An RVE-based multiscale theory of solids with micro-scale inertia and body force effects

A multiscale theory of solids based on the concept of representative volume element (RVE) and accounting for micro-scale inertia and body forces is proposed. A simple extension of the classical Hill–Mandel Principle together with suitable kinematical constraints on the micro-scale displacements provide the variational framework within which the theory is devised. In this context, the micro-scale equilibrium equation and the homogenisation relations among the relevant macro- and micro-scale quantities are rigorously derived by means of straightforward variational arguments. In particular, it is shown that only the fluctuations of micro-scale inertia and body forces about their RVE volume averages may affect the micro-scale equilibrium problem and the resulting homogenised stress. The volume average themselves are mechanically relevant only to the macro-scale

Damage-driven strain localisation in networks of fibres: A computational homogenisation approach

In many applications, such as textiles, fibreglass, paper and several kinds of biological fibrous tissues, the main load-bearing constituents at the micro-scale are arranged as a fibre network. In these materials, rupture is usually driven by micro-mechanical failure mechanisms, and strain localisation due to progressive damage evolution in the fibres is the main cause of macro-scale instability. We propose a strain-driven computational homogenisation formulationbased on Representative Volume Element (RVE), within a framework in which micro-scale fibre damage can lead to macro-scale localisation phenomena. The mechanical stiffness considered here for the fibrous structure system is due to: i) an intra-fibre mechanism in which each fibre is axially stretched, and as a result, it can suffer damage; ii) an inter-fibre mechanism in which the stiffness results from the variation of the relative angle between pairs of fibres. The homogenised tangent tensor, which comes from the contribution of these two mechanisms, is required to detect the so-called bifurcation point at the macro-scale, through the spectral analysis of the acoustic tensor. This analysis can precisely determine the instant at which the macro-scale problem becomes ill-posed. At such a point, the spectral analysis provides information about the macro-scale failure pattern (unit normal and crack-opening vectors). Special attention is devoted to present the theoretical fundamentals rigorously in the light of variational formulations for multi-scale models. Also, the impact of a recent derived more general boundary condition for fibre networks is assessed in the context of materials undergoing softening. Numerical examples showing the suitability of the present methodology are also shown and discussed

Mechanical Characterization of the Vessel Wall by Data Assimilation of Intravascular Ultrasound Studies

Atherosclerotic plaque rupture and erosion are the most important mechanisms underlying the sudden plaque growth, responsible for acute coronary syndromes and even fatal cardiac events. Advances in the understanding of the culprit plaque structure and composition are already reported in the literature, however, there is still much work to be done toward in-vivo plaque visualization and mechanical characterization to assess plaque stability, patient risk, diagnosis and treatment prognosis. In this work, a methodology for the mechanical characterization of the vessel wall plaque and tissues is proposed based on the combination of intravascular ultrasound (IVUS) imaging processing, data assimilation and continuum mechanics models within a high performance computing (HPC) environment. Initially, the IVUS study is gated to obtain volumes of image sequences corresponding to the vessel of interest at different cardiac phases. These sequences are registered against the sequence of the end-diastolic phase to remove transversal and longitudinal rigid motions prescribed by the moving environment due to the heartbeat. Then, optical flow between the image sequences is computed to obtain the displacement fields of the vessel (each associated to a certain pressure level). The obtained displacement fields are regarded as observations within a data assimilation paradigm, which aims to estimate the material parameters of the tissues within the vessel wall. Specifically, a reduced order unscented Kalman filter is employed, endowed with a forward operator which amounts to address the solution of a hyperelastic solid mechanics model in the finite strain regime taking into account the axially stretched state of the vessel, as well as the effect of internal and external forces acting on the arterial wall. Due to the computational burden, a HPC approach is mandatory. Hence, the data assimilation and computational solid mechanics computations are parallelized at three levels: (i) a Kalman filter level; (ii) a cardiac phase level; and (iii) a mesh partitioning level. To illustrate the capabilities of this novel methodology toward the in-vivo analysis of patient-specific vessel constituents, mechanical material parameters are estimated using in-silico and in-vivo data retrieved from IVUS studies. Limitations and potentials of this approach are exposed and discussed.Fil: Maso Talou, Gonzalo Daniel. Laboratorio Nacional de Computacao Cientifica; BrasilFil: Blanco, Pablo Javier. Laboratorio Nacional de Computacao Cientifica; BrasilFil: Ares, Gonzalo Damián. Universidad Nacional de Mar del Plata. Facultad de Ingeniería. Departamento de Mecanica. Grupo de Ingeniería Asistida Por Computador; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Mar del Plata; ArgentinaFil: Guedes Bezerra, Cristiano. Heart Institute (Incor); BrasilFil: Lemos, Pedro A.. Heart Institute (Incor); BrasilFil: Feijóo, Raúl Antonino. Laboratorio Nacional de Computacao Cientifica; Brasi

