physically non-linear operation of the concrete material. The effect of a clear redistribution of stresses is in favor of elements with a variotropic cross section in height.

Ultrasonic characterization of complete anisotropic elasticity coefficients of compressed oral solid dosage forms.

In compacted materials, elastic anisotropy coupled with residual stresses could play a determining role in the manifestation of various types of defects such as capping and lamination, as it creates shear planes/bands and temporal relaxation. This internal micro-structure leads to time-delayed flaw initiation/formation, crack tip propagation under residual stresses, and ultimately product quality failures. Thus, their accurate characterization and variations are useful for understanding underlying failure mechanisms and to monitor variations in materials, processes and product quality during production prior to onset of failure. The extraction of tablet anisotropic elasticity properties is a challenging task, especially for commercial tablets with complex shapes, as shape often prevents the use of traditional destructive techniques (e.g., diametric compression testers) to produce accurate measurements. This study introduces and applies an ultrasonic approach to extracting the complete transverse isotropic elastic properties of compressed oral solid dosage forms to a commercial tablet product. A complete set of waveforms and the constitutive matrix for the compacted materials are reported. In addition, a perturbation analysis is carried out to analytically relate propagation speeds in various directions to the elastic coefficients. The proposed characterization approach is non-destructive, rapid, easy, and reliable in evaluating tablet anisotropy.

Determination of a Strain Energy Density Function for the Tricuspid Valve Leaflets Using Constant Invariant-Based Mechanical Characterizations.

The tricuspid valve (TV) regulates the blood flow within the right side of the heart. Despite recent improvements in understanding TV mechanical and microstructural properties, limited attention has been devoted to the development of TV-specific constitutive models. The objective of this work is to use the first-of-its-kind experimental data from constant invariant-based mechanical characterizations to determine a suitable invariant-based strain energy density function (SEDF). Six specimens for each TV leaflet are characterized using constant invariant mechanical testing. The data is then fit with three candidate SEDF forms: (i) a polynomial model-the transversely isotropic version of the Mooney-Rivlin model, (ii) an exponential model, and (iii) a combined polynomial-exponential model. Similar fitting capabilities were found for the exponential and the polynomial forms (R2=0.92-0.99 versus 0.91-0.97) compared to the combined polynomial-exponential SEDF (R2=0.65-0.95). Furthermore, the polynomial form had larger Pearson's correlation coefficients than the exponential form (0.51 versus 0.30), indicating a more well-defined search space. Finally, the exponential and the combined polynomial-exponential forms had notably smaller but more eccentric model parameter's confidence regions than the polynomial form. Further evaluations of invariant decoupling revealed that the decoupling of the invariant terms within the exponential form leads to a less satisfactory performance. From these results, we conclude that the exponential form is better suited for the TV leaflets owing to its superb fitting capabilities and smaller parameter's confidence regions.

The effect of fiber-matrix interaction on the kinking instability arising in the torsion of stretched fibrous biofilaments.

The response of fibrous soft tissues undergoing torsional deformations is a topic of current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. The problem of torsion superimposed on extension of incompressible hyperelastic solid circular cylinders is a classic problem of nonlinear elasticity that has been considered by many authors in the context of rubber elasticity particularly for isotropic materials. A striking feature of such problems is the instability that arises with sufficiently large twist where a kink and then a knot suddenly appears. An energy approach to examining this instability when the extension and twist are prescribed was described by Gent and Hua (2004) and illustrated there for a neo-Hookean isotropic elastic material. The theoretical results were compared with experimental observations on natural rubber rods. Murphy (2015) has shown that the approach of Gent and Hua (2004) for isotropic materials can be simplified when the rods are assumed to be thin and this theory was applied to transversely isotropic materials by Horgan and Murphy (2016). In contrast with the case for isotropic materials, it was shown there that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. Here we are concerned with the implications of this simplified thin rod instability theory for fiber-reinforced transversely isotropic materials that reflect fiber-matrix interaction. It is again shown that the kinking instability occurs even in the absence of stretch, i.e., for the case of pure torsion. The results are illustrated for a specific strain-energy density function that models fiber-matrix interaction. It is shown that the critical twist at which kinking occurs decreases as a measure of fiber-matrix interaction is increased so that the fiber-matrix interaction has a destabilizing effect. The results are illustrated using experimental data of other authors for skeletal muscles and for porcine brain white matter tissue.

Uniqueness of shear wave modeling in an incompressible, transversely isotropic (ITI) material.

