Nonlinear Deformation of a Thin Interface Inclusion

Effect of Frictional Slipping on the Strength of Ribbon-Reinforced Composite

“…av shows the coincidence of the results with those obtained in[6,7,18]. Additionally, note the expected trends of linear dependence of the growth of the critical value Q * on the increase in the value τ max± yz = τ max± yz G av , as well as on the increase in the distance d of the points of application of the concentrated force.…”

“…Due to the small thickness of the inclusion, it is possible to construct approximate relations between the components of the stress tensor and displacement vector on the opposite sides of the inclusion, which adequately describe its SSS. For example, a rather general model of a physically nonlinear thin inclusion is built in [ 6 ]: where and are the variable shear moduli of the inclusion material. Taking them to be constant, we obtain a special case of Hooke’s law.…”

“…To solve the external problem, it is convenient to apply the method referenced in [ 6 , 7 ], which uses the well-known jump function method (JFM). According to its paradigm, a thin inclusion in the matrix is modeled by jumps of the components of the stresses and displacement vectors on the line : …”

“…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 2 and 15% [ 1 , 2 , 3 , 4 , 5 , 6 , 7 ]. 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.…”

“…The need to take into account the aforementioned geometric nonlinearity (a priori unknown contact spots) significantly complicates the process of problem-solving and requires the use of various approximate methods, even for bodies of simple geometry [ 4 , 6 ]. However, these methods do not always allow for the correct consideration of thin-walled heterogeneity, nor do they guarantee the accuracy of a solution for load optimization in future applications.…”