On computational homogenization of transient poromechanics problems

Many engineering materials are, in fact, microscopically heterogeneous. This is true fornatural materials, such as timber and clay, as well as manmade materials, like metal alloysand concrete. By means of numerical simulation, it is possible to increase the understandingof physical phenomena within such materials, allowing for a better structural designwith improved safety and prolonged service life. However, the existing simulation methodseither require pre-calculated effective material properties, or they are based on veryfine discretization of the domain in order to capture the complex interaction between theconstituents. The former approach is based on strong assumptions and cannot provide ageneral solution, while the latter is often computationally too expensive.This thesis is devoted to the development of an effective computational strategy for simulatingthe response of heterogeneous materials. A multiscale modeling framework based ona generalized macro-homogeneity condition is proposed for the analysis of a class of transientproblems. Within this framework the classical approach of first order homogenizationfor stationary problems is extended to transient problems in a consistent manner. Homogenizationis carried out on Representative Volume Elements (RVE), which are introducedin quadrature points of the macroscale elements in the spatial domain. The correspondingalgorithm is thus of a nested character (FE2).The most commonly used material for road pavement is asphalt concrete, which is a highlyheterogenous porous material consisting of asphalt (bitumen) binder and particulate constructionaggregates. Our proposed computational strategy is used to simulate the transientand nonlinear problem of consolidation of an asphalt concrete layer. In particular,the degree of scale separation, i.e. the choice of RVE size, is investigated. The influence ofinclusion distribution inside the RVE and the size effect of the inclusions are also examined.Furthermore, different decoupling strategies are considered