Abstract
A structural macroscopic theory of stiff and soft composites, which generalizes the theory in [1] constructed with application of a model of one-dimensional stressed state of reinforcing fibers in the current configuration of a composite is presented. The theory combines the micro- and macromechanics of composite materials. The two trends in the mechanics of composites are based on the idea of a field of macroscopic displacements and the concept of macroscopic stresses of the composite material when changes in the metrics of the matrix and reinforcing fibers in the current state of a composite medium are taken into consideration. The fibers of the reinforcing systems and matrix are analyzed on the basis of a general 3D model of deformation. No limits on the stiffness of the materials of the structural components are imposed. The analysis of the composite medium, on the macromechanical level, includes a definition of macrodisplacement and macrodeformation fields, as well as parametric structural fields in the current configuration. On the micromechanical level, the fields of macroscopic stresses in the medium, together with the fields of microscopic strains and stresses in the structural components, are defined on the basis of information obtained from the analysis of the field of the macroscopic displacements. With the corresponding interpretation of the field of macroscopic displacements, the structural macroscopic theory is applied to composite media with fibrous, laminated, and matrix structures.
Similar content being viewed by others
References
V. M. Akhundov, “Structural theory of elastomeric composites based on fiber systems — invariant description,” Mech. Compos. Mater.,32, No. 2, 156–175 (1996).
R. M. Christensen, Mechanics of Composite Materials, John Wiley & Sons New York (1979).
G. A. Vanin, Micromechanics of Composite Materials [in Russian], Naukova Dumka, Kiev (1985).
Yu. M. Tarnopol'skii, I. G. Zhigun, and V. A. Polyakov, Spatially Reinforced Composites, Technomic Publ. Co. Inc., Lancaster, Pa (1992).
Additional information
State Metallurgical Academy of Ukraine, Dniepropetrovsk, Ukraine. Translated from Mekhanika Kompozitnykh Materialov, Vol. 34, No. 5, pp. 595–612, September–October, 1998.
Rights and permissions
About this article
Cite this article
Akhundov, V.M. Structural macroscopic theory of stiff and soft composites. Invariant description. Mech Compos Mater 34, 419–432 (1998). https://doi.org/10.1007/BF02254706
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02254706