Experimental investigation of the mechanical behaviour and structure of the bovine periodontal ligament

One of the key problems in dental biomechanics is the prediction of tooth mobility under functional loads. Understanding tooth displacement due to load is becoming more important as new solutions in dental restorations, prosthodontics and orthodontic treatments become increasingly more advanced. The mechanical characterization of the alveolar bone, the tooth and the periodontal ligament surrounding the root of the tooth, is necessary to predict tooth mobility. The common assumption is that the periodontal ligament acts as the major element in the stress distribution to the supporting tissues. Obtaining parameters that describe periodontal ligament mechanical behaviour is a challenging problem. Isolating the tissue for testing, the small size of the specimen, and the necessity to maintain, as much as possible, the ligament in vitro under normal physiological conditions, are all factors that contribute to the complexity of the problem. The aim of this thesis is twofold and can be subdivided into two primary objectives. The first objective is to describe its morphology, anatomy, histology and structure of the components in order to determine its geometric parameters at different length scales. The second objective is to determine its mechanical properties by identifying key parameters through shear and uniaxial tension-compression tests. Four studies are performed to describe the morphology, anatomy and histology of the periodontal ligament. First, macroscopic and microscopic measurements of the tooth, bone, and the periodontal ligament are obtained. Second, a bovine first molar system is reconstructed in three dimensions from microcomputerized tomography scans. Third, the morphology of the ligament is observed during deformation using optical microscopy. Fourth, the histology of bovine periodontium tissue is investigated. In order to characterise the mechanical behaviour of the bovine periodontal ligament, custom- designed machines and gripping devices are constructed to subject speciallyprepared tissue specimens to shear and uniaxial tension-compression experiments. Shear experiments are performed on 2 millimetre thick transverse sections, and specimens of toothligament- bone of approximately 8x5x2 millimetres for uniaxial experiments. All specimens are obtained from first molar sites of freshly slaughtered bovines. In both shear and uniaxial testing, the specimens are subjected non-destructively to preconditioning, stress-relaxation, constant strain rate, and sinusoidal loading profiles before testing to rupture. The experiments reported in this thesis elucidate geometrical and mechanical characteristics of the periodontal ligament. Concerning its geometry, a variation in collagen fibre orientation is observed in transverse sections, moreover the symmetry of the shear tests in the apicocoronal direction suggests the periodontal ligament is vertically isotropic. Uniaxial specimens, however, may be considered to be transverse isotropic. Concerning its mechanical behaviour, the periodontal ligament is nonlinear viscoelastic in that it exhibits stiffening, nonlinear elasticity, and nonlinear pseudo-plastic viscosity. The interaction between various constituents of the periodontal ligament (collagen fibres, blood vessels, interstitial fluid etc...) during deformation contribute to the observed stress-strain response of this tissue. A nonlinear viscoelastic model presented in the literature, the Power Law, adequately simulates the nonlinear behaviour of the periodontal ligament using finite element analysis.

With applications to the periodontal ligament: a nonlinear large strain viscoelastic law

Jörn Justiz

The soft tissue, called periodontal ligament (PDL), that connects the alveolar bone and the tooth root accounts to a large extent for the mobility, stress-distribution and, due to its viscoelastic properties, damping of the bone-tooth complex. The accurate prediction of these quantities is essential to new solutions in dental health care making the PDL one of the most important materials in dental biomechanics. Experimental data clearly shows that both the elastic and viscous responses of the PDL are highly nonlinear and different in tension and compression, furthermore its elasticity is stiffening at large strains whereas its viscosity is thinning, i.e. pseudo-plastic, at low strain-rates, both realized within the physiological range of the PDL. The mechanical models for the PDL found in literature, except for one, are simplistic because they use only linear elasticity and few incorporate a viscous contribution. In this thesis a new nonlinear large strain viscoelastic three-dimensional law is developed and applied to the PDL. To begin, a one-dimensional viscoelastic law is proposed based on the standard linear model with the linear springs and dash-pots replaced by nonlinear power law analogs possessing adjustable exponents. The elastic exponent controls the elastic nonlinearity rendering the elastic law either hardening or softening. Likewise, the viscous exponent controls the viscous nonlinearity, rendering the viscous law either thickening or thinning. A thorough investigation of this new nonlinear viscoelastic standard model reveals two key features: first, a finite stress relaxation time as a response of a step strain for a certain choice of viscous and elastic exponents; second, the controllable width of the phase-shift spectrum through the choice of combinations of the exponents. Since viscoelastic biological tissues show a large phase-shift spectrum this feature is an advantage of this original nonlinear law over linear ones. A family of (hyper)elastic closed-form invertible material laws is proposed and it is shown that the three-dimensional extension of the one-dimensional power law falls into that family. Now, the three-dimensional extension of the nonlinear model can be formulated using the appropriate potentials. After implementing the law into a finite element software, representative experiments, namely elastic traction and shear tests at low strain-rates, stress relaxation tests as responses to step strains and sinusoidal strain excitations, are performed in order to obtain reliable data needed for the identification of the law's parameters. The results of these experiments agree with existing data in the literature. After calibrating the law to the PDL's parameters using finite element simulations corresponding to the previous experiments the experimental and the numerical results agree well for the elastic tests and for the phase-shift spectra of the sinusoidal viscoelastic tests indicating nonlinear stiffening elastic and nonlinear pseudo-plastic viscous behavior. They agree less well for the amplitude as a function of frequency. Overall the proposed new nonlinear viscoelastic law based on the power law is capable of simulating the PDL better than a linear viscoelastic law.

