**3.1 Analysis models and metrics**

The FE analysis of the anode and cathode models was carried out to investigate the effect of various temperature loads, as well as the effect of variation of material properties with temperature, on the mechanical response and probability of failure. In the case of the anode, the effect of nonlinear (elastic-plastic) behavior versus linear elastic behavior of nickel was also investigated, which has not been studied in the literature.

The next step involved the creation of a single 2-D FE model from a single 2-D SEM image. FE modeling was carried out using the commercial FE software ABAQUS v6.9 (Dassault Systems Simulia Corp., Providence, Rhode Island, USA). This was done by writing a MATLAB ® program (R2010a, The MathWorks, Inc., Natick, Massachusetts, USA) to recreate the geometry of the image using 2-D finite elements (4-node quadrilateral elements) and write the geometry data to an ABAQUS input file. Exactly one element was assigned to each pixel in the image, and the element was assigned to the appropriate element set (nickel or YSZ) based on the pixel value. Information concerning the material properties, boundary conditions, initial temperature, temperature field, and required outputs (e.g. principal stresses) was also specified in the input file. The input file was then run using ABAQUS to

Fig. 2. Two-dimensional FE model of a single cross-section of the SOFC anode

free-body cuts of the 3-D FE anode model are shown in Figure 3.

Fig. 3. Free-body cuts of the three-dimensional FE model of the SOFC anode

The FE analysis of the anode and cathode models was carried out to investigate the effect of various temperature loads, as well as the effect of variation of material properties with temperature, on the mechanical response and probability of failure. In the case of the anode, the effect of nonlinear (elastic-plastic) behavior versus linear elastic behavior of nickel was

**3. Finite element analysis of anode and cathode models** 

also investigated, which has not been studied in the literature.

**3.1 Analysis models and metrics** 

The 3-D FE anode and cathode models were created by making a stack of all the 2-D images and introducing a "buffer" plane between each pair of consecutive images. This was necessary and useful to ensure a simple step variation in material properties between corresponding regions in two consecutive images. Then the gaps between consecutive images were interpolated by assigning one three-dimensional 8-node brick element to each volumetric pixel (or voxel). Thus, the 3-D geometries of the anode and cathode microstructures were recreated in the 3-D FE models of the anode and cathode. Various

generate the 2-D FE model as shown in Figure 2.

The FE analyses of the anode and cathode models were divided into different categories as explained in Tables 1 and 2. In each case, the FE model was subjected to fixed boundary conditions (i.e. all nodes on each of the six faces were allowed neither to translate nor to rotate). The behavior of the model with increasing temperature loads was investigated by subjecting the model to eight different spatially uniform predefined temperature fields of magnitude 120⁰C, 220⁰C, 320⁰C, ..., 820⁰C. In each analysis, the initial temperature was specified as 20⁰C (room temperature), so that the model was subjected to eight different magnitudes of temperature change (ΔT = 100⁰C, 200⁰C, 300⁰C, ..., 800⁰C)..


Table 1. Metrics for finite element analyses of anode


Table 2. Metrics for finite element analyses of cathode
