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This work aims at studying the mechanical and acoustic behaviours of a new bio-based porous epoxy resin obtained by a "green" adapted combination of the cationic photopolymerization and the porogen leaching technique. This new kind of material generally possesses interconnected complex morphology and it would be useful to consider this feature in a model. In this study, the effective properties of the material were estimated by using the asymptotic homogenization method. Four types of ordered pore arrangements together with systematic variations of the porosity and the pore size have been studied. Based on the results of these investigations, a subtle relation between the microstructure and mechanical/acoustic properties has been established. The estimated equivalent dynamic density and equivalent dynamic bulk modulus were compared with experimental results obtained by conducting the three-microphone impedance tube testing. The processing parameters of material elaboration could be adjusted so that the obtained porous material would possess the best sound absorption performance.

Inserting a titanium implant in the bone tissue may modify its physiological loading and therefore cause bone resorption, via a phenomenon called stress-shielding. The local stress field around the bone-implant interphase (BII) created under shear loading may be influenced by different parameters such as the bone-implant contact (BIC) ratio, the bone Young's modulus, the implant roughness and the implant material. A 2-D finite element model was developed to model the BII and evaluate the impact of the aforementioned parameters. The implant roughness was described by a sinusoidal function (height 2Δ, wavelength λ), and different values of the BIC ratio were simulated. A heterogeneous distribution of the maximum shear stress was evidenced in the periprosthetic bone tissue, with high interfacial stress for low BIC ratios and low implant roughness and underloaded regions near the roughness valleys. Both phenomena may lead to stress-shielding-related effects, which were concentrated within a distance lower than 0.8λ from the implant surface. Choosing an implant material with mechanical properties matching those of bone tissue leads to a homogenized shear stress field and could help to prevent stress-shielding effects. Finally, the equivalent shear modulus of the BII was derived to replace its complex behavior with a simpler analytical model in future studies. Schematic illustrations of the 2-D finite element model used in the present study and spatial variation of the maximal shear stress in the periprosthetic bone tissue for different implant roughness and bone-implant contact ratios.

The long-term success of cementless surgery strongly depends on the implant primary stability. The femoral stem initial fixation relies on multiple geometrical and material factors, but their influence on the biomechanical phenomena occurring during the implant insertion is still poorly understood, as they are difficult to quantify in vivo. The aim of the present study is to evaluate the relationship between the resonance frequencies of the bone-implant-ancillary system and the stability of the femoral stem under various biomechanical environments. The interference fit IF, the trabecular bone Young's modulus [Formula: see text] and the bone-implant contact friction coefficient [Formula: see text] are varied to investigate their influence on the implant insertion phenomena and on the system vibration behavior. The results exhibit for all the configurations, a nonlinear increase in the bone-implant contact throughout femoral stem insertion, until the proximal contact is reached. While the pull-out force increases with [Formula: see text], IF and [Formula: see text], the bone-implant contact ratio decreases, which shows that a compromise on the set of parameters could be found in order to achieve the largest bone-implant contact while maintaining sufficient pull-out force. The modal analysis on the range [2-7] kHz shows that the resonance frequencies of the bone-implant-ancillary system increase with the bone-implant contact ratio and the trabecular bone Young's modulus, with a sensitivity that varies over the modes. Both the pull-out forces and the vibration behavior are consistent with previous experimental studies. This study demonstrates the potential of using vibration methods to guide the surgeons for optimizing implant stability in various patients and surgical configurations.

This paper has carried out numerical characterizations of effective thermal properties of a new kind of macroporous bio-based epoxy resin. This new kind of material was synthesized by a free-solvent and free-amine-hardener process combining the cationic photopolymerization and the solid porogen leaching technique. In order to determine the effective thermal properties of the material, the asymptotic homogenization method has been used, deriving a cell problem from microscopic thermal equations. By solving this problem on a representative volume element consisting of elementary fillet-edge cubic pore and matrix which have been idealized from experimental pore characterizations, the effective thermal conductivity and diffusivity tensors have been attained. The asymptotic homogenization method revealed the effect of microstructural characteristics via pore arrangements, porosity and pore size on the effective thermal properties of the porous material. This first stage in the material development allows to propose adjustments in the elaboration process to improve the thermal insulation characteristics of a biosourced epoxy resin with two porosity levels. The paper has also provided examples of multilayer walls using the studied epoxy resins as thermally insulating materials. These walls including two or three insulation layers with different thicknesses have been assumed to suffer either a step change or a harmonic variation of the temperature at one side of the walls. Transient thermal responses of multilayer walls to the above thermal excitations have been dealt with by a semi-analytical approach in the context of one-dimension problems.

