Georges Limbert

An elastomeric material for facial prostheses: synthesis, experimental and numerical testing aspects

Current materials used for maxillofacial prostheses are far from ideal and there is a need for new improved materials which better simulate the tissues they are replacing. This study was based on a mixed experimental/analytical/numerical approach. A new polymeric material was developed to provide a better alternative to the materials currently used in maxillofacial prosthetics. A series of experimental tensile tests were performed in order to characterise the tensile properties of the material. A Mooney-Rivlin type hyperelastic formulation was chosen to describe the constitutive behaviour of the polymer which operates at the finite strain regime. The material parameters (two) of the constitutive law were identified with the experimental data. The Mooney-Rivlin material was found to be suitable to represent accurately the mechanical behaviour of the polymer up to 50% strain as shown by the excellent agreement between analytical and experimental results. An FE model reproducing all the characteristics of the experimental tensile tests was built and a series of three FE analyses were conducted and has proven the proper finite element implementation of the material model. This preliminary study will serve as a basis to introduce more complex features such as viscoelasticity and wrinkling of the soft polymeric structure in order to optimise the performances of the final prosthetic material.

On the constitutive modeling of biological soft connective tissues: A general theoretical framework and explicit forms of the tensors of elasticity for strongly anisotropic continuum fiber-reinforced composites at finite strain

This research describes a general theoretical framework for the constitutive modeling of biological soft connective tissues. The approach is based on the theory of continuum fiber-reinforced composites at finite strain. Explicit expressions of the stress tensors in the material and spatial configurations are first established in the general case, without precluding any assumption regarding possible kinematic constraints or any particular mechanical symmetry of the material. Original expressions of the elasticity tensors in the material and spatial configurations are derived and new coupling terms, characterizing the interactions between the constituents of the continuum composite material, are isolated and their biological significance highlighted. Further to this, expressions of the elasticity tensors are degenerated in order to take into account special type of material symmetries. Kinematic constraints and constitutive requirements are also briefly discussed.

Trabecular bone strains around a dental implant and associated micromotions-A micro-CT-based three-dimensional finite element study

The first objective of this computational study was to assess the strain magnitude and distribution within the three-dimensional (3D) trabecular bone structure around an osseointegrated dental implant loaded axially. The second objective was to investigate the relative micromotions between the implant and the surrounding bone. The work hypothesis adopted was that these virtual measurements would be a useful indicator of bone adaptation (resorption, homeostasis, formation). In order to reach these objectives, a microCT-based finite element model of an oral implant implanted into a Berkshire pig mandible was developed along with a robust software methodology. The finite element mesh of the 3D trabecular bone architecture was generated from the segmentation of microCT scans. The implant was meshed independently from its CAD file obtained from the manufacturer. The meshes of the implant and the bone sample were registered together in an integrated software environment. A series of non-linear contact finite element (FE) analyses considering an axial load applied to the top of the implant in combination with three sets of mechanical properties for the trabecular bone tissue was devised. Complex strain distribution patterns are reported and discussed. It was found that considering the Youngs modulus of the trabecular bone tissue to be 5, 10 and 15GPa resulted in maximum peri-implant bone microstrains of about 3000, 2100 and 1400. These results indicate that, for the three sets of mechanical properties considered, the magnitude of maximum strain lies within an homeostatic range known to be sufficient to maintain/form bone. The corresponding micro-motions of the implant with respect to the bone microstructure were shown to be sufficiently low to prevent fibrous tissue formation and to favour long-term osseointegration.

On the constitutive modelling of biological soft connective tissues. A general theoretical framework for strongly anisotropic fiber-reinforced composites at finite strain

This research describes a general theoretical framework for the constitutive modeling of biological soft connective tissues. The approach is based on the theory of continuum fiber-reinforced composites at finite strain. Explicit expressions of the stress tensors in the material and spatial configurations are first established in the general case, without precluding any assumption regarding possible kinematic constraints or any particular mechanical symmetry of the material. Original expressions of the elasticity tensors in the material and spatial configurations are derived and new coupling terms, characterizing the interactions between the constituents of the continuum composite material, are isolated and their biological significance highlighted. Further to this, expressions of the elasticity tensors are degenerated in order to take into account special type of material symmetries. Kinematic constraints and constitutive requirements are also briefly discussed.

