The purpose of this paper is to present a simple micromechanics-based model to estimate the effective thermal conductivity of macroscopically isotropic materials of matrix-inclusion type. The methodology is based on the well-established Mori-Tanaka method for composite media reinforced with ellipsoidal inclusions, extended to account for imperfect thermal contact at the matrix-inclusion interface, random orientation of particles and particle size distribution. Using simple ensemble averaging arguments, we show that the Mori-Tanaka relations are still applicable for these complex systems, provided that the inclusion conductivity is appropriately modified. Such conclusion is supported by the verification of the model against a detailed finite-element study as well as its validation against experimental data for a wide range of engineering material systems.

Most commercial finite-element programs use the Jaumann (or co-rotational) rate of Cauchy stress in their incremental (Riks) updated Lagrangian loading procedure. This rate was shown long ago not to be work-conjugate with the Hencky (logarithmic) finite strain tensor used in these programs, nor with any other finite strain tensor. The lack of work-conjugacy has been either overlooked or believed to cause only negligible errors. Presented are examples of indentation of a naval-type sandwich plate with a polymeric foam core, in which the error can reach 28.8 per cent in the load and 15.3 per cent in the work of load (relative to uncorrected results). Generally, similar errors must be expected for all highly compressible materials, such as metallic and ceramic foams, honeycomb, loess, silt, organic soils, pumice, tuff, osteoporotic bone, light wood, carton and various biological tissues. It is shown that a previously derived equation relating the tangential moduli tensors associated with the Jaumann rates of Cauchy and Kirchhoff stresses can be used in the user’s material subroutine of a black-box commercial program to cancel the error due to the lack of work-conjugacy and make the program perform exactly as if the Jaumann rate of Kirchhoff stress, which is work-conjugate, were used.

In recent years, post-installed anchors are widely used to connect structural members and to fix appliances to load-bearing elements. A bonded anchor typically denotes a threaded bar placed into a borehole filled with adhesive mortar. The high complexity of the problem, owing to the multiple materials and failure mechanisms involved, requires a numerical support for the experimental investigation. A reliable model able to reproduce a system’s short-term behavior is needed before the development of a more complex framework for the subsequent investigation of the lifetime of fasteners subjected to various deterioration processes can commence. The focus of this contribution is the development and validation of such a model for bonded anchors under pure tension load. Compression, modulus, fracture and splitting tests are performed on standard concrete specimens. These serve for the calibration and validation of the concrete constitutive model. The behavior of the adhesive mortar layer is modeled with a stress-slip law, calibrated on a set of confined pull-out tests. The model validation is performed on tests with different configurations comparing load-displacement curves, crack patterns and concrete cone shapes. A model sensitivity analysis and the evaluation of the bond stress and slippage along the anchor complete the study.