A Brittle Damage Model in Thermoelastodynamics

Open Access
Author:
Pitt, Jonathan S
Graduate Program:
Engineering Science and Mechanics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
May 05, 2009
Committee Members:
  • Francesco Costanzo, Dissertation Advisor
  • Joseph Paul Cusumano, Committee Member
  • Francesco Costanzo, Committee Chair
  • Ludmil Tomov Zikatanov, Committee Member
  • Lawrence Friedman, Committee Member
Keywords:
  • Finite Element Method
  • Fracture
  • Continuum Damage Mechanics
Abstract:
The response of brittle materials subjected to dynamic thermomechanical loading is investigated. In particular, simulations are used to determine the role of material property dependence on the microstructure of a brittle material, and to determine the viability of modeling thermal phenomena associated with brittle failure within the framework of continuum damage mechanics (CDM). A system of equations is derived via the theory of internal state variables that ful ly couples the elastic, thermal, and microstructure evolution of a thermoelastic material with isotropic damage. Dynamic effects in the equations of motion and the intrinsically local nature of the constitutive equations are carefully studied. A new implementation of the finite element method is proposed for finding approximate solutions to the derived model. The damage variable is treated as a field, as opposed to the common method of considering values of the damage at the quadrature points. In this way, the damage is treated in the general framework of finite element methods. A key element of the proposed numerical formulation is the use of a piecewise constant approximate solution space for the damage variable. This is physically motivated; not only is the damage variable local, it is most often the result of homogenization over a representative volume element, and therefore evolves in a piecewise constant manner according to the mesh. Adaptive mesh refinement is implemented to keep the size of higher dimensional problems reasonable, and also to properly resolve the morphology of the damage field. Brittle behavior is captured by defining a minimum mesh size and allowing the damage variable to grow rapidly, as is physically the case in fracture. Failure induced thermal heating is observed in the simulations. To the author’s knowledge, this is the first presentation of such a result in the context of CDM for brittle materials. The specific heat and its dependence on the damage vari- able/microstructure were found to play an extremely important role in this heating. Therefore, further study (both theoretical and experimental) of the effects of failure mechanisms on the specific heat appear to be particularly important to better understand the failure of brittle materials subjected to thermomechanical loading. Specific issues in the modeling of an intrinsically discontinuous phenomena like fracture within a continuous theory are discussed.