We consider fluid-saturated poroelastic media whose the mechanical response is governed by the Biot model relevant to a mesoscopic scale. Assuming the material properties being described by periodic functions, to analyze wave propagation in such heterogeneous and anisotropic media, we derive a formulation based on the Floquet-Bloch (FB) wave decomposition which enables to analyze waves within the whole first Brillouin zone associated with the periodic structure. The wave dispersion results obtained by the FB approach are compared with those computed using a model derived by the homogenization based on the asymptotic analysis with respect to the scale parameter. As another new ingredient, the homogenized model is extended to describe media saturated simultaneously by multiple different fluids, so that the model involves new permeability tensors and differs in structure from the model derived earlier. The dispersion analysis by the FB approach leads to a cumbersome quadratic eigenvalue problem to be solved for complex wave numbers. We suggest an efficient filtration strategy to identify the principle propagating modes (the fast and slow compressional waves and the shear waves). For comparison with results of the FB transformation applied at the mesoscopic heterogeneity scale, the homogenized model responses are reconstructed using the corrector results of the homogenization with fixing a finite scale. Numerical examples illustrate very good correspondence of the dispersion results, as computed by both the approaches.

International audience; While cementless implants are now widely used clinically, implant debonding still occur and is difficult to anticipate. Assessing the biomechanical strength of the bone-implant interface can help improving the understanding of osseointegration phenomena and thus preventing surgical failures. A dedicated and standardized implant model was considered. The samples were tested using a mode III cleavage device to assess the mechanical strength of the bone-implant interface by combining experimental and numerical approaches. Four rough (Sa = 24.5 µm) osseointegrated coin-shaped implants were left in sheep cortical bone during 15 weeks of healing time. Each sample was experimentally rotated at 0.03°/sec until complete rupture of the interface. The maximum values of the torque were comprised between 0.48 and 0.72 N.m, while a significant increase of the normal force from 7-12 N to 31-43 N was observed during the bone-implant interface debonding, suggesting the generation of bone debris at the bone-implant interface. The experimental results were compared to an isogeometric finite element model describing the adhesion and debonding phenomena through a modified Coulomb's law, based on a varying friction coefficient to represent the transition from an unbroken to a broken bone-implant interface. A good agreement was found between numerical and experimental torques, with numerical friction coefficients decreasing from 8.93 to 1.23 during the bone-implant interface rupture, which constitutes a validation of this model to simulate the debonding of an osseointegrated bone-implant interface subjected to torsion.

Periprosthetic femoral bone fractures are frequent complications of Total Hip Arthroplasty (THA) and may occur during the insertion of uncemented Femoral Stems (FS), due to the nature of the press-fit fixation. Such fracture may lead to the surgical failure of the THA and require a revision surgery, which may have dramatic consequences. Therefore, an early detection of intra-operative fractures is important to avoid worsening the fracture and/or to enable a peroperative treatment. The aim of this in vitro study is to determine the sensitivity of a method based on resonance frequency analysis of the bone-stem-ancillary system for periprosthetic fractures detection. A periprosthetic fracture was artificially created close to the lesser-trochanter of 10 femoral bone mimicking phantoms. The bone-stem-ancillary resonance frequencies in the range (2–12) kHz were measured on an ancillary instrumented with piezoelectric sensors, which was fixed to the femoral stem. The measurements were repeated for different fracture lengths from 4 to 55 mm. The results show a decrease of the resonance frequencies due to the fracture occurrence and propagation. The frequency shift reached up to 170 Hz. The minimum fracture length that can be detected varies from [Formula: see text] mm to [Formula: see text] mm according to the mode and to the specimen. A significantly higher sensitivity ( p = 0.011) was obtained for a resonance frequency around 10.6 kHz, corresponding to a mode vibrating in a plane perpendicular to the fracture. This study opens new paths toward the development of non-invasive vibration-based methods for intra-operative periprosthetic fractures detection.

The femoral stem primary stability achieved by the impaction of a beam called “ancillary” attached to the implant during its insertion is an important factor of success in cementless surgery. However, surgeons rely on their proprioception, making the process subjective. The use of experimental modal analysis (EMA) without sensor nor probe fixation on the implant or on the bone is a promising non-destructive approach to determine implant stability. This study investigates whether EMA performed directly on a beam, which is temporary fixed to the implant during its insertion, could provide information on the boundary condition, which corresponds to the implant stability. A cementless femoral stem was inserted into 10 bone phantoms of human femurs and EMA was carried out on the ancillary using a dedicated impact hammer for each insertion step. Two bending modes were identified in the frequency range 400–8000 Hz for which the resonance frequency was shown to be sensitive to the insertion step and to the bone-implant interface properties. A significant correlation was obtained between the two modal frequencies and the implant insertion depth (R² = 0.95 ±0.04 and R² = 0.94 ±0.06). This study opens new paths towards the development of noninvasive vibration-based evaluation methods to monitor cementless implant insertion.

The mechanical characterization of soft tissues is of great importance in different medical fields since a change of soft tissue properties may be of physio-pathologic nature. This study investigates the feasibility of using impact analysis to measure the mechanical properties of soft tissue mimicking phantoms made of agarose. The impact analysis is performed on agar-based specimens with various concentrations by applying small impacts on a beam in contact with the surface of the specimen. The time variation of the signal corresponding to the impact force is analyzed as a function of the agar concentration and the impact force amplitude. A temporal indicator τ is developed, corresponding to the time difference between the initial impact and the rebound of the beam on the hammer. The results show a decrease of τ when the agar concentration increases. The method appears to be sensitive to non-linear phenomena related to the material behavior and/or to contact phenomena between the beam and the specimen. The error on the estimation of the percentage of agar is of the same order of magnitude than the sensitivity obtained using elastography techniques. This study opens new perspective for fast, cheap, and non-invasive mechanical characterization of non-linear soft tissues.

