R. M. Natal Jorge

A new volumetric and shear locking‐free 3D enhanced strain element

This paper focuses on the development of a new class of eight‐node solid finite elements, suitable for the treatment of volumetric and transverse shear locking problems. Doing so, the proposed elements can be used efficiently for 3D and thin shell applications. The starting point of the work relies on the analysis of the subspace of incompressible deformations associated with the standard (displacement‐based) fully integrated and reduced integrated hexahedral elements. Prediction capabilities for both formulations are defined related to nearly‐incompressible problems and an enhanced strain approach is developed to improve the performance of the earlier formulation in this case. With the insight into volumetric locking gained and benefiting from a recently proposed enhanced transverse shear strain procedure for shell applications, a new element conjugating both the capabilities of efficient solid and shell formulations is obtained. Numerical results attest the robustness and efficiency of the proposed approach, when compared to solid and shell elements well‐established in the literature.

A shell finite element model of the pelvic floor muscles

The pelvic floor gives support to the organs in the abdominal cavity. Using the dataset made public in (Janda et al. J. Biomech. (2003) 36(6), pp. 749–757), we have reconstructed the geometry of one of the most important parts of the pelvic floor, the levator ani, using NURB surfaces. Once the surface is triangulated, the corresponding mesh is used in a finite element analysis with shell elements. Based on the 3D behavior of the muscle we have constructed a shell that takes into account the direction of the muscle fibers and the incompressibility of the tissue. The constitutive model for the isotropic strain energy and the passive strain energy stored in the fibers is adapted from Humphreys model for cardiac muscles. To this the active behavior of the skeletal muscle is added. We present preliminary results of a simulation of the levator ani muscle under pressure and with active contraction. This research aims at helping simulate the damages to the pelvic floor that can occur after childbirth.

Mechanical properties of polypropylene mesh used in pelvic floor repair

The aim of this study was the comparison of the stiffness of different meshes under two types of mechanical tests. Five different mesh types were mechanically tested. The methods used consisted on uniaxial tension test (tensile stiffness) and tape ring tests, experimental continuous compression of the mesh loops (flexural stiffness). The most significant difference of tensile stiffness behaviour appears between Aris™ and TVTO™. From the analysis of the experimental data, we divided the flexural stiffness, in two main groups. The first group includes Auto Suture™ and Aris™ meshes. The two meshes seem to have a similar flexural behaviour. The second group includes TVTO™, Uretex™ and Avaulta™. The difference between these two groups is clearly evident comparing TVTO™ and Aris™. This study shows that there are significant differences on the mechanical properties between urogynecology meshes.

New enhanced strain elements for incompressible problems

A new enhanced strain element, based on the definition of extra compatibles modes of deformation added to the standard four-node finite element, is initially presented. The element is built with the objective of addressing incompressible problems and avoiding locking effects. By analysing at the element level the deformation modes which form a basis for the incompressible subspace the extra modes of deformation are proposed in order to provide the maximum possible dimension to that subspace. Subsequently another new element with more degrees of freedom is formulated using a mixed method. This is done by including an extra field of variables related to the derivatives of the displacement field of the extra compatible modes defined previously. The performance of the elements proposed is assessed in linear and non-linear situations. Copyright ( 1999 John Wiley & Sons, Ltd.

Numerical modelling of ductile plastic damage in bulk metal forming

Abstract This work addresses the computational aspects of a model for rigid–plastic damage. The model is a modification of a previous established model formulated by Perzyna (Recent Advances in Applied Mechanics, Academic Press: New York, 1966, p. 243–377 (Chapter 9)) which is here extended to include isotropic damage. Such an extension is obtained by incorporating the constitutive equations introduced by Lemaitre (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31; A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) for ductile plastic damage into the original model. In its original version (J. Eng. Mater. Technol. 107 (1985) 83; Comput. Meth. Appl. Mech. Eng. 51 (1985) 31) this model does not distinguish tension and compression in the damage evolution law, so it was necessary to introduce a refinement proposed by Ladeveze (in: J.P. Boehler, (Ed.), Proceedings of CNRS International Colloquium 351 Villars-de-Lans, France (Failure Criteria of Structured Media, 1983, p. 355) and Lemaitre (A Course on Damage Mechanics, Springer, Berlin, Heidelberg, New York, 1996) which takes into account the partial crack closure effect with isotropic damage. The accuracy of the computational model, developed for the analysis of the material degradation in bulk metal forming processes, is shown through the discussion of the results of two examples, allowing to compare the simulation results with experimental and numerical results obtained by other authors.

On modelling damage process in vaginal tissue.

The goal of this study was to characterize and model the damage process in prolapsed vaginal tissue undergoing finite deformations. Experiments in prolapsed vaginal tissue revealed that a softening process occurs before tissues rupture. This nonlinear damage behavior requires a continuum damage theory commonly used to describe the softening behavior of soft tissues under large deformations. The structural model here presented was built within the framework of nonlinear continuum mechanics. Tissue damage was simulated considering different damage behaviors for the matrix and the fibers. The model parameters were fit to the experimental data obtained from prolapsed vaginal tissue undergoing finite deformations in uniaxial tension tests. The tests were developed with samples cut along the longitudinal axis of the vagina. The damage model was able to predict the stress-strain behavior and the damage process accurately. The error estimations pointed to an excellent agreement between experimental results and model fittings. For all the fitted data, the normalized RMS error epsilon presented very low values and the coefficient of determination R2 was close to 1.

