Quantification of structural and material failure mechanisms across different length scales: from instability to brittle-ductile transitions

Abstract

Structures may fail due to a myriad of different causes. Often, distinction is made between structural and material failure, that means a structure can fail, while the material is still intact (this is the case in so-called stability loss), or the material fails, which, as consequence, may lead to structural failure. The material behavior may turn out difficult to be mathematically guessed at the macro-level. On the other hand, a lot may be known about the chemistry or the microstructure of the material of interest. Herein, we aim at categorizing different scenarios which in the end provoke structural failure, discussing various cases investigated during the last five years, at the Institute for Mechanics of Materials and Structures of Vienna University of Technology: A well-chosen eigenvalue problem shows considerable potential for categorizing stability loss. We then turn to complex composite materials with a hierarchical organization, where a single constituent dominates the overall quasi-brittle failure of the material, such as lignin in wood and wood products, or the cement–water reaction products (shortly called hydrates) in cement-based materials. The picture changes if the first inelastically behaving constituent is related to ductile load carrying, then the loads within the microstructure are re-distributed before the overall material fails: this turns out to be the case in bone. Finally, due to highly confined multiaxial stress states, the elastic portion of the overall energy invested into the material may become negligible—and then yield design analysis employed on material volumes gives an idea of the highly ductile behavior of complex confined materials, such as asphalt. What integrates all the reported cases is the high capacity of mature mathematical and mechanical formulations to reveal the intricate, yet decipherable nature of the (continuum) mechanics of materials and structures.