相关论文: Computation of effective elastic moduli of rocks u…
We consider a system of differential equations in a fast long range dependent random environment and prove a homogenization theorem involving multiple scaling constants. The effective dynamics solves a rough differential equation, which is…
Computational models in cardiac electrophysiology are notorious for long runtimes, restricting the numbers of nodes and mesh elements in the numerical discretisations used for their solution. This makes it particularly challenging to…
This study presents an automated method for objectively measuring rock heterogeneity via raw X-ray micro-computed tomography (micro-CT) images, thereby addressing the limitations of traditional methods, which are time-consuming, costly, and…
This paper investigates the homogenization, dimension reduction, and linearization of a composite plate subjected to external loading within the framework of non-linear elasticity problem. The total elastic energy of the problem is of order…
Numerical homogenization aims to efficiently and accurately approximate the solution space of an elliptic partial differential operator with arbitrarily rough coefficients in a $d$-dimensional domain. The application of the inverse operator…
Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their…
Two approaches to incorporate heterogeneity in discrete models are compared. In the first, standard approach, the heterogeneity is dictated by geometrical structure of the discrete system. In the second approach, the heterogeneity is…
In this work we present a formalism for the calculation of the local elastic constants in inhomogeneous systems based on a method of planes. Unlike previous work, this formalism does not require the partitioning of the system into a set of…
Micro- and mesostructures of multiphase materials obtained from tomography and image acquisition are an ever more important database for simulation analyses. Huge data sets for reconstructed 3d volumes typically as voxel grids call for…
We deal with the shape reconstruction of inclusions in elastic bodies. For solving this inverse problem in practice, data fitting functionals are used. Those work better than the rigorous monotonicity methods from [5], but have no…
This work develops a dynamic homogenization approach for metamaterials. It finds an approximate macroscopic homogenized equation with constant coefficients posed in space and time; however, the resulting homogenized equation is higher order…
Biological cells are built up from many different constituents of varying size and stiffness which all contribute to the cell's mechanical properties. Despite this heterogeneity, in the analysis of experimental measurements such as atomic…
The revolutionary advancements in metal additive manufacturing have enabled the production of alloy-based lattice structures with complex geometrical features and high resolutions. This has encouraged the development of nonlinear material…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
We consider a class of elasticity equations in ${\mathbb R}^d$ whose elastic moduli depend on $n$ separated microscopic scales, are random and expressed as a linear expansion of a countable sequence of random variables which are…
A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields…
De-homogenization is becoming an effective method to significantly expedite the design of high-resolution multiscale structures, but existing methods have thus far been confined to simple static compliance minimization. There are two…
The aim of this work is to efficiently and robustly solve the statistical inverse problem related to the identification of the elastic properties at both macroscopic and mesoscopic scales of heterogeneous anisotropic materials with a…
Computational homogenization is the gold standard for concurrent multi-scale simulations (e.g., FE2) in scale-bridging applications. Experimental and synthetic material microstructures are often represented by 3D image data. The…
We introduce a new Partition of Unity Method for the numerical homogenization of elliptic partial differential equations with arbitrarily rough coefficients. We do not restrict to a particular ansatz space or the existence of a finite…