The influence of the material properties on the biomechanical behavior of the pelvic floor muscles during vaginal delivery

In this work, a finite element model intends to represent the effects that the passage of a fetal head can induce on the muscles of the pelvic floor, from a mechanical point of view. The finite element method is a valuable tool, that is contributing to the clarification of the mechanisms behind pelvic floor disorders related to vaginal deliveries, although some care is necessary in order to obtain correct results. The present work shows how the variation of the material parameters, used in the constitutive model, can affect the obtained results from a finite element simulation. The constitutive equation adopted in this work for the pelvic floor muscles is a modified form of the incompressible transversely isotropic hyperelastic model proposed earlier by Humphrey and Yin. Results for the pelvic floor strain and stresses obtained during the passage of the fetus head are presented. The results show the importance of the material parameters and the need for a correct constitutive model.

Finite Element Studies of the Deformation of the Pelvic Floor

Abstract:  This article describes research involving finite element simulations of womens pelvic floor, undertaken in the engineering schools of Lisbon and Oporto, in collaboration with the medical school of Oporto. These studies are motivated by the pelvic floor dysfunctions that lead namely to urinary incontinence and pelvic organ prolapse. This research ultimately aims at: (i) contributing to clarify the primary mechanism behind such disorders; (ii) providing tools to simulate the pelvic floor function and the effects of its dysfunctions; (iii) contributing to planning and performing surgeries in a more controlled and reliable way. The finite element meshes of the levator ani are based on a publicly available geometric data set, and use triangular thin shell or special brick elements. Muscle and soft tissues are assumed as (quasi‐)incompressible hyperelastic materials. Skeletal muscles are transversely isotropic with a single fiber direction, embedded in an isotropic matrix. The fibers considered in this work may be purely passive, or active with input of neuronal excitation and consideration of the muscle activation process. The first assumption may be adequate to simulate passive deformations of the pelvic muscles and tissues (namely, under the extreme loading conditions of childbirth). The latter may be adequate to model faster contractions that occur in time intervals of the same order as those of muscle activation and deactivation (as in preventing urinary incontinence in coughing or sneezing). Numerical simulations are presented for the active deformation of the levator ani muscle under constant pressure and neural excitation, and for the deformation induced by a vaginal childbirth.

Mechanical characterization of the softening behavior of human vaginal tissue

The mechanical properties of vaginal tissue need to be characterized to perform accurate simulations of prolapse and other pelvic disorders that commonly affect women. This is also a fundamental step towards the improvement of therapeutic techniques such as surgery. In this paper, the softening behavior or Mullins effect of vaginal tissue is studied by proposing an appropriate constitutive model. This effect is an important factor after the birth, since vaginal tissue has been supporting a high load distribution and therefore does not recover its original behavior. Due to the anisotropy of the tissue, the mechanical testing of vaginal tissue, consists in loading-unloading uniaxial tension tests performed along the longitudinal and transverse axes of the vagina. A directional pseudo-elastic model was used to reproduce the inelastic behavior of the tissue. The obtained results may be helpful in the design of surgical procedures with autologous tissue or smart prostheses. A good qualitative agreement has been found between the numerical and experimental results for the vaginal tissue examples, indicating that the constitutive softening model can capture the typical stress-strain behavior observed in this kind of fibrous soft tissue.

Mechanical characterization and constitutive modelling of the damage process in rectus sheath

The aim of this study is to characterize and model the damage process in the anterior rectus abdominal aponeurosis (anterior rectus sheath) undergoing finite deformations. The resistance of the anterolateral abdominal aponeuroses is important when planning the surgical repair of incisional hernias, among other medical procedures. Previous experiments in prolapsed vaginal tissue revealed that a softening process occurs before tissue rupture. This nonlinear damage behaviour requires a continuum damage theory commonly used to describe the softening behaviour of soft tissues under large deformations. The structural model presented here was built within the framework of non-linear continuum mechanics. Tissue damage was simulated considering different damage behaviours for the matrix and the collagen fibres. The model parameters were fit to the experimental data obtained from anterior rectus sheath samples undergoing finite deformations in uniaxial tension tests. The tests were carried out with samples cut along the direction of the collagen fibres, and transversal to the fibres. Longitudinal and transverse mechanical properties of human anterior rectus sheath are significantly different. The damage model was able to predict the stress-strain behaviour and the damage process accurately. The error estimations pointed to an excellent agreement between experimental results and model fittings. For all the fitted data, the normalized RMS error ε presented very low values and the coefficient of determination R(2) was close to 1. The present work constitutes the first attempt (as far as the authors know) to present a damage model for the human rectus sheath.