Five material parameters are required to describe a transversely isotropic (TI) material including two Poisson's ratios that characterize the compressibility of the material. Both Poisson's ratios must be specified to model an incompressible, TI (ITI) material. However, a previous analysis of the procedure used to evaluate the incompressible limit in a two-dimensional (2D) space of Poisson's ratios has shown that elements of the stiffness tensor are not unique in this limit, and that an additional, fourth parameter is required to model these elements for an ITI material. In this study, we extend this analysis to the case of shear wave propagation in an ITI material. Shear wave signals are modeled using analytic Green's tensor methods to express the signals in terms of the phase velocity and polarization vectors of the shear horizontal (SH) and shear vertical (SV) propagation modes. In contrast to the previous result, the current analysis demonstrates that the phase velocity and polarization vectors are independent of the procedure used to evaluate the 2D limit of Poisson's ratios without the need to include an additional parameter. Thus, calculated shear wave signals are unique and can be used for comparison with experimental measurements to determine all three model parameters that characterize an ITI material.

Numerical Simulations of Components Produced by Fused Deposition 3D Printing.

Three-dimensional printing technology using fused deposition modeling processes is becoming more and more widespread thanks to the improvements in the mechanical properties of materials with the addition of short fibers into the polymeric filaments. The final mechanical properties of the printed components depend, not only on the properties of the filament, but also on several printing parameters. The main purpose of this study was the development of a tool for designers to predict the real mechanical properties of printed components by performing finite element analyses. Two different materials (nylon reinforced with glass or carbon fibers) were investigated. The experimental identification of the elastic material model parameters was performed by testing printed fully filled dog bone specimens in two different directions. The obtained parameters were used in numerical analyses to predict the mechanical response of simple structures. Blocks of 20 mm × 20 mm × 160 mm were printed in four different percentages of a triangular infill pattern. Experimental and numerical four-point bending tests were performed, and the results were compared in terms of load versus curvature. The analysis of the results demonstrated that the purely elastic transversely isotropic material model is adequate for predicting behavior, at least before nonlinearities occur.

Acousto-elasticity of transversely isotropic incompressible soft tissues: characterization of skeletal striated muscle.

Using shear wave elastography, we measure the changes in the wave speed with the stress produced by a striated muscle during isometric voluntary contraction. To isolate the behaviour of an individual muscle from complementary or antagonistic actions of adjacent muscles, we select theflexor digiti minimimuscle, whose sole function is to extend the little finger. To link the wave speed to the stiffness, we develop an acousto-elastic theory for shear waves in homogeneous, transversely isotropic, incompressible solids subject to an uniaxial stress. We then provide measurements of the apparent shear elastic modulus along, and transversely to, the fibre axis for six healthy human volunteers of different age and sex. The results display a great variety across the six subjects. We find that the slope of the apparent shear elastic modulus along the fibre direction changes inversely to the maximum voluntary contraction (MVC) produced by the volunteer. We propose an interpretation of our results by introducing the S (slow) or F (fast) nature of the fibres, which harden the muscle differently and accordingly, produce different MVCs. A natural follow-up on this study is to apply the method to patients with musculoskeletal disorders or neurodegenerative diseases.

Biomechanical impact of the porous-fibrous tissue behaviour in the temporomandibular joint movements. An in silico approach.

The movement of the temporomandibular joint (TMJ) is a function of its complex geometry and its interaction with the surrounding soft tissues. Owing to an increase in the prevalence of temporomandibular joint disorders (TMDs), many computational studies have attempted to characterize its biomechanical behaviour in the last 2 decades. However, most such studies are based on a single computational model that markedly simplifies the complex geometry and mechanical properties of the TMJ's soft tissues. The present study aims to computationally evaluate in a wider sample the importance of considering their complex anatomy and behaviour for simulating both damping and motion responses of this joint. Hence, 6 finite element models of healthy volunteers' TMJ were developed and subjected to both conditions in two different behavioural scenarios. In one, the soft tissues' behaviour was modelled by considering the porous-fibrous properties, whereas in the other case they were simplified assuming isotropic-hyperelastic response, as had been traditionally considered. The damping analysis, which mimic the conditions of an experimental test of the literature, consisted of applying two different compressive loads to the jaw. The motion analysis evaluated the condylar path during the mandible centric depression by the action of muscular forces. From the results of both analyses, the contact pressures, intra-articular fluid pressure, path features, and stress/strain values were compared using the porous-fibrous and isotropic-hyperelastic models. Besides the great differences observed between patients due patient-specific morphology, the porous-fibrous approach yielded results closer to the reference experimental values and to the outcomes of other computational studies of the literature. Our findings underscore, therefore, the importance of considering realistic joint geometries and porous-fibrous contribution in the computational modelling of the TMJ, but also in the design of further joint replacements or in the development of new biomaterials for this joint.

The effect of fiber-matrix interaction on the Poynting effect for torsion of fibrous soft biomaterials.

