L. Rakotomanana

Technical NoteViscoelastic constitutive law in large deformations: application to human knee ligaments and tendons

Traction tests on soft tissues show that the shape of the stress strain curves depends on the strain rate at which the tests are performed. Many of the constitutive models that have been proposed fail to properly consider the effect of the strain rate when large deformations are encountered. In the present study, a framework based on elastic and viscous potentials is developed. The resulting constitutive law is valid for large deformations and satisfies the principles of thermodynamics. Three parameters -- two for the elasticity and one for the viscosity -- were enough to precisely fit the non-linear stress strain curves obtained at different strain rates with human cruciate ligaments and patellar tendons. The identification results then in a realistic, three-dimensional viscoelastic constitutive law. The developed constitutive law can be used regardless of the strain or rotation values. It can be incorporated into a finite element program to model the viscoelastic behavior of ligaments and tendons under dynamic situations.

Displacements of the tibial tuberosity - Effects of the surgical parameters

A three-dimensional computer model is used, based on the finite element method, to investigate the effects of 1-, 1.5-, and 2-cm tibial tubercle elevations and of 0.5- and 1-cm medial displacements of the tuberosity, performed with different bone shingles. Patellar kinematics and patellofemoral interface peak pressure, between 45 degrees and 135 degrees of passive knee flexion, are compared for these different surgical parameters with those of a normal knee not surgically treated. The shingle lengths of 3, 5, 7, and 10 cm have little influence on the results. Augmenting tubercle medializations decrease the lateral peak pressure but result in an overpressure of the medial facet that is 154% of the normal peak value. With knee flexion between 45 degrees and 60 degrees, increasing tubercle elevations decreases later and medial peak pressures. With flexion of more than 60 degrees, increasing elevations decrease the lateral peak pressure, but they augment and even cause overpressure on the medial facet. An overpressure on the lateral facet also is seen in midrange knee flexion (75 degrees-90 degrees) for all tubercle elevation values. Increasing tubercle elevations and medializations appear to be the predominant parameters from a biomechanical point of view.

Peri-implant bone remodeling after total hip replacement combined with systemic alendronate treatment: a finite element analysis

In order to decrease the peri-implant bone loss during the life-time of the implant, oral use of anti-osteoporosis drugs (like bisphosphonates) has been suggested. In this study, bone remodeling parameters identified from clinical trials of alendronate were used to simulate the effect of those drugs used after total hip arthroplasty on the peri-implant bone density. Results of the simulation show that the oral administrated drugs increase bone density around the implant and decreases, at the same time, the micromovements between the implant and the surrounding bone tissue. Incorporation of drug effect in numerical studies of bone remodeling is a promising tool especially to predetermine safe bisphosphonate doses that could be used with orthopedic implants.

Determination of the bulk elastic moduli of various concretes by resonance frequency analysis of slabs submitted to impact echo

ABSTRACT The presented study aims at evaluating the bulk elastic Youngs modulus of six different concrete mixes as a function of porosity and water content. The impact echo method consists of a frequency analysis of ultrasonic waves generated by the impact of a steel ball. It is commonly used to measure the thickness of large concrete slabs, to detect voids in concrete structural elements considered as infinite. This method was employed on reduced size slabs (0.5 × 0.25 × 0.12 m3). As a consequence, it was necessary to identify the frequencies corresponding to resonance modes or pseudo-stationary modes. This modal analysis was performed with simplified models (for beam in particular) and used to extract the dynamic Youngs modulus Edyn and the Poissons ratio. The results are then analysed. The Edyn-modulus, inverted for all concrete mixes, is compared to static Youngs modulus Estat measured by destructive testing, to the porosity and to the water content of the specimens.