The Method of Multiscale Virtual Power for the derivation of a second order mechanical model

A multi-scale model, based on the concept of Representative Volume Element (RVE), is proposed linking a classical continuum at RVE level to a macro-scale strain-gradient theory. The multi-scale model accounts for the effect of body forces and inertia phenomena occurring at the micro-scale. The Method of Multiscale Virtual Power recently proposed by the authors drives the construction of the model. In this context, the coupling between the macro- and micro-scale kinematical descriptors is defined by means of kinematical insertion and homogenisation operators, carefully postulated to ensure kinematical conservation in the scale transition. Micro-scale equilibrium equations as well as formulae for the homogenised (macro-scale) force- and stress-like quantities are naturally derived from the Principle of Multiscale Virtual Power - a variational extension of the Hill-Mandel Principle that enforces the balance of the virtual powers of both scales. As an additional contribution, further insight into the theory is gained with the enforcement of the RVE kinematical constraints by means of Lagrange multipliers. This approach unveils the reactive nature of homogenised force- and stress-like quantities and allows the characterisation of the homogenised stress-like quantities exclusively in terms of RVE boundary data in a straightforward manner.Fil: Blanco, Pablo Javier. Ministério da Ciência, Tecnologia, Inovações e Comunicações. Laboratório Nacional de Computação Científica; BrasilFil: Sánchez, Pablo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; ArgentinaFil: De Souza Neto, Eduardo Alberto. Swansea University; Reino UnidoFil: Feijóo, Raúl Antonino. Ministério da Ciência, Tecnologia, Inovações e Comunicações. Laboratório Nacional de Computação Científica; Brasi

Um elemento finito curvo para a análise dinâmica de cascas axissimétricas com cargas arbitrárias

Apresenta-se um estudo para a obtenção da resposta dinâmica de cascas finas de revolução, submetidas a cargas arbitrárias, utilizando as teorias lineares de Fugge ou Love. Para obtenção de soluções aproximadas, utilizou-se conjuntamente o Princípio dos Trabalhos Virtuais e o Método dos Elementos Finitos, com um elemento finito de três nós e quatro graus de liberdade por nó. Alguns resultados numéricos são apresentados e comparados aos obtidos por outros autores

Homogenization of the Navier-Stokes equations by means of the Multi-scale Virtual Power Principle

This work addresses the multi-scale modeling of fluid flow in highly complex media based on the concept of Representative Volume Element (RVE). The Method of Multi-scale Virtual Power developed by the authors is employed to construct a coarse-scale model from standard fluid flow model at a fine-scale. Kinematic conservation principles, duality arguments and the balance of virtual power between scales are employed to set the grounds of the scale transition of physical fields. This allows to derive in a variationally consistent manner (i) the fine-scale problem to be solved at the RVE, and (ii) the homogenization formulae for coarse-scale dual quantities, namely, the force-like and stress-like fields. Examples of application of flow in permeable media are presented to show the potential of the present approach.Fil: Blanco, Pablo Javier. Instituto Nacional de Ciência E Tecnologia Em Medicina Assistida Por Computação Científica; Brasil. Laboratorio Nacional de Computacao Cientifica; BrasilFil: Clausse, Alejandro. Universidad Nacional del Centro de la Provincia de Buenos Aires; Argentina. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Feijóo, Raúl Antonino. Laboratorio Nacional de Computacao Cientifica; Brasil. Instituto Nacional de Ciência E Tecnologia Em Medicina Assistida Por Computação Científica; Brasi

