The stochastic finite element method and its possible use in thermo-mechanical drift calculations

The finite element method is a well established technique used to predict the performance of engineering materials, components and structures under a range of environmental and loading conditions (Smith et al, 2014). In recent work, the authors have investigated why cracks in nuclear graphite bricks do not appear in the same location as predicted by simulation. We have shown that one of the issues is that engineers typically use mean values for any mechanical property and the virtual material is therefore "too perfect". Real materials, even homogeneous isotropic materials (such as Gilsocarbon), will have some degree of spatial variability in their properties. We know this as the experimental methods used to determine properties invariably give a range of values for a set of test samples (Arregui-Mena et al, 2016). When our computer simulation includes tiny spatial fluctuations in the material properties (calibrated using random fields based on the mean and standard deviation values derived from the experimental data), stress concentrations (sometimes) arise in regions of the brick where cracks are observed to develop (Arregui-Mena et al, 2015). This methodology is also useful in the context of understanding and predicting thermo-mechanical drift. The deterministic finite element method (using mean values) will predict that an unconstrained isotropic material will expand or contract freely and elastically under a uniform temperature change (without the generation of internal stresses). When there are tiny spatial fluctuations in the thermo-mechanical properties, internal stresses arise and the surface of the component will become distorted. Cyclic thermal loading may result in increasing distortion as some of these stresses will lead to permanent inelastic deformation. The authors propose that the stochastic finite element method (Arregui-Mena et al, 2014) could be a valuable predictive tool in designing new materials that are less susceptible to thermo-mechanical drift.

Smith IM, Griffiths DV and Margetts L, "Programming the Finite Element Method", 5th Edition, Wiley, 2014.

Arregui-Mena JD, Bodel W, Worth RN, Margetts L and Mummery PM, "Spatial variability in the mechanical properties of Gilsocarbon", Carbon, 2016 (accepted for publication).

Arregui-Mena JD, Margetts L and Mummery PM, "Practical Application of the Stochastic Finite Element Method", Archives of Computational Methods in Engineering, 2014

Arregui-Mena JD, Margetts L, Griffiths DV, Lever LM, Hall GN, Mummery PM, "Spatial variability in the coefficient of thermal expansion induces pre-service stresses in computer models of virgin Gilsocarbon bricks", Journal of Nuclear Materials, 2015.