Miguel A. Gutiérrez

Effects of intima stiffness and plaque morphology on peak cap stress

BackgroundRupture of the cap of a vulnerable plaque present in a coronary vessel may cause myocardial infarction and death. Cap rupture occurs when the peak cap stress exceeds the cap strength. The mechanical stress within a cap depends on the plaque morphology and the material characteristics of the plaque components. A parametric study was conducted to assess the effect of intima stiffness and plaque morphology on peak cap stress.MethodsModels with idealized geometries based on histology images of human coronary arteries were generated by varying geometric plaque features. The constructed multi-layer models contained adventitia, media, intima, and necrotic core sections. For adventitia and media layers, anisotropic hyperelastic material models were used. For necrotic core and intima sections, isotropic hyperelastic material models were employed. Three different intima stiffness values were used to cover the wide range reported in literature. According to the intima stiffness, the models were classified as stiff, intermediate and soft intima models. Finite element method was used to compute peak cap stress.ResultsThe intima stiffness was an essential determinant of cap stresses. The computed peak cap stresses for the soft intima models were much lower than for stiff and intermediate intima models. Intima stiffness also affected the influence of morphological parameters on cap stresses. For the stiff and intermediate intima models, the cap thickness and necrotic core thickness were the most important determinants of cap stresses. The peak cap stress increased three-fold when the cap thickness was reduced from 0.25 mm to 0.05 mm for both stiff and intermediate intima models. Doubling the thickness of the necrotic core elevated the peak cap stress by 60% for the stiff intima models and by 90% for the intermediate intima models. Two-fold increase in the intima thickness behind the necrotic core reduced the peak cap stress by approximately 25% for both intima models. For the soft intima models, cap thickness was less critical and changed the peak cap stress by 55%. However, the necrotic core thickness was more influential and changed the peak cap stress by 100%. The necrotic core angle emerged as a critical determinant of cap stresses where a larger angle lowered the cap stresses. Contrary to the stiff and intermediate intima models, a thicker intima behind the necrotic core increased the peak cap stress by approximately 25% for the soft intima models. Adventitia thickness and local media regression had limited effects for all three intima models.ConclusionsFor the stiff and intermediate intima models, the cap thickness was the most important morphological risk factor. However for soft intima models, the necrotic core thickness and necrotic core angle had a bigger impact on the peak cap stress. We therefore need to enhance our knowledge of intima material properties if we want to derive critical morphological plaque features for risk evaluation.

A unified framework for concrete damage and fracture models including size effects

A unified approach is given for isotropic and anisotropic damage formulations for concrete fracture. The formulation encompasses the classical fixed and rotating smeared crack models, but also more refined approaches based on the microplane concept. Higher-order strain gradients are introduced to avoid the boundary value problem from becoming ill-posed at the onset of softening. Again, this has been accomplished in a unified setting. By analysing a geometrically identical anchor bolt of three different sizes it is shown that higher-order strain gradients also introduce a proper size effect in the model.

Uncertainty and reliability analysis of fluid-structure stability boundaries

Fluid–structure interactions provide design constraints in many fields, yet methods available for their analysis normally assume that the structural properties are exactly known. In this contribution, these properties are more realistically modeled using random fields. Stochastic finite element methods are applied to perform uncertainty and reliability analysis on fluid–structure interaction problems with random input parameters. As an example we consider panel divergence and panel flutter. Numerical simulations demonstrate the appropriateness of sensitivitybased methods for characterization of the statistical moments of the critical points as well as for the determination of the probability of occurrence of undesired phenomena

Stochastic aspects of localised failure: material and boundary imperfections

This paper presents the application of the finite element reliability method to the evaluation of the statistical properties of localisation phenomena. Material and boundary constraint imperfections are considered. The latter are imposed through Lagrange multipliers. The evaluation of the sensitivity to the stochastic basic variables, which is needed in the reliability method, is outlined. Numerical simulations of mode-I and mode-II localisation phenomena are presented.

Studies in material parameter sensitivity of softening solids

A methodology is presented for the evaluation of the material parameter sensitivity of softening solids. The algorithm is based on the differentiation of the implicit (Euler-backward) return-mapping algorithm used for integration of the constitutive equations and the system of nonlinear algebraic equations obtained from the discretization in finite elements together with an arc-length constraint. The necessity of a stable equilibrium path and the meaning of left-hand and right-hand derivatives are discussed. Examples illustrate the theoretical developments as well as the capabilities of the algorithm to predict possible localization patterns.

Simulation of size-effect behaviour through sensitivity analyses

Sensitivity analysis techniques are applied to the simulation of size effect behaviour. The scale factor is included in the discretised equilibrium equations. A gradient-enhanced damage model is used. The sensitivity of the equilibrium path with respect to the loading factor is then obtained through the direct differentiation method. Particular attention is paid to the proper differentiation of constitutive internal variables. The predictive possibilities of the algorithm are illustrated by means of an example.

Discontinuities without discontinuity : the Weakly-enforced Slip Method

Abstract Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.

Overview of a range of solution methods for elastic dislocation problems in geophysics

Tectonic faults are commonly modeled as Volterra or Somigliana dislocations in an elastic medium. Over the years, many practical solutionmethods have been developed for problems of this type. This work presents a concise overview in consistent mathematical notation of the most prominent of these methods, emphasizing what the various methods have in common and in what aspects they are different. No models other than that of elastic dislocations are considered. Special attention is given to underlying assumptions and range of applicability.

Novel nonlocal continuum formulations. Part 1: gradient elasticity based on nonlocal displacements and nonlocal strains

Nonlocal continuum formulations exist in integral formats and differential formats. The latter, also known as gradient-enriched continua, have successfully been applied in elasticity, plasticity and damage and provide a robust framework to analyse size effects and dispersive waves. Moreover, gradient enhancement can be used to remove singularities from elastic fields as well as guarantee well-posedness in the modelling of post-peak phenomena. In this paper, the focus will be on novel formulations for gradient elasticity.

Iterative solution of the random eigenvalue problem

Algebraic eigenvalue problems play an important role in a variety of fields. In structural mechanics, eigenvalue problems commonly appear in the context of, e.g., vibrations and buckling. In the case that the considered structure as well as the considered loading conditions are exactly known, i.e. deterministic, efficient and robust methods for the computation of eigenvalues and corresponding eigenvectors exist. In the more realistic case that the structure and the loading conditions are uncertain (described by random fields), eigenvalues and eigenvectors will also be uncertain. These random eigenvalues and random eigenvectors can then be determined by solving the random eigenvalue problem, for which the availability of efficient and robust methods is limited.