Material Description

Abstract: Several different approaches are available in order to describe material behaviour. Considering material on the higher (macro) level of observation constitutes the macroscopic approach. However, the key to understand a macro materials behaviour lies in its mesostructure. As such the mesoscopic approach can be used which is based on the detailed material description of the lower (meso) observational level. The main focus of this dissertation is the combination of the two above techniques -- the multi-scale approach. The idea is, by means of a hierarchical multi-scale procedure, to bring the homogenised information of the detailed mesostructural description to the macro-level in the form of effective properties. Thus, the homogeneous macrostructural behaviour is driven by the heterogeneous mesostructure. Traditionally, the size of a Representative Volume Element (RVE) of the material on the meso-level is chosen as a model parameter within the multi-scale framework. Two questions arise: what should this size be and how stable is this multi-scale model based on an RVE? As an answer to the first question, a unique procedure to determine the RVE size is proposed in the dissertation. An extensive study of this size sensitivity to different test and material parameters, both deterministic and stochastic, has been discussed. With knowledge of the RVE size, the multi-scale procedure can be introduced, in which the meso-level RVE plays the role of a macro-level length-scale parameter. However, the answer to the second question is not always positive. As an example the material behaviour due to mechanical loading can be considered. Although the results are stable and reliable in the linear-elastic and hardening regimes, the picture changes in softening. This is caused by the material developing strain localisation and as a consequence losing its statistical homogeneity. For such a material a Representative Volume cannot be found and as an inference cannot be used in the multi-scale framework. A conceptually new so-called coupled-volume multi-scale approach is introduced, based on abandoning the separation of scales principle. This approach does not require an RVE be a model parameter. The idea of the approach is to uniquely link the size of the mesostructural unit cell and element size of the discretised macrostructure. The results of this coupled-volume approach show stable and reliable behaviour in all mechanical regimes.

Abstract: The high-throughput screening of periodic inorganic solids using machine learning methods requires atomic positions to encode structural and compositional details into appropriate material descriptors. These atomic positions are not available a priori for new materials, which severely limits exploration of novel materials. We overcome this limitation by using only crystallographic symmetry information in the structural description of materials. We show that for materials with identical structural symmetry, machine learning is trivial, and accuracies similar to that of density functional theory calculations can be achieved by using only atomic numbers in the material description. For machine learning of formation energies of bulk crystalline solids, this simple material descriptor is able to achieve prediction mean absolute errors of only 0.07 eV/at on a test dataset consisting of more than 85 000 diverse materials. This atomic-position independent material descriptor presents a new route of materials discovery wherein millions of materials can be screened by training a machine learning model over a drastically reduced subspace of materials.

Abstract: This work is concerned with the computational modelling of non‐linear solid material behaviour in the finite strain regime. Based on the recent computational formulations for modelling of inelastic material behaviour, a generalized material model is presented for inelastic materials incorporating classical elastic, viscoelastic, plastic and viscoplastic material description, all operating in the finite strain regime. The underlying rheological model corresponds to the combined action of several rheological components, such as Hooke, Maxwell and Prandtl elements, arranged in parallel. This work summarizes the theoretical basis of the material model and presents the computational treatment in the framework of a finite element solution procedure. Numerical examples are provided to illustrate the scope of the described computational strategy.