Multiscale Analysis of Heterogeneous Materials

Heterogeneous materials have been widely studied over the past decades. They are able to withstand extreme loading conditions and have a huge variety of applications in engineering and material sciences. Heterogeneous materials, such as polycrystals, composites and biological tissue present complex discontinuous microstructure, with porous and micro-cracks, that considerably affect the mechanical properties at the macroscale. Thus, further comprehensive studies on the influence of the microscale features on the macroscale behaviour are needed. Furthermore, linking different length scales is not trivial and can be performed in many different ways. Numerical methods have proven to be a powerful tool for studying the behavior of heterogeneous materials. The Boundary Element Method (BEM) displays several advantages in large scale computationally expensive problems and benefits the evaluation of high mechanical gradients. Its main advantage compared to other numerical methods is the reduction of the number of degrees of freedom due to the use of surface information. The homogenized behavior of macroscopic effective properties in 3D polycrystals is studied using the elasto-static BEM formulation. Intergranular failure analysis is performed considering the dependence of the constitutive equation to grain boundary lattice structures. In the multiscale approach, Molecular Dynamics (MD) simulations of large grain boundaries number are performed, in order to define a generalized failure criterion. Asymptotic scaling is used to link molecular and microscales. Homogenization averaging theorems are used to link micro and macroscales. Following the line of research of heterogeneous materials, the failure in 3D laminated composites materials is studied. These are extensively used for aerospace applications. 3D printed composites are herein embraced. 3D printing facilitates the construction of new fiber reinforced composites featuring complex geometries and application-specific material properties. Bone, a biological composite, is also the main research focus (as bone replacements). Osteoporosis-induced bone fracture is a major health concern, which has shown to be a heavy social and financial burden worldwide. By identifying bone structure failure criteria and correlating them to early signs of tissue deterioration, the predictive diagnosis willbe improved. A patient-specific CT-data based 3D multiscale modeling and simulation of osteoporosis-induced bone fracture using MD and the BEM is proposed.