EPFL2004

Comportement mécanique des milieux granulaires sous sollicitations cycliques

Frédéric Mayoraz

The following work deals with the characterisation of the behaviour of road bases granular material, made of tunnel excavation material and loaded by passing vehicle axles. This granular media, don't correspond generally to the standards demanded for the construction of road pavements. The thesis is a part of the project COST 337 ("Unbound granular materials for road pavements") whose aim is to develop a guideline for the design of road pavements in Europe (material production, laboratory tests, modelling of mechanical behaviour). At the beginning, several loadings of road pavements are described (mechanical, thermal, hydric), concentrating on mechanical loading. Full-scale tests and finite element simulations led to the knowledge of the order of magnitude of stresses and deformations as well as to the understanding of the rotation of the principal stresses, due to the passing of a vehicle axle. This theoretical part is followed by laboratory cyclic tests with sand to estimate the influence of the principal stress rotation on the deformability of granular media and the importance to take this phenomenon into account for the modelling. Further laboratory tests were carried out on high diameter samples (160 and 250 mm) made of tunnel excavation material. Those tests were made by performing a large number of cycles (80'000 to 250'000 cycles) and various stress paths. The aim of the tests was to measure the evolution of elastic (stiffening of material) and plastic (accumulation of permanent deformations) material characteristics during the cycles. Tools have been developed in the framework of image analysis to assess the eventual change of morphology of this non-standard granular media. Finally the modelling of the accumulation of plastic deformations is discussed in accordance to the theory of elasto-plasticity and visco-plasticity. To remove the limits of elasto-plasticity to simulate a large number of cycles, a visco-plastic approach is developed. The elegant approach, replacing the time by the number of cycles, allows to approximate the permanent deformations of a road pavement in dependence on the stress path. It provides a tool to estimate the rutting in road pavements.

EPFL2002

Time-Dependent Response of Ultra High Performance Fibre Reinforced Concrete (UHPFRC) under Low to High Tensile Stresses

Agnieszka Ewa Switek

Ultra High Performance Fibre Reinforced Concretes (UHPFRC) are characterised by high mechanical performance, extremely low permeability and tensile strain hardening. For structural applications, in composite structures they are very well adapted for reinforcement and protection of existing concrete members. Cast in-situ, they undergo under restraint development of tensile eigenstresses at early age, which can lead in some specific cases of applications to localised macrocracking of a new layer and loss of protective function. On the other hand their tensile viscoelastic potential helps mitigate these stresses. The objective of this study was to investigate the tensile viscoelastic properties of UHPFRC at early ages and long-term in creep and relaxation tests. A large experimental campaign with tensile creep and relaxation tests was performed, with load levels ranging from 30 to 90% of the tensile strength, including creep and relaxation tests during the strain hardening phase, at two different loading ages of 3 and 7 days. Three main testing setups were used: TSTM (Temperature Stress Testing Machine), creep rigs and closed-loop servo-hydraulic testing machine with additional Acoustic Emission detection. The influence of early age evolution in mechanical response and underlying mechanisms governing this response were discussed. Linear viscoelastic models were used to analyse and to highlight on the basis of the experimental results the non-linear behavior depending on solicitation level and loading sequence. The non-linear threshold for viscoelastic response was estimated for the material loaded at 3 and 7 days. The early age mechanical response at 3 days was proportional to the load level in the instantaneous part for three stress levels tested 30, 60 and 90% of the tensile strength, and showed non-linear creep from 60% on. It was observed that for a very low stress level of 13% the creep deformation was decreasing. Relaxation tests with compensation of simultaneously monitored shrinkage deformation were performed, and showed a viscoelastic potential similar to the one observed for creep for the low load level of 30%. Incremental creep and relaxation tests were successfully performed for 3 days age specimens. For higher stress levels, the viscoelastic response from creep tests was more pronounced than in relaxation tests, which was highlighted by analysis with linear viscoelastic models. The creep response at 7 days showed that the threshold for non-linear viscoelasticity is close to 9 MPa (81% of the tensile strength) load level. The Acoustic Emission non-destructive testing method was used to get insight on the physical mechanisms involved in viscoelastic deformations. A strong correlation between AE number of events and the deformation was found, also the amplitude and energy of AE events was found to be of the same order during the instantaneous and delayed deformations. UHPFRC loaded at 7 days age in incremental test showed linear behavior until very high stress level corresponding to the hardening domain. The non-linear and tertiary creep was obtained during the last loading step, for 12 and 11 MPa respectively, which occurred in the hardening domain. The Acoustic Emission monitoring confirmed very close correlation between non-linear creep and AE cumulative number of events induced by microcracking. In order to precisely detect non-linear phenomena in incremental test, analysis with linear viscoelastic models was performed. Comparison between creep and relaxation test results showed that non-linear viscoelastic phenomena were more actively involved in creep tests. The outcomes of this research, bridging the material science and structural engineering, provide useful data to foster applications in new and existing structures, making the best use of the tensile viscoelastic potential of UHPFRC.

EPFL2011