Mechanical interaction between cells and fluid for bone tissue engineering scaffold: modulation of the interfacial shear stress

An analytical model of the fluid/cell mechanical interaction was developed. The interfacial shear stress, due to the coupling between the fluid and the cell deformation, was characterized by a new dimensionless number N(fs). For N(fs) above a critical value, the fluid/cell interaction had a damping effect on the interfacial shear stress. Conversely, for N(fs) below this critical value, interfacial shear stress was amplified. As illustration, the role of the dynamic fluid/cell mechanical coupling was studied in a specific biological situation involving cells seeded in a bone scaffold. For the particular bone scaffold chosen, the dimensionless number N(fs) was higher than the critical value. In this case, the dynamic shear stress at the fluid/cell interface is damped for increasing excitation frequency. Interestingly, this damping effect is correlated to the pore diameter of the scaffold, furnishing thus target values in the design of the scaffold. Correspondingly, an efficient cell stimulation might be achieved with a scaffold of pore size larger than 300 microm as no dynamic damping effect is likely to take place. The analytical model proposed in this study, while being a simplification of a fluid/cell mechanical interaction, brings complementary insights to numerical studies by analyzing the effect of different physical parameters.

Prediction of spatio-temporal bone formation in scaffold by diffusion equation

Developing a successful bone tissue engineering strategy entails translation of experimental findings to clinical needs. A major leap forward toward this goal is developing a quantitative tool to predict spatial and temporal bone formation in scaffold. We hypothesized that bone formation in scaffold follows diffusion phenomenon. Subsequently, we developed an analytical formulation for bone formation, which had only three unknown parameters: C, the final bone volume fraction, α, the so-called scaffold osteoconduction coefficient, and h, the so-called peri-scaffold osteoinduction coefficient. The three parameters were estimated by identifying the model within vivo data of polymeric scaffolds implanted in the femoral condyle of rats. In vivo data were obtained by longitudinal micro-CT scanning of the animals. Having identified the three parameters, we used the model to predict the course of bone formation in two previously published in vivo studies. We found the predicted values to be consistent with the experimental ones. Bone formation into a scaffold can then adequately be described through diffusion phenomenon. This model allowed us to spatially and temporally predict the outcome of tissue engineering scaffolds with only 3 physically relevant parameters.

2D dynamical efficiency of a swimfin: a fluid–structure interaction approach

Recent literature has shown a great interest in evaluating the propulsive efficiency in order to enhance performances in fin swimming or development of biomimetic systems. Such problems appear to be complex for two reasons. On the one hand, for realistic undulatory motion, there is a strong interaction between the fluid and the moving fin. On the other hand, the deformable feature of the structure plays an important role on the dynamical response during the locomotion. A coupled fluid–structure interaction model is therefore necessary to quantify the energy transfer between the fin and the water and to evaluate the accurate propulsive force generated.

Some Class of SG Continuum Models to Connect Various Length Scales in Plastic Deformation

The present work proposes a continuum theory of strain gradient plasticity with additional plastic spin rate and plastic strain rate tensors defined by the Cartan coefficients of structure.

Objective measurement of biomechanics effects of brace use for adolescent idiopathic scoliosis: a comparison between standing and supine position

Although numerous studies reported on doubts about the effectiveness of brace treatment in adolescent idiopathic scoliosis (AIS; Dickson and Weinstein 1999; Goldberg et al. 1993; Winter 1994), the use of spinal bracing still remains the standard non-operative treatment of this 3D spine deformity which remains a pathology with unclear etiology. Various brace designs have been developed to manage spinal curvatures while waiting for skeletal maturation. Basically, brace treatment attempts to modify the spine deformity by applying mechanical pressure on the torso. However little is known about the effect of different brace designs and about the different time of bracing, especially full time and nightime bracing (Howard et al. 1998; D’Amato et al. 2001). Some studies used pressure sensors to measure contact pressure between the brace and torso to assess the brace’s effectiveness (Aubin et al. 1999; Wong et al. 2000; Mac-Thiong et al. 2004). Although effects of spinal orthosis treatment have been investigated in several studies, to the best of our knowledge, no previous authors have examined its biomechanics effects on different wearing positions (standing and supine). We hypothesised that nightime bracing induces different biomechanical effects on the torso than a daily bracing. The aim of the present study was to objectively quantify this influence to better understand the action of different braces or the action of different standing or supine position in braces. The study was conducted using two brace designs: CAEN and Cheneau–Toulouse–Munster (CTM) braces (Cheneau, 1981).

Topics in Continuum Mechanics and Gravitation

Modelling spacetime and more generally an arbitrary continuum requires the definition of the background geometry adapted for capturing all subtleties of the medium.