Nonlinear Mechanics Of Soft Fibrous Materials (cism International Centre For Mechanical Sciences)

The book presents a state-of-the-art overview of the fundamental theories, established models and ongoing research related to the modeling of these materials. Two approaches are conventionally used to develop constitutive relations for highly deformable fibrous materials. According to the phenomenological approach, a strain energy density function can be defined in terms of strain invariants. The other approach is based on kinetic theories, which treats a fibrous material as a randomly oriented inter-tangled network of long molecular chains bridged by permanent and temporary junctions. At the micro-level, these are associated with chemical crosslinks and active entanglements, respectively. The papers include carefully crafted overviews of the fundamental formulation of the three-dimensional theory from several points of view, and address their equivalences and differences. Also included are solutions to boundary-value problems which are amenable to experimental verification. A further aspect is the elasticity of filaments, stability of equilibrium and thermodynamics of the molecular network theory. Front Matter....Pages i-vii Nonlinear Elasticity with Application to Soft Fibre-reinforced Materials....Pages 1-48 Porous Materials with Statistically Oriented Reinforcing Fibres....Pages 49-120 Nonlinear Elasticity for Soft Fibrous Materials....Pages 121-173 Modeling Bioactive Materials....Pages 175-232 Incremental Equations for Soft Fibrous Materials....Pages 233-267 Effects of Fiber Bending and Twisting Resistance on the Mechanics of Fiber-reinforced Elastomers....Pages 269-305