While implant surgical interventions are now routinely performed, failures still occur and may have dramatic consequences. The clinical outcome depends on the evolution of the biomechanical properties of the bone-implant interface (BII). This chapter reviews studies investigating the use of quantitative ultrasound (QUS) techniques for the characterization of the BII.First, studies on controlled configurations evidenced the influence of healing processes and of the loading conditions on the ultrasonic response of the BII. The gap of acoustical properties at the BII increases (i) during healing and (ii) when stress at the BII increases, therefore inducing a decrease of the reflection coefficient at the BII.Second, an acoustical model of the BII is proposed to better understand the parameters influencing the interaction between ultrasound and the BII. The reflection coefficient is shown to decrease when (i) the BII is better osseointegrated, (ii) the implant roughness decreases, (iii) the frequency of QUS decreases and (iv) the bone mass density increases.Finally, a 10 MHz device aiming at assessing dental implant stability was validated in vitro, in silico and in vivo. A comparison between QUS and resonance frequency analysis (RFA) techniques showed a better sensitivity of QUS to changes of the parameters related to the implant stability.

Cementless implants have become widely used for total hip replacement surgery. The long-term stability of these implants is achieved by bone growing around and into the porous surface of the implant, a process called osseointegration. However, debonding of the bone-implant interface can still occur due to aseptic implant loosening and insufficient osseointegration, which may have dramatic consequences. The aim of this work is to describe a new 3D finite element frictional contact formulation for the debonding of partially osseointegrated implants. The contact model is based on a modified Coulomb's friction law (Immel et al. 2020, Biomech. Model. Mechanobiol.) that takes into account the tangential debonding of the bone-implant interface. This model is extended in the direction normal to the bone-implant interface by considering a cohesive zone model, to account for adhesion phenomena in the normal direction and for adhesive friction of partially bonded interfaces. The model is applied to simulate the debonding of an acetabular cup implant. The influence of partial osseointegration and adhesive effects on the long-term stability of the implant is assessed. The influence of different patient- and implant-specific parameters such as the friction coefficient, the trabecular Young's modulus and the interference fit is also analyzed, in order to determine the optimal stability for different configurations. Furthermore, this work provides guidelines for future experimental and computational studies, that are necessary for further parameter calibration., Biomech Model Mechanobiol (2022)

Short and long-term stabilities of cementless implants are strongly determined by the interfacial load transfer between implants and bone tissue. Stress-shielding effects arise from shear stresses due to the difference of material properties between bone and the implant. It remains difficult to measure the stress field in periprosthetic bone tissue. This study proposes to investigate the dependence of the stress field in periprosthetic bone tissue on i) the implant surface roughness, ii) material properties of bone and of the implant, iii) the bone-implant contact ratio. To do so, a microscale 2-D finite element model of an osseointegrated boneimplant interface was developed where the surface roughness was modeled by a sinusoidal surface. The results show that the isostatic pressure is not affected by the presence of the bone-implant interface while shear stresses arise due to the combined effects of a geometrical singularity (for low surface roughness) and of shear stresses at the bone-implant interface (for high surface roughness). Stress-shielding effects are likely to be more important when the bone-implant contact ratio value is low, which corresponds to a case of relatively low implant stability. Shear stress reach a maximum value at a distance from the interface comprised between 0 and 0.1 time roughness wavelength $\lambda$ and tend to 0 at a distance from the implant surface higher than $\lambda$, independently from bone-implant contact ratio and waviness ratio. A comparison with an analytical model allows validating the numerical results. Future work should use the present approach to model osseointegration phenomena., Comment: Journal of Orthopaedic Research, Wiley, In press

In this paper, we present a new approach to study Lamb-type waves of anisotropic elastic plates in a probabilistic framework. The study and analysis are carried out on an elastic plate whose randomly varied elastic properties in the through-thickness direction. By introducing a stochastic model for quantitative description of heterogeneous elastic properties in the plate, the effect of material heterogeneity on Lamb modes may be investigated from a stochastic point of view. To the our best knowledge, this study is the first to investigate Lamb-type waves in a probabilistic framework. Different plate thicknesses are considered and associated dispersion curves are computed. A sensitivity study is performed, highlighting effect of the uncertainty of elasticity properties on the fluctuation of Lamb modes via phase velocities, energy velocities and modes shapes. Next, we discuss the relevance of introducing random media to identify branches associated with experimental dispersion curves.

