Mesomechanical constitutive modeling (Q2718906)

There exist various theories in continuum mechanics which incorporate the internal structure of materials and extend the range of applicability of the classical continuum approach. One of the most rational is the micromorphic theory developed by Eringen and his coworkers, whose validity is corroborated in several physical fields. This research monograph is a simplified version of a more general theory. The fluctuations in strain and stress fields due to the internal structure of materials are expressed through some statistical distribution functions. The effect of internal structure on the macroscopic behaviour of the material is characterized by certain averages of the products of distribution functions called here structural parameters. The crucial assumption is that material is statistically homogeneous and isotropic. Therefore structural parameters become scalar constants which can, in principle, be determined relatively easily by appropriate experiments. In various cases the author shows that structural parameters can be obtained from uniaxial tests, and usually an excellent agreement is found between theoretical and experimental results related to uniaxial deformations. However, there is no evidence that the approach will be similarly successful in more complex deformation modes.NEWLINENEWLINENEWLINEThe book comprises 8 chapters. Chapter I ``General mesomechanical model of heterogeneous, statistically homogeneous materials'' is a very short exposition of the general approach. Chapter II ``Models of materials with statistically isotropic structure'' introduces the general theory of statistically homogeneous isotropic multiphase materials, in which structural parameters are scalar constants. However, the model is quickly simplified to two-phase materials, and the remainder of the book deals only with binary materials. In chapter III ``Plasticity of polycrystalline metals'', the author investigates a two-phase material in which one substructure is elastic and the other is elastoplastic. The solution of the identification problem for structural parameters is given, and experimental data for some uniaxial and elementarily complex deformations are compared with theoretical results. Chapter IV ``Time-dependent deformation'' is concerned with a two-phase material in which one substructure is elastic and the other is viscoelastic. The theory is applied to the creep of concrete. In chapter V ``Fracturing'', the cumulative damage leading to fracturing of material is measured by an appropriate structural parameter which reflects properties of the microstructure. Models for brittle and ductile fracture are proposed, and the theory is applied to structural concrete. Chapter VI ``Shape memory'' studies a binary shape memory alloy as a two-phase material. One set of atoms constitutes the substructure, and the other set of atoms constitutes the other substructure. The theory is focused on a shape memory material called nitinol and made of nickel and titanium atoms. The shape memory effects are controlled by a transformation from an austenitic to a martensitic configuration, which allows changes in atomic distances by keeping the volume constant. In the case considered theoretical results are in good agreement with experimental data. In chapter VII ``Transversely isotropic materials'', directionally-dependent structural parameters are employed to model a transversely isotropic two-phase material, a practically important example of which is an isotropic homogeneous elastoplastic matrix reinforced with unidirectional uniformly distributed elastic fibres. The theory is applied to a composite with an aluminium matrix and silicon carbide coated boron fibres. The final chapter VIII ``Appendices'' contains 8 appendices related to derivation of some expressions given in the main text.