Analysis of cracked general cross-ply laminates under general bending loads: A variational approach

A novel variational model is developed that can predict the stress transfer between plies in cracked general cross-ply laminates subject to general in-plane (Nxx, Nyy, Nxy) and out-of-plane bending (Mxx, Myy, Mxy) loading. The effects of thermal residual stresses are taken into account. Admissible stress systems, which satisfy equilibrium and all boundary and interface conditions, are constructed and the principle of minimum complementary energy is employed to find the optimal solution. The approach yields rigorous lower bounds for stiffness matrices. A methodology based on Levin's theorem is developed to evaluate the effective thermal expansion coefficients of non-symmetric cracked laminates. A ply-refinement technique is used in order that through-thickness variations of the stress components can be precisely taken into account. It is found that the developed method, when used in conjunction with ply refinement technique, results in stress fields and thermo-mechanical properties comparable in accuracy to refined finite and boundary element solutions.

Micromechanical Background of Random Structure Thermoperistatic Composites

In contrast to the classical local and nonlocal theories, the peridynamic equation of motion introduced by Silling (J. Mech. Phys. Solids 2000; 48: 175–209) is free of any spatial derivatives of displacement. The new general integral equations (GIE) connecting the displacement fields in the point being considered and the surrounding points of random structure composite materials (CMs) is proposed. For statistically homogemneous thermoperistatic media subjected to homogeneous volumetric boundary loading, one proved that the effective behaviour of this media is governing by conventional effective constitutive equation which is intrinsic to the local thermoelasticity theory. It was made by the most exploitation of the popular tools and concepts used in conventional thermoelasticity of CMs and adapted to thermoperistatics. The general results establishing the links between the effective properties (effective elastic moduli, effective thermal expansion) and the corresponding mechanical and transformation influence functions are obtained by the use of decomposition of local fields into the load and residual fields similarly to the locally elastic CMs. This similarity opens a way for straightforward expansion of analytical micromechanics tools for locally elastic CMs to the new area of random structure peridynamic CMs. Detailed numerical examples for 1D case are considered.

Thermal Expansion Coefficient Prediction of Asphalt Mixture with the Eshelby Equivalent Inclusion Theory

Asphalt mixture was considered as a two-phase composite, in which coarse aggregates are embedded into asphalt mastic matrix, namely a mix of fine aggregates and asphalt, so that a theoretical framework was proposed to correlate its effective thermal expansion coefficient with its components and microstructures based on the Eshelby equivalent inclusion theory. A four-parameter model with the experimentally determined parameters was used to characterize the viscoelastic constitutive behavior of asphalt mastic. The thermal expansion coefficient prediction of asphalt mixture was conducted and compared with the predictions by the sparse method and the self-consistent method. It was revealed that the prediction from the proposed theoretical framework is reasonable.