Development of a block-coupled finite volume methodology for non linear elasticity

A "rheinforce'' composite consists of a laminar sheet of compacted micro-agglomerated cork engraved by laser with a network of microchannels and filled with a concentrated aqueous solution of shear-thickening fluid. Using it for personal protection equipment, as an energy-absorbing material layer, is one of its important applications. An accurate numerical modeling of such material is not currently available and would be a valuable tool during design and manufacturing processes. A virtual dynamic drop tower test can be used to shed lights on the dynamics of the energy dissipation of the "rheinforce" composite. From the continuum mechanics point of view, it can be translated into an initial-boundary value problem with enclosed-Fluid-Structure Interaction, contact boundary and rigid body dynamics. The open-source OpenFOAM toolbox called Solids4foam (S4F) offers a very attractive starting point to build a solver for that initial-boundary value problem. Not only because no commercial software available (as far as the author is aware) is as customizable as needed, but also because S4F offers a strongly-coupled Fluid-Structure Interaction with fully customizable and replaceable solid and fluid solvers. Furthermore, these solvers are constructed based on only one numerical framework, the Finite Volume Method. Unfortunately, numerical simulations revealed that the current finite volume methodologies for solid mechanics implemented in S4F, i.e. Segregated (SEG) and the recently developed Block-Coupled (BC), cannot simulate the solid part of the "rheinforce'' composite under the finite strain regime. Moreover, the SEG method supports general materials (in theory any material law can be used), but it can be very slow. The BC method is fast, but only Hooke's law (an infinitesimal strain model) is supported. The principal aim of the thesis is to present the development of a new BC methodology that preserves, in a great extent, the fast convergence of the original BC and material generality (only requiring the elasticity tensor to have right-minor symmetry) of SEG. This work also demonstrates that the Field Operation and Manipulation (FOAM) concept should be implemented in a high-level programming environment to fill an important "prototyping gap'' left untouched by OpenFOAM and S4F, that is, between concept development and concept implementation in a high-performance programming language