On computational homogenization of transient poromechanics problems

Many engineering materials are, in fact, microscopically heterogeneous. This is true for natural materials, such as timber and clay, as well as manmade materials, like metal alloys and concrete. By means of numerical simulation, it is possible to increase the understanding of physical phenomena within such materials, allowing for a better structural design with improved safety and prolonged service life. However, the existing simulation methods either require pre-calculated effective material properties, or they are based on very fine discretization of the domain in order to capture the complex interaction between the constituents. The former approach is based on strong assumptions and cannot provide a general solution, while the latter is often computationally too expensive. This thesis is devoted to the development of an effective computational strategy for simulating the response of heterogeneous materials. A multiscale modeling framework based on a generalized macro-homogeneity condition is proposed for the analysis of a class of transient problems. Within this framework the classical approach of first order homogenization for stationary problems is extended to transient problems in a consistent manner. Homogenization is carried out on Representative Volume Elements (RVE), which are introduced in quadrature points of the macroscale elements in the spatial domain. The corresponding algorithm is thus of a nested character (FE2). The most commonly used material for road pavement is asphalt concrete, which is a highly heterogenous porous material consisting of asphalt (bitumen) binder and particulate construction aggregates. Our proposed computational strategy is used to simulate the transient and 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 of inclusion distribution inside the RVE and the size effect of the inclusions are also examined. Furthermore, different decoupling strategies are considered