Calculation of the Wöhler (S-N) Curve Using a Two-Scale Model

This chapter deals with the initiation of a short crack and subsequent growth of the long crack in a carbon steel under cyclic loading, concluded with the estimation of the complete lifetime represented by the Wöhler (S-N) curve. A micro-model containing the microstructure of the material is generated using the Finite Element Method and the according non-uniform stress distribution is calculated afterwards. The number of cycles needed for crack initiation is estimated on the basis of the stress distribution in the microstructural model and by applying the physically-based Tanaka-Mura model. The long crack growth is handled using the Paris law. The analysis yields good agreement with experimental results from literature.

Numerical Reconstruction of Porous Architecture for Suspension Plasma Sprayed Coatings

The porous architecture of coatings has a significant influence on the coating performances and thus should be properly designed for the intended applications. For simulating the coating properties, it is necessary to determine the numerical representation of the coating microstructure. In this study, YSZ coatings were manufactured by suspension plasma spray (SPS). Afterwards, the porous architecture of as-prepared coatings was investigated by the combination of three techniques, imaging analysis, Ultra Small Angle X-ray Scattering (USAXS), and X-ray transmission. A microstructural model for reconstructing the porous architecture of the SPS coating was subsequently computed according to the collected experimental results. Finally, the coating thermal properties were simulated based on the model and were compared with the experimental results.

Diffusion-based degeneration of the collagen reinforcement in the pathologic human cornea

We describe a multiphysics model of the collagen structure of the cornea undergoing a progressive localized reduction of the stiffness, preluding to the development of ectasia and keratoconus. The architecture of the stromal collagen is assumed to follow the simplified two-family model proposed in Pandolfi et al. (A microstructural model of cross-link interaction between collagen fibrils in the human cornea. Philos Trans R Soc A 377:20180079, 2019), where the mechanical stiffness of the structure is supplied by transversal bonds within the fibrils of the same family (inter-crosslink bonds) and across the fibrils of the two families (intra-crosslink bonds). In Pandolfi et al. (A microstructural model of cross-link interaction between collagen fibrils in the human cornea. Philos Trans R Soc A 377:20180079, 2019), it was shown that the loss of the spherical shape due to the protrusion of a cone can be ascribed to the mechanical weakening of the intra-crosslink bonds in the central region of the collagen structure. In the present study, the reduction of bond stiffness is coupled to an evolutive pathologic phenomenon, modeled as a reaction–diffusion process of a normalized scalar field. We assume that the scalar field is a concentration-like measure of the degeneration of the chemical bonds stabilizing the structural collagen. We follow the evolution of the mechanical response of the system in terms of shape change, according to the propagation of the degeneration field, and identify the critical loss of mechanical stability resulting in the typical bulging of keratoconus corneas.