International audience; The femoral stem primary stability achieved by the impaction of an ancillary during its insertion is an important factor of success in cementless surgery. However, surgeons still rely on their proprioception, making the process highly subjective. The use of Experimental Modal Analysis (EMA) without sensor nor probe fixation on the implant or on the bone is a promising non destructive approach to determine the femoral stem stability. The aim of this study is to investigate whether EMA performed directly on the ancillary could be used to monitor the femoral stem insertion into the bone. To do so, a cementless femoral stem was inserted into 10 bone phantoms of human femurs and EMA was carried out on the ancillary using a dedicated impact hammer for each insertion step. Two bending modes could be identified in the frequency range [400–8000] Hz for which the resonance frequency was shown to be sensitive to the insertion step and to the bone-implant interface properties. A significant correlation was obtained between the two modal frequencies and the implant insertion depth (R2 = 0.95 ± 0.04 and R2 = 0.94 ± 0.06). This study opens new paths towards the development of noninvasive vibration based evaluation methods to monitor cementless implant insertion.

Understanding dispersion relations and wave mode shapes is vital in nondestructive control of dynamic behaviors of poroelastic composites. In the framework of semi-analytical finite element (SAFE) method, this paper presents two numerical approaches so-called semi-analytical isogeometric Galerkin (SAIGA-G) and semi-analytical isogeometric collocation (SAIGA-C) for computing dispersion of guided-waves in anisotropic poroelastic plates immersed in acoustic fluids. Biot’s theory was used for describing the dynamic behavior of anisotropic poroelastic material. Assuming the structures is homogeneous along its axial direction, the Non-Uniform Rational B-splines (NURBS) was successfully employed in procedures using isogeometric Galerkin and collocation methods. The numeral studies showed that the SAIGA-G method using high continuity NURBS basis allowed to significantly improve the accuracy as well as the convergence rate of the wave dispersion solutions in compared with the conventional SAFE method, which used Lagrange basis functions. Otherwise, the SAIGA-C method was shown to have similar performance in terms of accuracy to the SAFE method.

Material and structural non-destructive evaluations using guided-wave (GW) testing techniques rely on the knowledge of wave dispersion characteristics. When studying coupled fluid–solid waveguides having complex geometries using the semi-analytical finite element (SAFE) method, an excessive computational effort may be required, especially at high-frequency ranges. In this paper, we show the robustness of an efficient computational approach so-called the semi-analytical isogeometric analysis (SAIGA) for computing the wave dispersion in 3D anisotropic elastic waveguides coupled with acoustic fluids. This approach is based on the use of Non-Uniform Rational B-splines (NURBS) as the basis functions for the geometry representation as well as for the approximation of pressure/displacement fields. The obtained results are compared with the ones derived from using the conventional SAFE method which uses Lagrange polynomials. It is shown that for computing the dispersion of GWs, using SAIGA leads to a much faster convergence rate than using the conventional SAFE with the same shape function’s order. For hollow prismatic structures immersed in fluids, using high-order NURBS ( e.g, p = 8 ) is particularly efficient as it only requires a few elements to achieve solutions having the same precision as the ones obtained by SAFE which requires up to five times of number of DOFs. Moreover, the continuity of normal displacement at fluid–solid interfaces could be significantly improved thanks to the smoothness feature of NURBS, showing the advantage of SAIGA over SAFE in the evaluation of the shape modes of GWs in coupled fluid–solid systems.

The early diagnosis of osteoporosis through bone quality assessment has been extensively studied in the past few years. Research in axial transmission in long cortical bone using ultrasonic guided waves was shown to be sensitive to variations of the bone properties such as the geometry and the mechanical properties. The aim of this presentation is, therefore, to simulate a complex bone-like geometry using 3D finite elements (FE) in order to investigate the influence of the cortical thickness mechanical properties degradation. Three parameters were investigated: (1) the thickness of the periosteal region, (2) the degradation of the endosteal region, and (3) the position of the transition zone from periosteal to endosteal regions. Moreover, the influence of soft tissue was investigated on a plate-like structure using semi-analytical iso-geometric analysis method (SAIGA). Two cortical bone phantom plates with different mechanical properties covered with a soft tissue mimicking material were used to perform axial transmission measurement. The dispersion curves of the propagating modes were experimentally measured and then were compared to the solutions obtained with the SAIGA method. The results showed the possibility to retrieve the properties of the bone phantom plates through an inversion of the dispersion curves.

In this study, a nonlinear grid-search inversion has been developed to estimate the thickness and elastic velocities of long cortical bones, which are important determinants of bone strength, from axially-transmitted ultrasonic data. The inversion scheme is formulated in the dispersive frequency-phase velocity domain to recover bone properties. The method uses ultrasonic guided waves to retrieve overlying soft tissue thickness, cortical thickness, compressional, and shear-wave velocities of the cortex. The inversion strategy requires systematic examination of a large set of trial dispersion-curve solutions within a pre-defined model space to match the data with minimum cost in a least-squares sense. The theoretical dispersion curves required to solve the inverse problem are computed for bilayered bone models using a semi-analytical finite-element method. The feasibility of the proposed approach was demonstrated by the numerically simulated data for a 1 mm soft tissue-5 mm bone bilayer and ex-vivo data from a bovine femur plate with an overlying 2 mm-thick soft-tissue mimic. The bootstrap method was employed to evaluate the inversion uncertainty and stability. Our results have shown that the cortical thickness and wave speeds could be recovered with fair accuracy.

