Computing elastic moduli on 3-D X-ray computed tomography image stacks

X-ray CT imaging and finite element computations of the elastic properties of a rigid organic foam compared to experimental measurements: insights into foam variability

“…Both are 4.62 lm/ pixel resolution images, approximately 1000 9 1000 pixels in size, black is pore space, white is solid backbone, and gray is the uniform outer matrix material that has given and known elastic moduli Fig. 7 Schematic of X-ray CT cylindrical stack of images embedded into a rectangular box of known moduli material material, are used together with exact composite theory for a periodic array of right cylinders in a matrix to extract the effective moduli of just the inner foam cylinder [26]. This method, which has been thoroughly tested [26], allowed us to use all of the microstructural information from the X-ray CT images and did not require reduction of the analyzed volume to a smaller cubic sub-sample of the image cylinder.…”

“…7 Schematic of X-ray CT cylindrical stack of images embedded into a rectangular box of known moduli material material, are used together with exact composite theory for a periodic array of right cylinders in a matrix to extract the effective moduli of just the inner foam cylinder [26]. This method, which has been thoroughly tested [26], allowed us to use all of the microstructural information from the X-ray CT images and did not require reduction of the analyzed volume to a smaller cubic sub-sample of the image cylinder. The exact solution for the composite elastic moduli of a periodic array composite of right cylinders in a matrix, where both cylinder and matrix are uniform linear elastic isotropic materials, is a function of the volume fraction of cylinders and the elastic moduli of the two phases [26,53].…”

“…This method, which has been thoroughly tested [26], allowed us to use all of the microstructural information from the X-ray CT images and did not require reduction of the analyzed volume to a smaller cubic sub-sample of the image cylinder. The exact solution for the composite elastic moduli of a periodic array composite of right cylinders in a matrix, where both cylinder and matrix are uniform linear elastic isotropic materials, is a function of the volume fraction of cylinders and the elastic moduli of the two phases [26,53].…”

“…In the method used in this paper and in [26], the finite element computation gives the composite moduli, and the matrix moduli are known, since they were set before the computation. Therefore, the exact periodic cylinder solution is inverted to give the effective uniform elastic moduli of the foam-filled cylinder that must be such that the predicted composite moduli equal the computed result.…”

“…Even if such a surface can be adequately defined, there are various kinds of boundary conditions used, including fixed displacement, fixed stress, or some kind of effective medium surrounding the sample [10,23,25]. A recently developed combined numerical/analytical technique [26] reduces the challenge of sample size using a parallel finite element method, capable of easily handling systems of order 1000 3 or larger. The technique also removes the challenges of rough boundaries and selection of boundary conditions using an exact analytical expression for a periodic composite of cylinders, where the cylindrical X-ray CT image is surrounded by a known elastic medium.…”