Sensitivity problems of the effective properties for composite materials
Marcin Kamiński Politechnika Łódzka, Katedra Mechaniki Materiałów, al. Politechniki 6, 93-590 Łódź
Annals 3 No. 7, 2003 pages 232-237
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abstract The main aim is to present theoretical aspects and the Finite Element Method implementation of sensitivity analysis in homogenization of composite materials with linear elastic components using the effective modules theory. Sensitivity analysis of effective material properties is presented in a general form for n-component periodic composite and is illustrated by the examples of periodic 1D as well as 2D heterogeneous structures; sensitivity coefficients are determined for the effective elasticity tensor components. The structural response functional for the fiber-reinforced elastic composite is proposed in a form of total strain energy resulting from some uniform strain state imposed on the composite Representative Volume Element (RVE). Numerical results confirm the usefulness of the homogenization method in computational analysis of composite materials sensitivity and may be applied in composite optimization, identification, shape sensitivity studies as well as in stochastic sensitivity analysis of random composites. Key words: homogenization method, design sensitivity analysis, Finite Element Method, elastic periodic composites, symbolic computations