The characterization of the interphase condition between two materials is current in mechanics. In general, its modeling is achieved by considering an interface with only purely elastic properties. In this paper, following previous works, also inertial interface properties are taken into account. For sufficiently low-frequency regime, we investigate two density profiles (affine and quadratic), for the interphase. Moreover, the interface and the interphase are placed between two solids with different characteristics. The first one is non-dispersive, while for the second one three cases are considered: (a) solid without microstructure, i.e., a Cauchy continuum, (b) solid with microstructure characterized by normal dispersion, i.e., a strain gradient continuum, and (c) by anomalous dispersion. The reflection coefficients are plotted for each case. These results are evaluated with respect to a benchmark finite elements simulation of the finite heterogeneous interphase, and the error is discussed. It is shown that the effects of microstructure can be appreciated at higher frequencies and that the proposed model results to be accurate.

This paper presents for the first time an eco-friendly combination of cationic photopolymerization and the solid template technique to obtain macroporous epoxy resins from resorcinol diglycidyl ether (RDGE) with defined cell size and distribution. The polymerization was performed by cationic polymerization under UV irradiation in the presence of NaCl particles template sintered through the spark plasma sintering process (SPS). After removal of NaCl by water, a porous material with interconnected pores was obtained. The influence of processing parameters, i.e., reactant contents, UV irradiation time, and post-curing conditions on the reticulation achievement and the thermomechanical behavior have been pointed out. Mechanical, physical, acoustic and morphological properties were deeply investigated. For instance, the specific compressive modulus is of 50.9 MPa cm3.g−1 for a density of 0.224 g.cm−3 and the glass transition is around 137 °C, which makes this system an interesting alternative for sustainable building materials.

This study has developed novel fully bio-based resorcinol epoxy resin&ndash, diatomite composites by a green two-stage process based on the living character of the cationic polymerization. This process comprises the photoinitiation and subsequently the thermal dark curing, enabling the obtaining of thick and non-transparent epoxy-diatomite composites without any solvent and amine-based hardeners. The effects of the diatomite content and the compacting pressure on microstructural, thermal, mechanical, acoustic properties, as well as the flame behavior of such composites have been thoroughly investigated. Towards the development of sound absorbing and flame-retardant construction materials, a compromise among mechanical, acoustic and flame-retardant properties was considered. Consequently, the composite obtained with 50 wt.% diatomite and 3.9 MPa compacting pressure is considered the optimal composite in the present work. Such composite exhibits the enhanced flexural modulus of 2.9 MPa, a satisfying sound absorption performance at low frequencies with Modified Sound Absorption Average (MSAA) of 0.08 (for a sample thickness of only 5 mm), and an outstanding flame retardancy behavior with the peak of heat release rate (pHRR) of 109 W/g and the total heat release of 5 kJ/g in the pyrolysis combustion flow calorimeter (PCFC) analysis.

International audience; Although endosseous implants are widely used in the clinic, failures still occur and their clinical performance depends on the quality of osseointegration phenomena at the bone-implant interface (BII), which are given by bone ingrowth around the BII. The difficulties to ensure clinical reliability come from the complex nature of this interphase related to the implant surface roughness and the presence of a soft tissue layer (non-mineralized bone tissue) at the BII. The aim of the present study is to develop a method to assess the soft tissue thickness at the BII based on the analysis of its ultrasonic response using simulation based-convolution neural network (CNN). A large-annotated dataset was constructed using a 2-D finite element model in the frequency domain considering a sinusoidal description of the BII. The proposed network was trained by the synthesized ultrasound responses and was validated by a separate dataset from the training process. The linear correlation between actual and estimated soft tissue thickness shows excellent R 2 values equal to 99.52% and 99.65%, and narrow limit of agreement corresponded to [-2.56, 4.32 µm] and [-15.75, 30.35 µm] for the microscopic and macroscopic roughness respectively, supporting the reliability of the proposed assessment for the osseointegration phenomena.

The semi-analytical finite element (SAFE) method is widely used for studying properties of guided waves along composite waveguides. However, evaluating the modes associated to high wave numbers requires important mesh refinements and may significantly increase the computational cost. This paper presents a semi-analytical isogeometric analysis (SAIGA) to calculate the dispersion relation of functionally graded or multilayer plates coupling with fluids. High-order elements based on non-uniform B-splines (NURBS) basis functions are used. Several numerical examples are then studied for different problems in order to assess the efficiency of proposed method: (i) homogeneous plates; (ii) functionally graded plates; (iii) composite plates (with strong contrast of rigidity between layers); (iv) fluid-immersed plates. The results obtained are compared with the ones derived from analytical approaches and by the conventional SAFE method using Lagrange polynomials. For all cases, the dispersion curves evaluated by using enriched-NURBS basis functions achieve a significant better precision than using conventional Lagrangian functions (for the same number of degrees of freedom or the same order of shape functions), especially for the higher modes. The continuity of the stress shape modes at the interfaces is also shown to be much improved by using SAIGA.

