Fracture processes in indentation and cutting of soft biomaterials

Abstract

Understanding the mechanics lying behind the behaviour of biological materials is not only vital to the current knowledge of living systems but also a keystone of the design of new materials, with relevant applications in engineering and related areas. This thesis is dedicated to the fracture process during cutting of soft biomaterials, specifically those with a porous microstructure such as the brain tissue. Various aspects are considered, including (i) the interaction between cutting tools and crack propagation; (ii) the effect of cracks in soft elastic solids exposed to large deformations; (iii) the role of rate-dependent energy dissipation during crack propagation. Each point is treated separately, in order to tackle the complexity of the material behaviour and propose theoretical models based on simplifying assumptions. The mechanics of cutting is analysed in depth combining analytical, numerical and experimental data. Focusing on some peculiar aspects of cutting, our investigation is centred on the stage of cut propagation in elastic materials and carried out borrowing the classical concepts of fracture mechanics. In particular, the mechanism of propagation during cutting is found to depend on a tool sharpness parameter, whose influence is considered analytically and with respect to experimental data. The behaviour of soft biomaterials is analysed taking into account their large strain elastic response and the presence of rate-dependent effects, associated to various dissipative processes. Numerical simulations of fracture in soft materials are performed, adopting different models to describe the behaviour of biological materials. Hyperelastic incompressible models with strain hardening are adopted to investigate the role of large deformations. Viscoelasticity and poroelasticity are included in the bulk material separately, combined with the hyperelastic behaviour and with a cohesive model of the crack-tip process zone. The ultimate goal of our work is to develop efficient and reliable computational tools to simulate cutting in soft biomaterials, with possible applications in the fields of healthcare, bioengineering, food industry and robotics. A finite element based algorithm is presented, which can be applied to different cutting tools or needles, providing detailed analyses of the tool-tissue interactions, damage and fracture process in soft materials, and replicating specific features of the insertion process, including needle steering.