A Unified Approach to Determining the Effective Physicomechanical Characteristics of Filled Polymer Composites Based on Variational Principles

• Published in: Mechanics of composite materials Vol. 54; no. 6; pp. 775 - 788
• Main Authors: Bochkareva, S. A., Grishaeva, N. Yu, Lyukshin, B. A., Lyukshin, P. A., Matolygina, N. Yu, Panin, S. V., Reutov, Yu. A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.01.2019; Springer; Springer Nature B.V
• Subjects: Analysis; Boundary value problems; Ceramics; Characterization and Evaluation of Materials; Chemistry and Materials Science; Classical Mechanics; Composite materials; Composites; Composition; Elasticity; Electric properties; Electrical conductivity; Electrical resistivity; Electromagnetism; Electrostatics; Finite element method; Glass; Internal energy; Materials Science; Mathematical models; Mechanical properties; Natural Materials; Polymer composites; Polymer industry; Polymer matrix composites; Polymers; Solid Mechanics; Thermal conductivity; Variational principles; effective properties; thermophysical properties; numerical model; deformation-strength characteristics
• ISSN: 0191-5665; 1573-8922
• DOI: 10.1007/s11029-019-9782-8

An approach to solving the known problem on determination of the effective physical and mechanical properties of dispersedly filled compositions is presented. The solution is based on the formulation and numerical implementation of boundary-value problems based on the fundamental equations of the theories of elasticity, thermal conductivity, electrostatics, and electrical conductivity. The general concept is to obtain detailed parameters of state of the composition under external actions with account of the real structure of the material. Averaging procedures are used to determine the effective properties of the compositions. The formulation and solution of boundary-value problems, in all cases, is reduced to the formulation of corresponding variational principles and their implementation by the methods of computational mechanics, in particular, by the finite element method. The effective characteristics of the composite under mechanical, thermal, and electromagnetic actions are calculated on the basis of energy considerations: the stored energy of a structurally inhomogeneous body is equal to the energy of a homogeneous comparison body under various actions. A comparison of calculated and experimental values of the effective characteristics attests to the applicability of the models proposed and the methods of their implementation.