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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 this contribution, a computational framework for the analysis of tertiary concrete creep is presented, combining a discrete element framework with linear visco-elasticity and rate-dependency of crack opening. The well-established Lattice Discrete Particle Model (LDPM) serves as constitutive model. Aging visco-elasticity is implemented based on the Micro-Prestress-Solidification (MPS) theory, linking the mechanical response to the underlying physical and chemical processes of hydration, heat transfer and moisture transport through a multi-physics approach. The numerical framework is calibrated on literature data, which include tensile and compressive creep tests, and tests at various loading rates. Afterwards, the framework is validated on time-to-failure tests, both for flexure and compression. It is shown that the numerical framework is capable of predicting the time-dependent evolution of concrete creep deformations in the primary, secondary but also tertiary domains, including very accurate estimates of times to failure. Finally, a predictive numerical study on the time-to-failure response is presented for load levels that can not be experimentally tested, showing a deviation from the simple linear trend that is

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.