Finite difference adaptation of the decomposition of layered composite structures on irregular grid

Abstract

The finite difference method is used to solve the time-dependent thermo mechanical response of a layered composite structure subjected to fire. State variables of the composite are chosen whereby the external and internal boundary conditions are derived for an irregular grid through the thickness of the structure. The homogenised mass flux and specific heat capacity of pyrolysis gases over a layered composite is also defined. The formulations are tested against documented results found in the literature.

A computational homogenization framework for non-ordinary state-based peridynamics

“…Observe that, unlike in local calculus which deals with point functions only, nonlocal calculus involves two kinds of functions: point and two-point functions. This, therefore, necessitates the definition of alternative forms of the nonlocal operators defined in (7) and (8). The alternative forms of the nonlocal divergence and gradient operators were given in [28] to be the pairs D, −G * and G, −D * .…”

“…A straightforward solution is the use of micromodels in which the resolution is refined until the model can explicitly resolve all important microstructural details. This solution strategy has been utilised to model microstructurally heterogeneous materials such as composites using numerical techniques such as the Finite-Element method [1][2][3][4], Finite-Difference Method [5][6][7][8], and meshless methods such as the Element-free Galerkin method [9][10][11][12] to name just a few. This method of enriching the model suffers from several drawbacks amongst which include the fact that the microstructural details that plays important role in the response of the material may exist over wide orders of magnitude and explicit resolution of the microstructure for some applications may require computational resources that is prohibitively expensive.…”