Related papers: Multiscale modeling of vascularized tissues via no…
This paper presents a numerical method for the simulation of multiscale materials composed of an elastic matrix and slender active inclusions. The setting is motivated by the modeling of vascularized tissues and by problems arising in the…
The immersed boundary method is a mathematical formulation and numerical method for solving fluid-structure interaction problems. For many biological problems, such as models that include the cell membrane, the immersed structure is a…
We present a two dimensional model describing the elastic behaviour of the wall of a curved blood vessel. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in…
We describe a numerical method to simulate an elastic shell immersed in a viscous incompressible fluid. The method is developed as an extension of the immersed boundary method using shell equations based on the Kirchhoff-Love and the planar…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
Many biological examples of fluid-structure interaction, including the transit of red blood cells through the narrow slits in the spleen and the intracellular trafficking of vesicles into dendritic spines, involve the near-contact of…
We present a new method for modeling tissue perfusion on the capillary scale. The microvasculature is represented by a network of one-dimensional vessel segments embedded in the extra-vascular space. Vascular and extra-vascular space…
Heterogeneities in the cell membrane due to coexisting lipid phases have been conjectured to play a major functional role in cell signaling and membrane trafficking. Thereby the material properties of multiphase systems, such as the line…
Wrinkling of an inextensible elastic lining of an inner-lined tube under imposed pressure is considered. A simple equation modeling the elastic properties of the lining, the pressure, and the soft-substrate forces is derived. This equation…
The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin neural networks to investigate the properties of a fluid…
A variety of models for the membrane-mediated interaction of particles in lipid membranes, mostly well-established in theoretical physics, is reviewed from a mathematical perspective. We provide mathematically consistent formulations in a…
Materials exhibit geometric structures across mesoscopic to microscopic scales, influencing macroscale properties such as appearance, mechanical strength, and thermal behavior. Capturing and modeling these multiscale structures is…
We present a novel computational modeling framework to numerically investigate fluid-structure interaction in viscous fluids using the phase field embedding method. Each rigid body or elastic structure immersed in the incompressible viscous…
In a companion study \cite{patterson2020computing2D}, we present a numerical method for simulating 2D viscous flow through an open compliant closed channel, drive by pressure gradient. We consider the highly viscous regime, where fluid…
The study is devoted to geometrically non-linear modelling of viscoplastic structures with residual stresses. We advocate and develop a special approach to residual stresses based on the transition between reference configurations. The…
Mathematical models and numerical simulations offer a non-invasive way to explore cardiovascular phenomena, providing access to quantities that cannot be measured directly. In this study, we start with a one-dimensional multiscale blood…
This work aims to describe a mathematical model and a numerical method to simulate a thin anisotropic composite membrane moving and deforming in 3D space under a dynamic load of an arbitrary time and space profile. The model and the method…
Mesoscale simulations of woven composites using parameterized analytical geometries offer a way to connect constituent material properties and their geometric arrangement to effective composite properties and performance. However, the…
Multiscale techniques have been widely shown to potentially overcome the limitation of homogenization schemes in representing the microscopic failure mechanisms in heterogeneous media as well as their influence on their structural response…
The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed,…