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.