A mesostructurally-based anisotropic continuum model for biological soft tissues--decoupled invariant formulation.

Characterising and modelling the mechanical behaviour of biological soft tissues is an essential step in the development of predictive computational models to assist research for a wide range of applications in medicine, biology, tissue engineering, pharmaceutics, consumer goods, cosmetics, transport or military. It is therefore critical to develop constitutive models that can capture particular rheological mechanisms operating at specific length scales so that these models are adapted for their intended applications. Here, a novel mesoscopically-based decoupled invariant-based continuum constitutive framework for transversely isotropic and orthotropic biological soft tissues is developed. A notable feature of the formulation is the full decoupling of shear interactions. The constitutive model is based on a combination of the framework proposed by Lu and Zhang [Lu, J., Zhang, L., 2005. Physically motivated invariant formulation for transversely isotropic hyperelasticity. International Journal of Solids and Structures 42, 6015-6031] and the entropic mechanics of tropocollagen molecules and collagen assemblies. One of the key aspects of the formulation is to use physically-based nanoscopic quantities that could be extracted from experiments and/or atomistic/molecular dynamics simulations to inform the macroscopic constitutive behaviour. This effectively couples the material properties at different levels of the multi-scale hierarchical structure of collagenous tissues. The orthotropic hyperelastic model was shown to reproduce very well the experimental multi-axial properties of rabbit skin. A new insight into the shear response of a skin sample subjected to a simulated indentation test was obtained using numerical direct sensitivity analyses.

A mechanistic insight into the mechanical role of the stratum corneum during stretching and compression of the skin

The study of skin biophysics has largely been driven by consumer goods, biomedical and cosmetic industries which aim to design products that efficiently interact with the skin and/or modify its biophysical properties for health or cosmetic benefits. The skin is a hierarchical biological structure featuring several layers with their own distinct geometry and mechanical properties. Up to now, no computational models of the skin have simultaneously accounted for these geometrical and material characteristics to study their complex biomechanical interactions under particular macroscopic deformation modes. The goal of this study was, therefore, to develop a robust methodology combining histological sections of human skin, image-processing and finite element techniques to address fundamental questions about skin mechanics and, more particularly, about how macroscopic strains are transmitted and modulated through the epidermis and dermis. The work hypothesis was that, as skin deforms under macroscopic loads, the stratum corneum does not experience significant strains but rather folds/unfolds during skin extension/compression. A sample of fresh human mid-back skin was processed for wax histology. Sections were stained and photographed by optical microscopy. The multiple images were stitched together to produce a larger region of interest and segmented to extract the geometry of the stratum corneum, viable epidermis and dermis. From the segmented structures a 2D finite element mesh of the skin composite model was created and geometrically non-linear plane-strain finite element analyses were conducted to study the sensitivity of the model to variations in mechanical properties. The hybrid experimental-computational methodology has offered valuable insights into the simulated mechanics of the skin, and that of the stratum corneum in particular, by providing qualitative and quantitative information on strain magnitude and distribution. Through a complex non-linear interplay, the geometry and mechanical characteristics of the skin layers (and their relative balance), play a critical role in conditioning the skin mechanical response to macroscopic in-plane compression and extension. Topographical features of the skin surface such as furrows were shown to act as an efficient means to deflect, convert and redistribute strain-and so stress-within the stratum corneum, viable epidermis and dermis. Strain reduction and amplification phenomena were also observed and quantified. Despite the small thickness of the stratum corneum, its Young׳s modulus has a significant effect not only on the strain magnitude and directions within the stratum corneum layer but also on those of the underlying layers. This effect is reflected in the deformed shape of the skin surface in simulated compression and extension and is intrinsically linked to the rather complex geometrical characteristics of each skin layer. Moreover, if the Young׳s modulus of the viable epidermis is assumed to be reduced by a factor 12, the area of skin folding is likely to increase under skin compression. These results should be considered in the light of published computational models of the skin which, up to now, have ignored these characteristics.

