SUMMARYWe present a regularized phenomenological multiscale model where elastic properties are computed using direct homogenization and subsequently evolved using a simple three‐parameter orthotropic continuum damage model. The salient feature of the model is a unified regularization framework based on the concept of effective softening strain. The unified regularization scheme has been employed in the context of constitutive law rescaling and the staggered nonlocal approach. We show that an element erosion technique for crack propagation when exercised with one of the two regularization schemes (1) possesses a characteristic length, (2) is consistent with fracture mechanics approach, and (3) does not suffer from pathological mesh sensitivity. Copyright © 2014 John Wiley & Sons, Ltd.

SUMMARY The manuscript presents a dispersive nonlinear continuum theory for the case where the shortest wavelength is several times larger than the characteristic size of the microstructure and the observation window is large. We develop a general purpose computational framework, which is valid for nonlinear problems and requires standard C 0 continuous formalism. The fine‐scale inertia effect is accounted for by formulating a quasi‐dynamic unit cell problem where the fine‐scale inertia effect is represented by so‐called inertia induced eigenstrain. The solution of the nonlinear quasi‐dynamic unit cell problem gives rise to the modification of either coarse‐scale mass matrix in the implicit solvers or internal force in the explicit solvers. Similarly to the classical homogenization theory, scale‐separation is assumed, but higher order homogenization is not pursued to avoid higher order coarse‐scale gradients, higher order continuity, and higher order boundary conditions. Numerical examples for both the one‐dimensional model problem and three‐dimensional heterogeneous medium with layered and fibrous composite microstructure are used to validate the computational framework proposed. Copyright © 2012 John Wiley & Sons, Ltd.

SUMMARYWe present a constitutive framework for a periodic heterogeneous medium with minimal number of internal variables. The method is based on a variant of the transformation field analysis (TFA) where eigenstrains are discretized using C 0 continuous approximation in matrix dominated mode of deformation, hereafter referred to as impotent eigenstrain mode, whereas in multiphase mode of deformation, the eigenstrains are approximated using the usual C  − 1 approximation. The delay in the onset of inelastic response and the eigenstrain induced anisotropy in a microphase, both characteristic to averaging methods, are alleviated by introducing an eigenstrain upwinding scheme and by enhancing constitutive laws of microphases. The proposed formulation has been verified against a direct numerical simulation. The method has been found to be very accurate in predicting an overall material response at a computational cost comparable with the phenomenological modeling of a periodic heterogeneous medium. Copyright © 2013 John Wiley & Sons, Ltd.

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization.

In this paper, we perform a verification study of the Coupled‐Momentum Method (CMM), a 3D fluid‐structure interaction (FSI) model which uses a thin linear elastic membrane and linear kinematics to describe the mechanical behavior of the vessel wall. The verification of this model is done using Womersley's deformable wall analytical solution for pulsatile flow in a semi‐infinite cylindrical vessel. This solution is, under certain premises, the analytical solution of the CMM and can thus be used for model verification. For the numerical solution, we employ an impedance boundary condition to define a reflection‐free outflow boundary condition and thus mimic the physics of the analytical solution, which is defined on a semi‐infinite domain. We first provide a rigorous derivation of Womersley's deformable wall theory via scale analysis. We then illustrate different characteristics of the analytical solution such as space‐time wave periodicity and attenuation. Finally, we present the verification tests comparing the CMM with Womersley's theory.

SUMMARYIn the recent paper, Fish and Kuznetsov introduced the so-called computational continua .C 2 / approach, which is a variant of the higher order computational homogenization that does not require higher order continuity, introduces no new degrees of freedom, and is free of higher order boundary conditions. In a follow-up paper on reduced order computational continua, the C 2 formulation has been enhanced with a model reduction scheme based on construction of residual-free fields to yield a computationally efficient framework coined as RC 2 . The original C 2 formulations were limited to rectangular and box elements. The primary objectives of the present manuscript is to revisit the original formulation in three respects: (i) consistent formulation of boundary conditions for unit cells subjected to higher order coarse scale fields, (ii) effective solution of the unit cell problem for lower order approximation of eigenstrains, and (iii) development of nonlocal quadrature schemes for general two-dimensional (quad and triangle) and three-dimensional (hexahedral and tetrahedral) elements.

In this work, we describe the CRIMSON (CardiovasculaR Integrated Modelling and SimulatiON) software environment. CRIMSON provides a powerful, customizable and user-friendly system for performing three-dimensional and reduced-order computational haemodynamics studies via a pipeline which involves: 1) segmenting vascular structures from medical images; 2) constructing analytic arterial and venous geometric models; 3) performing finite element mesh generation; 4) designing, and 5) applying boundary conditions; 6) running incompressible Navier-Stokes simulations of blood flow with fluid-structure interaction capabilities; and 7) post-processing and visualizing the results, including velocity, pressure and wall shear stress fields. A key aim of CRIMSON is to create a software environment that makes powerful computational haemodynamics tools accessible to a wide audience, including clinicians and students, both within our research laboratories and throughout the community. The overall philosophy is to leverage best-in-class open source standards for medical image processing, parallel flow computation, geometric solid modelling, data assimilation, and mesh generation. It is actively used by researchers in Europe, North and South America, Asia, and Australia. It has been applied to numerous clinical problems; we illustrate applications of CRIMSON to real-world problems using examples ranging from pre-operative surgical planning to medical device design optimization. CRIMSON binaries for Microsoft Windows 10, documentation and example input files are freely available for download from www.crimson.software, and the source code with compilation instructions is available on GitHub https://github.com/carthurs/CRIMSONFlowsolver (CRIMSON Flowsolver) under the GPL v3.0 license, and https://github.com/carthurs/CRIMSONGUI (CRIMSON GUI), under the AGPL v3.0 license. Support is available on the CRIMSON Google Groups forum, located at https://groups.google.com/forum/#!forum/crimson-users.

Please cite this article as: V. Filonova, D. Fafalis, J. Fish, Dispersive computational continua, Comput. Methods Appl. Mech. Engrg. (2015), http://dx. ABSTRACTThe two primary objectives of the present manuscript are: (i) to develop a variant of the computational continua formulation (C 2 ) with outstanding dispersive properties, and (ii) to conduct a rigorous dispersion analysis of it. The ability of the C 2 formulation to capture dispersive behavior stems from its underlying formulation, which does not explicitly assume scale separation and accounts for microstructures of finite size. The dispersion study in heterogeneous elastic media with periodic microstructure has been conducted using both analytical and numerical approaches. The so-called analytical dispersion analysis is based on the Floquet-Bloch wave solution, while the numerical dispersion analysis is based on the modal analysis of the discrete coupled fine-coarse-scale equations. The dispersive curves obtained from the dispersive C 2 formulations were compared with the classical exact Floquet-Bloch wave solution, hereafter referred to as the reference dispersive curve. It has been observed that in the case of the unit cell sizes being either half of the coarse-scale element size or equal to it, the dispersive curves obtained by the dispersive C 2 formulation are practically identical to the reference solution. For other cases, the dispersive C 2 solution is in good agreement with the reference solution provided that the wavelength is resolved by at least two coarse-scale quadratic elements. The dispersion analysis results have been further verified by the wave propagation problem in a periodic heterogeneous medium with a wavelength comparable to the microstructural size.