Micromechanically Based Constitutive Laws and Random Fields in Solid Mechanics: Elasticity, Plasticity, and Fracture
A stochastic formulation of constitutive laws in solid and structural mechanics, as is typically needed in the setting up of stochastic finite elements and differences [1, 2, 3], has to be based on micromechanical analyses. In this paper we give an account of our recent studies on the development and use of such laws in three areas: elasticity, plasticity and fracture/damage phenomena.
KeywordsRandom Medium Natural Boundary Condition Finite Size Scaling Micromechanical Analysis Stochastic Finite Element Method
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- 6.C. Huet: Experimental characterization, micromechanical simulation and spatio-stochastic approach of concrete behaviours below the representative volume, Probabilities and Materials - Tests, Models and Applications, Proc. NATO Adv. Res. Workshop E-269 (1994), 241–271.Google Scholar
- 10.M. Ostoja-Starzewski and J. Schulte: Bounding of effective thermal conductivities of multiscale materials by essential and natural boundary conditions, (1995), to be published.Google Scholar
- 11.M. Ostoja-Starzewski and H. Ilies: The Cauchy and characteristic boundary value problems for weakly random rigid-perfectly plastic media, Intl. J. Solids Struct. (1995), in press.Google Scholar
- 13.V.V. Sokolovskii: Statics of Granular Media, Pergamon Press, (1965).Google Scholar
- 14.W. Szczepinski: Limit States and Kinematics of Granular Media (in Polish), Polish Scientific Publishers (1974).Google Scholar
- 15.M. Ostoja-Starzewski and I. Horea: Plasticity of random inhomogeneous media, ASME Summer Ann. Mtg., Symp. on Fracture and Plastic Instabilities (N. Ghoniem, Ed.), (1995), in press.Google Scholar
- 16.H.J. Herrmann and S. Roux (eds.): Statistical Models for the Fracture of Disordered Systems, Elsevier/North-Holland (1990).Google Scholar
- 19.I. Jasiuk, P.Y. Sheng and M. Ostoja-Starzewski: Influence of random fiber arrangement on crack propagation in brittle-matrix composites, Brittle-Matrix Composites 4 (A.M. Brandt, V.C. Li and I.H. Marshall, Eds.), (1994), 200–208.Google Scholar