Tkachuk M. Micromechanical models and averaging methods for properties of materials with network microstructure and interface layers between contacting bodies.

The work delivers solution to a relevant scientific problem of solid mechanics. It consists in developing theoretical basis of micromechanics of new materials with spatial fiber network microstructure that undergoes deformations and contact interaction of elastic bodies with account for micromechanical models of roughness and other intermediate or surface layers. A unified approach has been developed to solve the formulated problems. It connects micro- and macroscale models of material deformation for network microstructures in the bulk of a solid and contact interaction of bodies with rough or microstructurally modified surfaces and intermediate layers. The mathematical formulation is derived in a form of variational principles that lead to a well-posed problems of nonlinear optimization. The advanced approach to the micromechanics of spatial network structures of elongated one-dimensional elements have been used to develop novel material models. The corresponding numerical methods have been proposed to solve the obtained systems of equations. The new micromechanical approach to the elastic homogenization of permanently bonded networks accounts initial orientation of the fibers and introduces a vectorial variable for the microstretch. It distinguishes this model from the rest of the alternative theories that are based on a simplified representation of the network. A totally new concept of maximal advance paths have been proposed. This have led to a well-justified kinematical relation between microand macrodeformations. The obtained equation restricts kinematically admissible rotations and elongations of the fibers to the actual macroscopic deformation gradient. The variational principle of minimum averaged energy forms the equilibrium conditions for the network response and the homogenized response of the material. A fundamentally new mechanism of irreversible deformations and failure was introduced for the discrete models of nonwoven P:\Dissery\2014-Dissery\Diss-KK\!!!!!!!!!!-JORDAN2020\DDKK_mater_fromHome\Avtoref_DDKK_28_01__20_Madrid.doc 43 materials. It models the relative sliding of connected fibers and their consequent pull-out. New methods and models have been developed for the analysis of contact interaction of complex-shaped bodies with account for the micromechanical properties of surface and intermediate layers characterized by nonlinear local contact stiffness. A set of structurally and physically nonlinear relations have been derived. A weak problem statement has been formulated as a minimum principle for the complementary energy in terms of the variable contact pressure distribution. The problem has been discretized by means of a boundary element approximation. The derived set of algebraic equations and inequalities is solved by the newly developed methods of auxiliary gap and variable compliance. The effect of the geometrical shape and intermediate layer properties on the distribution of the contact pressure have been studied for representative cases. As a result qualitatively new regularities have been discovered. An inverse problem statement has been derived for the justification of the contact geometry. A correction of geometry profile by specially adjusted additional external loads has been proposed in order to achieve the desired distribution of the contact pressure. The developed methods and models as well as the numerical analysis tools have been applied to a series of model and applied problems. The deformation behaviour of novel materials with network microstructures of one-dimensional elements has been determined. Macroscopical properties of these materials have been evaluated based on the special microscopic models and the homogenization methods. Regularities in contact distribution and its dependence on geometrical and physical factors have been determined for various complexshaped bodies. New design solutions for machine elements that improve their strength and durability have been justified. The developed methods and analysis tools have been introduced into the design of new engineering products. Their implementation resulted in improved technical characteristics of protection, structural and functional elements of transport vehicles of special purpose, gear transmissions, technical equipment, hydrovolumetric drives and so on. The conducted computational and experimental studies showed good agreement with the real response of network materials and the observed behavior of interacting elastic bodies with intermediate contact layer. Two major scientific fields have been established: micro-macro mechanics of materials with random network microstructures composed of one-dimensional elements of enthalpic and entropic response; structurally and physically nonlinear problems of contact interaction of complex-shaped bodies with nonlinear intermediate layer.