Multi-scale modelling of arterial tissue: Linking networks of fibres to continua

In this work we develop a multi-scale model to characterise the large scale constitutive behaviour of a material featuring a small scale fibrous architecture. The Method of Multi-scale Virtual Power (MMVP) is employed to construct the model. At the macro-scale, a classical continuum mechanics problem is formulated in the finite strain regime. At the micro-scale, a network of fibres, modelled as one-dimensional continua, composes the representative volume element (RVE). The MMVP provides a full characterisation of the equilibrium problem at the RVE, with consistent boundary conditions, as well as the homogenisation formula which defines the first Piola–Kirchhoff stress tensor. Particular attention is given to the fact that the macro-scale continuum could be considered incompressible. Numerical experiments are presented and model consistency is verified against well-known phenomenological constitutive equations. Scenarios departing from the hypotheses of such phenomenological material models are discussed.Fil: Rocha, Felipe Figueredo. Laboratório Nacional de Computação Científica; Brasil. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; BrasilFil: Blanco, Pablo Javier. Laboratório Nacional de Computação Científica; Brasil. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; BrasilFil: Sánchez, Pablo Javier. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones en Métodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones en Métodos Computacionales; Argentina. Universidad Tecnológica Nacional; ArgentinaFil: Feijóo, Raúl Antonino. Laboratório Nacional de Computação Científica; Brasil. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; Brasi

Identification of residual stresses in multi-layered arterial wall tissues using a variational framework

In the past decades a considerable amount of literature has been published addressing the study of the mechanical behavior of arterial walls. Ex-vivo experimentation made possible the development of constitutive models and the characterization of material parameters contributing to the understanding of the mechanobiological response of vascular tissues. Moreover, the existence of residual stresses in configurations free of load was revealed, and its impact in the general stress state of the tissue was quantified. In recent years, data assimilation techniques have seen a rapid development in cardiovascular modeling field, primarily focusing on the estimation of material parameters for arterial wall segments using information provided by medical imaging as well as by in-vitro settings. However, concerning the estimation of residual stresses, this research field is in its early stages, and much work is still required for the full functional characterization of arterial tissues. In this context, a conceptual variational framework for the development of residual stress estimation tools is proposed. Particularly, a variational formulation for the characterization of residual deformations and the associated stresses in arterial walls, based on full displacement field measurements of the vessel, is presented. Considering as known data the material parameters characterizing the behavior of the tissue and a set of arterial wall configurations at equilibrium with well defined pressure loads, we propose a cost functional that measures the mechanical imbalance caused by the lack of knowledge of residual stresses. In this manner, the characterization of residual stresses becomes a problem of minimizing such cost functional. Three numerical examples are presented highlighting the potential of the proposed approach. Among these examples, the characterization of residual stresses in a cylindrical geometry representing a three-layered aorta artery is performed.Fil: Ares, Gonzalo Damián. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; Brasil. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Blanco, Pablo Javier. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; BrasilFil: Urquiza, Santiago Adrian. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; Brasil. Universidad Nacional de Mar del Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Feijóo, Raúl Antonino. Instituto Nacional de Ciência e Tecnologia em Medicina Assistida por Computação Científica; Brasi

A simple coronary blood flow model to study the collateral flow index

In this work, we present a novel modeling framework to investigate the effects of collateral circulation into the coronary blood flow physiology. A prototypical model of the coronary tree, integrated with the concept of Collateral Flow Index (CFI), is employed to gain insight about the role of model parameters associated with the collateral circuitry, which results in physically-realizable solutions for specific CFI data. Then, we discuss the mathematical feasibility of pressure-derived CFI, anatomical implications and practical considerations involving the estimation of model parameters in collateral connections. A sensitivity analysis is carried out, and the investigation of the impact of the collateral circulation on FFR values is also addressed.Fil: Blanco, Pablo Javier. No especifíca;Fil: Bulant, Carlos Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tandil; ArgentinaFil: Ares, Gonzalo Damián. Universidad Nacional de Mar del Plata; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Lemos, Pedro A.. No especifíca;Fil: Feijóo, Raúl Antonino. No especifíca