On elastodynamic fracture mechanics analysis of bi-material structures using finite element method

Abstract

An elastodynamic hybrid-displacement finite element model is developed to deal with problems involving bi-material cracked structures subjected to dynamic loadings. Based on a modified Hamilton's principle with relaxed continuity requirements for displacements at the interelement boundary, the mass and stiffness properties of circular-sector shaped singular elements embedded with the proper stress singularities at the bi-material imperfection fronts are derived. Interelement compatibility conditions are satisfied through the use of a Lagrangian multiplier technique and the assumption of interelement boundary dynamic displacements, thereby ensuring monotone convergence. To get the complete solutions for the bi-material cracked structure in a truely transient situation, a rigorous finite element modeling of the impact effects of two crack surfaces is devised and performed in this work. To illustrate the analysis procedure developed, Chen's homogeneous problem is first tested. Excellent agreement between the computed results and referenced solutions can be drawn. Then, several typical bi-aterial crack problems subjected to Heaviside-function loadings are solved. These include: (a) a central crack normal to and terminating at a bi-material interface, (b) a central crack normal to and going through an interface and (c) an interface crack. Detailed results and discussions are presented.