A new thermomechanical fracture analysis approach for 3D integration technology
In this study, the peridynamic framework is applied to model heat diffusion to derive peridynamic heat diffusion equations. A numerical scheme is put forward and implemented in order to establish the validity of these equations. Finally, an approach is developed for coupled solution of heat conduction and solid mechanics equations in the realm of peridynamics.
Meshless Computational Tools for Damage and Failure Modeling
Typical damage simulation approaches are usually based on traditional finite element methods (FEM), extended FEM (xFEM) and cohesive zone method, need prescription of crack topology and complicated algorithms to facilitate crack growth – which severely limit the applicability of these theories. This limitation is a consequence of the continuum mechanics based governing equations which are cast as partial-differential equations (PDEs) that are not well-defined at cracks or singularities. Recently, a new non-local formulation of continuum mechanics named a Peridynamics (PD) theory has been proposed, which replaces PDEs with equivalent integrodifferential equations. The framework results in governing equations that do not require spatial derivatives and allows for treatment of solid-continua containing cracks/discontinuities in a unified meshless manner. In this talk, we will discuss recent advances in meshless Peridynamics-based crack/damage modeling and discuss the novel computational tools being developed Advanced Cooling Technologies, Inc. (ACT) for damage modeling. Using simple test cases we demonstrate the capabilities of the meshless approach to capture fatigue initiated damage and crack growth in composites. The mathematical structure of the PD approach automatically enables simulation of cracks propagation and failure, without the need for complicated crack path algorithms like that of XFEM or cohesive element method.
Thermodynamically consistent description of heat conduction with finite speed of heat propagation
Abstract In this work, governing equations for heat conduction with finite speed of heat propagation are derived directly from classical thermodynamics. For a one-dimensional flow of heat, the developed governing equation is linear and of parabolic type. In a three dimensional case, the system of nonlinear equations is formulated. Analytical solutions of the equations for one-dimensional flow of heat are obtained, and their analysis shows characteristic features of heat propagation with finite speed, being fully consistent with classical thermodynamics.