The response of fibrous soft tissues undergoing torsional deformations is a topic of considerable current interest. Such deformations are common in ligaments and tendons and are also of particular interest in cardiac mechanics. A well-known context where such issues arise is in understanding the mechanical response of papillary muscles of the heart. Thus the classical torsion problem for solid or hollow cylinders composed of rubber-like materials has received renewed recent attention in the context of anisotropic materials. Here we consider the torsion of a solid circular cylinder composed of a transversely isotropic incompressible fiber-reinforced hyperelastic material. The focus of the work is on examining the effect of fiber-matrix interaction on the axial stress response with emphasis on the Poynting effect. The classic Poynting effect for isotropic rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely isotropic models considered here. For sufficiently small total angles of twist, well within the range of physiological response, a reverse-Poynting effect is shown to hold where the cylinder tends to shorten on twisting while for larger angles of twist, the usual positive Poynting effect occurs. It is shown that the influence of the fiber-matrix interaction is to enhance the reverse Poynting effect. The results are illustrated using experimental data of other authors for skeletal muscles and for brain white matter.

Delineating Corneal Elastic Anisotropy in a Porcine Model Using Noncontact OCT Elastography and Ex Vivo Mechanical Tests.

Purpose: To compare noncontact acoustic microtapping (AµT) OCT elastography (OCE) with destructive mechanical tests to confirm corneal elastic anisotropy. Design: Ex vivo laboratory study with noncontact AµT-OCE followed by mechanical rheometry and extensometry. Participants: Inflated cornea of whole-globe porcine eyes (n = 9). Methods: A noncontact AµT transducer was used to launch propagating mechanical waves in the cornea that were imaged with phase-sensitive OCT at physiologically relevant controlled pressures. Reconstruction of both Young's modulus (E) and out-of-plane shear modulus (G) in the cornea from experimental data was performed using a nearly incompressible transversely isotropic (NITI) medium material model assuming spatial isotropy of corneal tensile properties. Corneal samples were excised and parallel plate rheometry was performed to measure shear modulus, G. Corneal samples were then subjected to strip extensometry to measure the Young's modulus, E. Main Outcome Measures: Strong corneal anisotropy was confirmed with both AµT-OCE and mechanical tests, with the Young's (E) and shear (G) moduli differing by more than an order of magnitude. These results show that AµT-OCE can quantify both moduli simultaneously with a noncontact, noninvasive, clinically translatable technique. Results: Mean of the OCE measured moduli were E = 12 ± 5 MPa and G = 31 ± 11 kPa at 5 mmHg and E = 20 ± 9 MPa and G = 61 ± 29 kPa at 20 mmHg. Tensile testing yielded a mean Young's modulus of 1 MPa - 20 MPa over a strain range of 1% to 7%. Shear storage and loss modulus (G'/G'') measured with rheometry was approximately 82/13 ± 12/4 kPa at 0.2 Hz and 133/29 ± 16/3 kPa at 16 Hz (0.1% strain). Conclusions: The cornea is confirmed to be a strongly anisotropic elastic material that cannot be characterized with a single elastic modulus. The NITI model is the simplest one that accounts for the cornea's incompressibility and in-plane distribution of lamellae. AµT-OCE has been shown to be the only reported noncontact, noninvasive method to measure both elastic moduli. Submillimeter spatial resolution and near real-time operation can be achieved. Quantifying corneal elasticity in vivo will enable significant innovation in ophthalmology, helping to develop personalized biomechanical models of the eye that can predict response to ophthalmic interventions.

A computational study of the effects of vocal fold stiffness parameters on voice production.

A three-dimensional flow-structure interaction model of voice production is used to investigate the effect of the stiffness parameters of vocal fold layers on voice production. The vocal fold is modeled as a three-layer structure consisting of the cover, ligament, and body layers. All the three layers are modeled as transversely isotropic materials for which the stiffness parameters include the transverse elastic modulus and longitudinal elastic modulus. The results show that, in addition to the obvious monotonic effects on the fundamental frequency, flow rate and glottis opening, the stiffness parameters also have significant and nonmonotonic effects on the divergent angle, open quotient, and closing velocity. It is further found that the longitudinal stiffness parameters generally have more significant impacts on glottal flows and vocal fold vibrations than the transverse stiffness parameters. The sensitivity analysis shows that, among all the stiffness parameters, the transverse and longitudinal stiffness of the ligament layer have the most dominant effect on most output measures.

Mechanical effects of distributed fibre orientation in the periodontal ligament of an idealised geometry.

In this study, we computationally assess the effects of the distributed fibre orientation in the periodontal ligament (PDL) on mechanical responses of the tooth-PDL complex. An idealised axial-symmetric geometry of a tooth-PDL complex was constructed. The fibre orientation in the PDL was modelled as a trigonometric function based on anatomical knowledge, and the PDL was modelled as a transversely isotropic hyperelastic material dependent on fibre orientations. Parametric studies of the fibre orientation on the mechanical responses of the tooth-PDL complex were conducted. Obtained results showed that the anatomically consistent fibre orientation functions as a supporting structure against not only vertical but also horizontal loads.