International audience; Primary stability of cementless implants is crucial for the surgical success and long–term stability. However, primary stability is difficult to quantify in vivo and the biomechanical phenomena occurring during the press–fit insertion of an acetabular cup (AC) implant are still poorly understood. The aim of this study is to investigate the influence of the cortical and trabecular bone Young's moduli Ec and Et, the interference fit IF and the sliding friction coefficient of the bone–implant interface μ on the primary stability of an AC implant. For each parameter combination, the insertion of the AC implant into the hip cavity and consequent pull–out are simulated with a 3D finite element model of a human hemi–pelvis. The primary stability is assessed by determining the polar gap and the maximum pull–out force. The polar gap increases along with all considered parameters. The pull–out force shows a continuous increase with Ec and Et and a non-linear variation as a function of μ and IF is obtained. For μ > 0.6 and IF > 1.4 mm the primary stability decreases, and a combination of smaller μ and IF lead to a better fixation. Based on the patient's bone stiffness, optimal combinations of μ and IF can be identified. The results are in good qualitative agreement with previous studies and provide a better understanding of the determinants of the AC implant primary stability. They suggest a guideline for the optimal choice of implant surface roughness and IF based on the patient's bone quality.

International audience

We present in this paper a combined technique of long short-term memory and hidden Markov model to prediction problems of crack propagation in engineering. The primary advantage of the hidden Markov model is that the ability to learn with less information, in other words, its future states do not depend on past ones, based only on the present state. We use long short-term memory to train data, and output consequences improved by adding predicted different changes that are computed by hidden Markov model. Applying this combined method to numerical examples of forecasting crack propagation of singled-edge-notched beam forced by 4-point shear, crack-height growth in Marcellus shale under the hydraulic fracturing and deformations of dam structures made from fiber reinforced concrete material is addressed. The tests were carried out with many different sizes of experimental data. It was found that a combined long short-term memory - hidden Markov model results in more accurate solution than only using long short-term memory, especially in the case of the dataset that is lack of information.

We consider acoustic waves in fluid-saturated periodic media with large contrasts in the permeability and other poroelastic coefficients, whereby some of the mesoscopic material parameters depend on the scale parameter. The effective behaviour is described by a model obtained using the homogenization of the heterogeneous Biot continuum relevant to the mesoscopic level at which the dual porosity is featured by low permeability, whereas the primary porosity is very compliant. All material coefficients of the homogenized model depend on the frequency of incident waves. The macroscopic fields can be employed to reconstruct solutions at the mesoscopic level relevant to the heterogeneities. To validate the model, we consider heterogeneous strips with a finite scale lattice defining the heterogeneity. For such structures, the recovered mesoscopic response computed using the numerical homogenization method is compared with direct numerical simulations for various contrasts. For media featured by large contrast the double porosity model provides much better estimates of the wavelengths and other dispersion properties than the standard single porosity homogenized model. Moreover, the performed tests show computational efficiency of the two-scale simulations using the homogenized model, while the direct simulations of a heterogeneous medium become unfeasible because of requirements on the finite element discretization.

Ultrasound stimulation is thought to influence bone remodelling process. But recently, the efficiency of ultrasound therapy for bone healing has been questioned. Despite an extensive literature describing the positive effect of ultrasound on bone regeneration-cell cultures, animal models, clinical studies-there are more and more reviews denouncing the inefficiency of clinical devices based on low-intensity pulsed ultrasound stimulation (LIPUS) of the bone healing. One of the reasons to cause controversy comes from the persistent misunderstanding of the underlying physical and biological mechanisms of ultrasound stimulation of bone repair. As ultrasonic waves are mechanical waves, the process to be studied is the one of the mechanotransduction. Previous studies on the bone mechanotransduction have demonstrated the key role of the osteocytes in bone mechano-sensing. Osteocytes are bone cells ubiquitous inside the bone matrix; they are immersed in the interstitial fluid (IF) inside the lacuno-canalicular network (LCN). They are considered as particularly sensitive to a particular type of mechanical stress: wall shear stress on osteocytes due to the IF flow in the LCN. Inspired from these findings and observations, the present work investigates the effect of LIPUS on the cortical bone from the tissue to the osteocytes, considering that the impact of the ultrasound stimulation applied at the tissue scale is related to the mechanical stress experimented by the bone cells. To do that simulations based on the finite element method are carried out in the commercial software Comsol Multiphysics to assess the wall shear stress levels induced by the LIPUS on the osteocytes. Two formulations of the wall shear stress were investigated based on two IF flow models inside the LCN and associated with two different values of the LCN permeability. The wall shear stress estimate is very different depending on the assumption considered. One of these two models provides wall shear stress values in accordance with previous works published on bone mechanotransduction. This study presents the preliminary results of a computational model that could provide keys to understanding the underlying mechanisms of the LIPUS.

Quantitative ultrasound is used to characterize osseointegration at the bone-implant interface (BII). However, the interaction between an ultrasonic wave and the implant remains poorly understood. Heriveaux, Nguyen, and Haiat [(2018). J. Acoust. Soc. Am. 144, 488–499] recently employed a two-dimensional (2D) model of a rough BII to investigate the sensitivity of the ultrasonic response to osseointegration. The present letter aimed at assessing the validity of the 2D assumption. The values of the reflection coefficient of the BII obtained with two and three-dimensional models were found not to be significantly different for implant roughness lower than 20 μm. 2D modeling is sufficient to describe the interaction between ultrasound and the BII.

