Leonid I. Slepyan

Bio: Leonid I. Slepyan is an academic researcher from Tel Aviv University. The author has contributed to research in topics: Fracture mechanics & Crack growth resistance curve. The author has an hindex of 28, co-authored 99 publications receiving 2236 citations. Previous affiliations of Leonid I. Slepyan include Aberystwyth University.

Transition waves in bistable structures. II. Analytical solution: wave speed and energy dissipation

Abstract: We consider dynamics of chains of rigid masses connected by links described by irreversible, piecewise linear constitutive relation: the force–elongation diagram consists of two stable branches with a jump discontinuity at the transition point. The transition from one stable state to the other propagates along the chain and excites a complex system of waves. In the first part of the paper ( Cherkaev et al., 2004 , Transition waves in bistable structures. I. Delocalization of damage), the branches could be separated by a gap where the tensile force is zero, the transition wave was treated as a wave of partial damage. Here we assume that there is no zero-force gap between the branches. This allows us to obtain steady-state analytical solutions for a general piecewise linear trimeric diagram with parallel and nonparallel branches and an arbitrary jump at the transition. We derive necessary conditions for the existence of the transition waves and compute the speed of the wave. We also determine the energy of dissipation which can be significantly increased in a structure characterized by a nonlinear discontinuous constitutive relation. The considered chain model reveals some phenomena typical for waves of failure or crushing in constructions and materials under collision, waves in a structure specially designed as a dynamic energy absorber and waves of phase transitions in artificial and natural passive and active systems.

Localised knife waves in a structured interface

Abstract: Mishuris, G; Movchan, A; Slepyan, L. (2009). Localised knife waves in a structured interface. Journal of the Mechanics and Physics of Solids, 57 (12), 1958-1979.

Dynamics of chains with non-monotone stress–strain relations. I. Model and numerical experiments

Abstract: We discuss dynamic processes in materials with non-monotonic constitutive relations. We introduce a model of a chain of masses joined by springs with a non-monotone strain–stress relation. Numerical experiments are conducted to find the dynamics of that chain under slow external excitation. We find that the dynamics leads either to a vibrating steady state (twinkling phase) with radiation of energy, or (if dissipation is introduced) to a hysteresis, rather than to an unique stress–strain dependence that would correspond to the energy minimization.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

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Numerical simulations of fast crack growth in brittle solids

Abstract: Dynamic crack growth is analysed numerically for a plane strain block with an initial central crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on crack branching, and the effect of an inhomogeneity in strength, as in crack growth along or up to an interface. The effect of cohesive surface orientation on crack path is also explored, and for a range of orientations zigzag crack growth precedes crack branching. Finer mesh calculations are carried out where crack growth is confined to the initial crack plane. The crack accelerates and then grows at a constant speed that, for high impact velocities, can exceed the Rayleigh wave speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of crack growth is not constrained. The crack speed reaches about 45% of the Rayleigh wave speed, then the crack speed begins to oscillate and crack branching at an angle of about 29° from the initial crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast crack growth in brittle solids.

Mechanics of composite materials

Abstract: 1.Introduction to Composite Materials 2. Macrochemical Behavior of a Lamina 3.Micromechanical Behavior of a Lamina 4.Macromechanical Behavior of a Laminate 5.Bending, Buckling, and Vibration of Laminated Plates 6.Other Analysis and Behavior Topics 7.Introduction to Design of Composite Structures Appendix A.Matrices and Tensors Appendix B.Maxima and Minima of Functions of a Single Variable Appendix C.Typical Stress-Strain Curves Appendix D.Governing Equations for Beam Equilibrium and Plate Equilibrium, Buckling, and Vibration Index

On the solution of integral equations with strong ly singular kernels

Abstract: In this paper some useful formulas are developed to evaluate integrals having a singularity of the form (t-x) sup-m, m or = 1 Interpreting the integrals with strong singularities in Hadamard sense, the results are used to obtain approximate solutions of singular integral equations A mixed boundary value problem from the theory of elasticity is considered as an example Particularly for integral equations where the kernel contains, in addition to the dominant term (t,x) sup-m, terms which become unbounded at the end points, the present technique appears to be extremely effective to obtain rapidly converging numerical results