A Transversely Isotropic Hyperelastic Constitutive Model of the PDL. Analytical and Computational Aspects

This study describes the development of a constitutive law for the modelling of the periodontal ligament (PDL) and its practical implementation into a commercial finite element code. The constitutive equations encompass the essential mechanical features of this biological soft tissue: non-linear behaviour, large deformations, anisotropy, distinct behaviour in tension and compression and the fibrous characteristics. The approach is based on the theory of continuum fibre-reinforced composites at finite strain where a compressible transversely isotropic hyperelastic strain energy function is defined. This strain energy density function is further split into volumetric and deviatoric contributions separating the bulk and shear responses of the material. Explicit expressions of the stress tensors in the material and spatial configurations are first established followed by original expressions of the elasticity tensors in the material and spatial configurations. As a simple application of the constitutive model, two finite element analyses simulating the mechanical behaviour of the PDL are performed. The results highlight the significance of integrating the fibrous architecture of the PDL as this feature is shown to be responsible for the complex strain distribution observed.

A constitutive model for the periodontal ligament as a compressible transversely isotropic visco-hyperelastic tissue

This study is devoted to the development of a non-linear anisotropic model for the human periodontal ligament (PDL). A thorough knowledge of the behaviour of the PDL is vital in understanding the mechanics of orthodontic tooth mobility, soft tissue response and proposed treatment plans. There is considerable evidence that the deformation of the PDL is the key factor determining the orthodontic tooth movement. The paper focuses on the biomechanical aspect of the behaviour of the PDL. In terms of continuous mechanics, the PDL may be treated as an anisotropic poro-visco-hyperelastic fibre-reinforced compressible material which is subject to large deformations and has an essentially non-linear behaviour. Furthermore, there are issues related to the non-linear tooth and PDL geometry. A new constitutive model for the PDL is proposed. The macroscopic continuum approach is used. The model is based on the non-linear large deformation theory, involving the Lagrangian description. The material is assumed to be compressible, visco-hyperelastic and transversely isotropic. A free-energy function is suggested that incorporates the properties. It also takes into account that the PDL behaves differently in tension and compression. The free-energy function and the associated constitutive equations involve several material parameters, which are to be evaluated from experimental strain–stress data available from the literature and the tooth movement experiments conducted by our team using novel optical motion analysis techniques.

Finite Element Analysis of the Human ACL Subjected to Passive Anterior Tibial Loads

In this study, a constitutive law based on a nearly incompressible transversely isotropic hyperelastic potential is proposed to describe the mechanical behaviour of the anterior cruciate ligament (ACL). The constitutive formulation is valid for arbitrary kinematics (finite elasticity) and is thermodynamically admissible. Based on anatomic measurements performed on a human cadaveric knee specimen, a three-dimensional continuum finite element model of the ACL was developed. The numerical model was used to simulate clinical procedures such as the Lachman and drawer tests, which are performed to assess the existence and severity of an ACL injury. Finite element analyses showed that the two procedures have distinct effects on the behaviour of the ACL and provided new insights into the stress distributions. Moreover, good qualitative and quantitative agreement was found between the present study and results obtained experimentally in comparable conditions.

Cement lines and interlamellar areas in compact bone as strain amplifiers - contributors to elasticity, fracture toughness and mechanotransduction.

Bone is multi-scale hierarchical composite material making the prediction of fragility, as well as pinning it to a certain cause, complicated. For proper mechanical simulation and reflection of bone properties in models, microscopic structural features of bone tissue need to be included. This study sets out to gain a mechanistic insight into the role of various microstructural features of bone tissue in particular cement lines and interlamellar areas. Further the hypothesis that compliant interlamellar areas and cement lines within osteonal bone act as strain amplifiers was explored. To this end, a series of experimentally-based micromechanical finite element models of bovine osteonal bone were developed. Different levels of detail for the bone microstructure were considered and combined with the results of physical three-point bending tests and an analytical composite model of a single osteon. The objective was to examine local and global effects of interface structures. The geometrical and microstructural characteristics of the bone samples were derived from microscopy imaging. Parametric finite element studies were conducted to determine optimal values of the elastic modulus of interstitial bone and interlamellar areas. The average isotropic elastic modulus of interfaces suggested in this study is 88.5MPa. Based on the modelling results, it is shown that interfaces are areas of accumulated strain in bone and are likely to act as potential paths for crack propagation. The strain amplification capability of interface structures in the order of 10 predicted by the models suggests a new explanation for the levels of strain required in bone homoeostasis for maintenance and adaptation.