Contents:

Overview and history, Discussion on inertial effects. Mathematical preliminaries. Basic linear elastodynamics, Waves in Periodic Structures, Causality Principle. One-dimensional Models. Static Cracks in a Linearly Elastic Body, Stress Intensity Factors and Crack Tip Singularity, Energy Release, General Crack System, Cohesive Zone Model. Elastodynamic solutions for a stationary crack, Scattering of a pulse and a time harmonic waves, Fracture initiation due to dynamic loading. Elastodynamic crack growth, the asymptotic crack tip field, Dynamic energy release rate. Onedimensional Discrete Models, Mode III fracture in square cell elastic lattice. Scattering of lattice waves. Instabilites in dynamic fracture. Modern topics and challenges in dynamic fracture.

Lecture-wise Breakup (50/75min)

I. Overview of the course. Historical origins. Discussion on inertial effects in fracture mechanics. (1/1 Lecture)

II. Mathematical preliminaries: Fourier and Laplace Transform, Green’s functions, Asymptotics. (3/2 Lectures)

III. Basic linear elastodynamics, Longitudinal and Shear Waves, Rayleigh Wave, Waves in PeriodicStructures, Energy Flux in a Wave, Causality Principle, Brittle vs Ductile behavior. (3/2 Lectures)

IV. One-dimensional Models, Difference Between Crack Initiation and Propagation Criteria. (3/2 Lectures)

V. Static Cracks in a Linearly Elastic Body, Kolosov-Muskhelishvili Representation, PapkovichRepresentation, Stress Intensity Factors and Crack Tip Singularity, Energy Release, Nonlinear elasticity effects, J-integral, Crack Opening and Stresses on the Crack Line, Integral Equations for a General Crack System, Cohesive Zone Model. (6/4 Lectures)

VI. Basic elastodynamic solutions for a stationary crack, Scattering of a pulse and a time harmonicwave by a mode III crack tip, Scattering of a pulse and a time harmonic wave by a mode I/II crack tip, scattering by a finite crack and several cracks, Fracture initiation due to dynamic loading. (6/4 Lectures)

VII. Dynamic Fracture in a Homogeneous Elastic Medium: Elastodynamic crack growth, the asymptotic crack tip field, Steady crack growth in a strip and in unbounded medium, Dynamic energy release rate, Crack growth due to time-dependent loading. (6/4 Lectures)

VIII. One-dimensional Discrete Models, Mode III fracture in square cell elastic lattice, Local energyrelease, Global energy release, Scattering of lattice waves, Dynamic Amplification Factor in Fracture. (6/4 Lectures)

IX. Crack growth at nonuniform speed, Fracture mode transition, Crack branching and instabilitesin dynamic fracture. (4/3 Lectures)

X. Modern topics and challenges in dynamic fracture: the role of material inelasticity, ElasticPlastic Fracture, rate effects, Cracks at material interfaces, Micromechanisms of fracture, Inverse problems in dynamic fracture, Intersonic and supersonic fracture, Earthquakes. (2/2 Lectures)

Text and References:

1. Freund, L. B., 1990. Dynamic Fracture Mechanics. Cambridge University Press (Textbook).

2. Slepyan, L. I., 2002. Models and Phenomena in Fracture Mechanics, Springer.