Abstract
A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.
Highlights
Reviews and monographs [3,4,7,8] note the advantages of flat reinforcement, which improves manufacturability and the mechanical properties of the composite, increases the reinforcement factor and the resistance to leakage failure, and reduces the statistical variation of the designed properties
We propose a different approach to solving such a problem, which can be called a structurally modified jump function method (JFM)
The accuracy of the solution in the case of non-ideal contact is very sensitive to the correct determination of the position and size of the slip zones
Summary
The theory and practice of the design and use of progressive composite materials with flat reinforcement provides indisputable evidence that their tensile strength in the transversal direction, in the case of unidirectional ribbon reinforcement, is between 50 and 75% of the strength in the longitudinal direction; the use of fibers typically yields only between. Reviews and monographs [3,4,7,8] note the advantages of flat reinforcement, which improves manufacturability and the mechanical properties of the composite, increases the reinforcement factor and the resistance to leakage failure, and reduces the statistical variation of the designed properties. It is a testament to the big prospective application of composites with ribbon-like reinforcement. Thin ribbon-like elements are a common phenomenon in micro- and nanostructures [8,9,10]
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