Ultrasound techniques can be used to characterize and stimulate dental implant osseointegration. However, the interaction between an ultrasonic wave and the implant-bone interface (IBI) remains unclear. This study-combining experimental and numerical approaches-investigates the propagation of an ultrasonic wave in a dental implant by assessing the amplitude of the displacements along the implant axis. An ultrasonic transducer was excited in a transient regime at 10 MHz. Laser interferometric techniques were employed to measure the amplitude of the displacements, which varied 3.2-8.9 nm along the implant axis. The results demonstrated the propagation of a guided wave mode along the implant axis. The velocity of the first arriving signal was equal to 2110 m.s-1, with frequency components lower than 1 MHz, in agreement with numerical results. Investigating guided wave propagation in dental implants should contribute to improved methods for the characterization and stimulation of the IBI.

The present work addresses the problem of multi-scale characterization and optimization of absorption properties of poroelastic materials. Considering the microstructural parameters, we compute the effective properties and field equations within the framework of Biot’s theory. Asymptotic homogenization method is used for computing the effective properties which are then applied to solve an acoustic problem. The solution of the latter problem enables the choice of the objective function for the optimization procedure of the optimal design of an unit cell. Preliminary numerical studies show that different skeleton rigidity (soft, stiff or perfectly rigid) may lead to distinct acoustic behavior and optimal parameters for the poroelastic panel.

BackgroundThe surgical success of cementless implants is determined by the evolution of the biomechanical properties of the bone–implant interface (BII). One difficulty to model the biomechanical behavior of the BII comes from the implant surface roughness and from the partial contact between bone tissue and the implant. The determination of the constitutive law of the BII would be of interest in the context of implant finite element (FE) modeling to take into account the imperfect characteristics of the BII. The aim of the present study is to determine an effective contact stiffness$$\left( {K_{c}^{\text{FEM}} } \right)$$KcFEMof an osseointegrated BII accounting for its micromechanical features such as surface roughness, bone–implant contact ratio (BIC) and periprosthetic bone properties. To do so, a 2D FE model of the BII under normal contact conditions was developed and was used to determine the behavior of$$K_{c}^{\text{FEM}}$$KcFEM.ResultsThe model is validated by comparison with three analytical schemes based on micromechanical homogenization including two Lekesiz’s models (considering interacting and non-interacting micro-cracks) and a Kachanov’s model.$$K_{c}^{\text{FEM}}$$KcFEMis found to be comprised between 1013and 1015 N/m3according to the properties of the BII.$$K_{c}^{\text{FEM}}$$KcFEMis shown to increase nonlinearly as a function of the BIC and to decrease as a function of the roughness amplitude for high BIC values (above around 20%). Moreover,$$K_{c}^{\text{FEM}}$$KcFEMdecreases as a function of the roughness wavelength and increases linearly as a function of the Young’s modulus of periprosthetic bone tissue.ConclusionsThese results open new paths in implant biomechanical modeling since this model may be used in future macroscopic finite element models modeling the bone–implant system to replace perfectly rigid BII conditions.

Background: The acetabular cup (AC) implant primary stability is an important determinant for the success of cementless hip surgery but it remains difficult to assess the AC implant fixation in the clinic. A method based on the analysis of the impact produced by an instrumented hammer on the ancillary has been developed by our group (Michel et al., 2016a). However, the soft tissue thickness present around the acetabulum may affect the impact response, which may hamper the robustness of the method. The aim of this study is to evaluate the influence of the soft tissue thickness (STT) on the acetabular cup implant primary fixation evaluation using impact analyses. Methods: To do so, different AC implants were inserted in five bovine bone samples. For each sample, different stability conditions were obtained by changing the cavity diameter. For each configuration, the AC implant was impacted 25 times with 10 and 30 mm of soft tissues positioned underneath the sample. The averaged indicator Im was determined based on the amplitude of the signal for each configuration and each STT and the pull-out force was measured. Findings: The results show that the resonance frequency of the system increases when the value of the soft tissue thickness decreases. Moreover, an ANOVA analysis shows that there was no significant effect of the value of soft tissue thickness on the values of the indicator Im (F = 2.33; p-value = 0.13). Interpretation: This study shows that soft tissue thickness does not appear to alter the prediction of the acetabular cup implant primary fixation obtained using the impact analysis approach, opening the path towards future clinical trials.

The paper deals with the homogenization approach to the modelling dynamics and wave dispersion of fluid-saturated periodic media. At the mesoscopic scale, the medium is described by the Biot model which is characterized by large contrasts in material properties of two mesoscopic constituents periodically distributed in the two porosities, called the matrix and the channels. By virtue of the homogenization, this contrast is related to the scale parameter which is subject of the asymptotic analysis. In the matrix, the material is much less permeable than in the channels, while the channels are much more compliant than the matrix. We analyze numerically properties of such a material using the homogenized double porosity model developed recently in [1]. The wave dispersion responses obtained using the double porosity model are compared with the analogous responses of a more standard homogenized model without the large contrast assumption (the single porosity model). The double porosity model exhibits much more important dispersion than the single porosity model.

