References
- Davis, T. A. (2004, June). Algorithm 832: UMFPACK V4.3—an unsymmetric-pattern multifrontal method. ACM Transactions on Mathematical Software, 30 (2), 196–199. doi: 10.1145/992200.992206
- Geuzaine, C., & Remacle, J.-F. (2009). Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities. International Journal for Numerical Methods in Engineering, 79 (11), 1309–1331. doi: 10.1002/nme.2579
- Gitman, I. M., Askes, H., & Sluys, L. J. (2007, November). Representative volume: Existence and size determination. Engineering Fracture Mechanics, 74 (16), 2518–2534. doi: 10.1016/j.engfracmech.2006.12.021
- Hazanov, S., & Amieur, M. (1995, July). On overall properties of elastic heterogeneous bodies smaller than the representative volume. International Journal of Engineering Science, 33 (9), 1289–1301. doi: 10.1016/0020-7225(94)00129-8
- Hazanov, S., & Huet, C. (1994, December). Order relationships for boundary conditions effect in heterogeneous bodies smaller than the representative volume. Journal of the Mechanics and Physics of Solids, 42 (12), 1995–2011. doi: 10.1016/0022-5096(94)90022-1
- Hill, R. (1963, September). Elastic properties of reinforced solids: Some theoretical principles. Journal of the Mechanics and Physics of Solids, 11 (5), 357–372. doi: 10.1016/0022-5096(63)90036-X
- Hill, R. (1965, August). A self-consistent mechanics of composite materials. Journal of the Mechanics and Physics of Solids, 13 (4), 213–222. doi: 10.1016/0022-5096(65)90010-4
- Huet, C. (1990, January). Application of variational concepts to size effects in elastic heterogeneous bodies. Journal of the Mechanics and Physics of Solids, 38 (6), 813–841. doi: 10.1016/0022-5096(90)90041-2
- Kanit, T., Forest, S., Galliet, I., Mounoury, V., & Jeulin, D. (2003, June). Determination of the size of the representative volume element for random composites: Statistical and numerical approach. International Journal of Solids and Structures, 40 (13), 3647–3679. doi: 10.1016/S0020-7683(03)00143-4
- Khisaeva, Z. F., & Ostoja-Starzewski, M. (2006, August). On the Size of RVE in Finite Elasticity of Random Composites. Journal of Elasticity, 85 (2), 153. doi: 10.1007/s10659-006-9076-y
- Mechleb, G., Gilbert, R., Christman, M., Gupta, R., & Gross, B. (2014, March). Use of Expanded Shale Amendment to Enhance Drainage Properties of Clays. Geo-Congress 2014 Technical Papers, 3444–3454. doi: 10.1061/9780784413272.334
- Ogierman, W., & Kokot, G. (2018, October). Generation of the representative volume elements of composite materials with misaligned inclusions. Composite Structures, 201, 636–646. doi: 10.1016/j.compstruct.2018.06.086
- Ostoja-Starzewski, M. (2006, April). Material spatial randomness: From statistical to representative volume element. Probabilistic Engineering Mechanics, 21 (2), 112–132. doi: 10.1016/j.probengmech.2005.07.007
- Pabst, W., & Gregorov’a, E. (2012, November). The sigmoidal average – a powerful tool for predicting the thermal conductivity of composite ceramics. Journal of Physics: Conference Series, 395 (1), 012021. doi: 10.1088/1742-6596/395/1/012021
- Ranganathan, S. I., & Ostoja-Starzewski, M. (2008, September). Scaling function, anisotropy and the size of RVE in elastic random polycrystals. Journal of the Mechanics and Physics of Solids, 56 (9), 2773–2791. doi: 10.1016/j.jmps.2008.05.001
- Savvas, D., Stefanou, G., & Papadrakakis, M. (2016, June). Determination of RVE size for random composites with local volume fraction variation. Computer Methods in Applied Mechanics and Engineering, 305, 340–358. doi: 10.1016/j.cma.2016.03.002
- Stefaniuk, D., Różański, A., & Łydżba, D. (2016). Recovery of microstructure properties: Random variability of soil solid thermal conductivity. Studia Geotechnica et Mechanica, Vol. 38 (nr 1). doi: 10.1515/sgem-2016-0011
- Trovalusci, P., Ostoja-Starzewski, M., De Bellis, M. L., & Murrali, A. (2015, January). Scale-dependent homogenization of random composites as micropolar continua. European Journal of Mechanics - A/Solids, 49, 396–407. doi: 10.1016/j.euromechsol.2014.08.010
- Wojciechowski, M. (n.d.). Fempy - finite element method in python. https://github.com/mrkwjc/fempy; http://fempy.org.
- Wojciechowski, M. (2017, September). Minimal Kinematic Boundary Conditions for Computational Homogenization of the Permeability Coefficient. Acta Mechanica et Automatica, 11 (3), 199–203. doi: 10.1515/ama-2017-0030
- Wojciechowski, M. (2022a, August). Dataset for random uniform distributions of 2D circles and 3D spheres. Data in Brief, 43, 108318. doi: 10.1016/j.dib.2022.108318
- Wojciechowski, M. (2022b, August). On generalized boundary conditions for mesoscopic volumes in computational homogenization. Composite Structures, 294, 115718. doi: 10.1016/j.compstruct.2022.115718