Biomechanical phenomena occurring at the bone–implant interface during the press-fit insertion of acetabular cup implants are still poorly understood. This article presents a nonlinear geometrical two-dimensional axisymmetric finite element model aiming at describing the biomechanical behavior of the acetabular cup implant as a function of the bone Young’s modulus Eb, the diametric interference fit ( IF), and the friction coefficient µ. The numerical model was compared with experimental results obtained from an in vitro test, which allows to determine a reference configuration with the parameter set: μ* = 0.3, [Formula: see text], and IF* = 1 mm for which the maximal contact pressure tN = 10.7 MPa was found to be localized at the peri-equatorial rim of the acetabular cavity. Parametric studies were carried out, showing that an optimal value of the pull-out force can be defined as a function of μ, Eb, and IF. For the reference configuration, the optimal pull-out force is obtained for μ = 0.6 (respectively, Eb = 0.35 GPa and IF = 1.4 mm). For relatively low value of µ ( µ b, while for µ > 0.2, the optimal value of IF has a nonlinear dependence on µ and decreases as a function of Eb. The results can be used to help surgeons determine the optimal value of IF in a patient specific manner.

Despite the unique mechanical strength and adhesion properties of epoxy resins, they still suffer from poor toughness and brittleness inducing poor resistance to cracks. Herein, we report an efficient method of synthesis of bioepoxy resin nanocomposites filled with highly exfoliated epoxy-grafted montmorillonite. The filled resin network was produced by covalent incorporation of a binary nanocomposite (MMT-PGMA) synthesized via in situ photoinduced polymerization of glycidyl methacrylate, into a Bioepoxy resin matrix to design a ternary nanocomposite (MMT-PGMA/Bioepoxy) and this in the presence of a green polyamine used as curing agent. The materials structure and morphology were characterized by FTIR, TGA, XRD, SEM, and TEM which show the key role of the MMT surface modification on its interfacial adhesion with the epoxy resin. The results showed that the clay interlayer d-spacing increases from 1.23 nm to more than 2.2 nm upon grafting of the polymer. The homogeneous solvent-free dispersion of hybrid cl...

Cementless implants are widely used in orthopedic and dental surgery. However, debonding-related failure still occurs at the bone-implant interface. It remains difficult to predict such implant failure since the underlying osseointegration phenomena are still poorly understood. Especially in terms of friction and adhesion at the macroscale, there is a lack of data and reliable models. The aim of this work was to present a new friction formulation that can model the tangential contact behavior between osseointegrated implants and bone tissue, with focus on debonding. The classical Coulomb's law is combined with a state variable friction law to model a displacement-dependent friction coefficient. A smooth state function, based on the sliding distance, is used to model implant debonding. The formulation is implemented in a 3D nonlinear finite element framework, and it is calibrated with experimental data and compared to an analytical model for mode III cleavage of a coin-shaped, titanium implant (Mathieu et al. in J Mech Behav Biomed Mater 8(1):194-203, 2012). Overall, the results show a close agreement with the experimental data, especially the peak and the softening part of the torque curve with a relative error of less than 2.25%. In addition, better estimates of the bone's shear modulus and the adhesion energy are obtained. The proposed model is particularly suitable to account for partial osseointegration.

International audience; Mechanical modelling and associated numerical methods are able to improve the design of absorbing materials which are otherwise difficult to accomplish through experimental studies only. In this paper, we provide an original procedure for obtaining high acoustic absorption of single and multi-layered panels with predefined microstructure. The procedure uses the homogenisation technique for obtaining effective properties of an airsaturated material and solution to acoustic problems. We study a certain topology of the material and point out the effect of matrix material stiffness on the results of the optimisation procedure. We demonstrate that for stiff and rigid frames of a single layer, the optimal design parameters do not differ much whereas for the soft frames, the same results may significantly change. Moreover, we show that the absorption properties can be essentially improved by arrangements of different materials (soft, stiff and air) in sandwich panels. It is also possible to design a material which efficiently absorbs acoustic energy at low frequencies which is hard to achieve by means of conventional materials.

Numerous problems in thermal engineering give rise to problems withabrupt changes in boundary conditions particularly as regards structural and construction applications. There is a continual need for improved analytical and numerical techniques for the study and analysis of such canonical problems. Thepresent work considers transient heat propagation in a two-dimensional half-space with mixed boundary conditions of the Dirichlet and the Robin (convective) type. The exact temperature field is obtained in double integral form by applying the Wiener-Hopf technique and this integral is then efficiently evaluated numerically with the help of numerical algorithms developed for the present problem and by exploiting the properties of the integrand. The results are then compared with numerical solutions using finite element methods and excellent agreement is shown. Some potential application areas of the theory are also discussed, specifically in the regime where edge effects can influence thermal convection processes.