Stanisław Jemioło

Orthotropic composite constitutive model of mineral–asphalt mix reinforced with grid and its approximation with an isotropic model

A theoretical model for an elastic anisotropic composite of road mixtures reinforced with grids together with its isotropic approximation is proposed. In the considered models, some elements of the mechanics of fibrous composite materials and optimisation theory are used. A composite model is an energy model; that is, constitutive relationships result from the differentiation of the stored energy function arising from two summed parts corresponding to the matrix and reinforcement grid energy via mixture theory. The obtained model is incorporated into the commercial finite element program ABAQUS via a user subroutine written in Fortran. The correctness of the proposed composite constitutive model has been tested by a numerical solution (with the application of a finite element program) of the structure, in which the matrix is modelled as a three-dimensional continuum region and the reinforcement as working in one dimension a set of truss elements. In addition, in the paper the proposition of approximation of the composite orthotropic model with an isotropic one is presented. The interpretation and application of this approximation are analysed. The energetically equivalent isotropic model for the layer with grid reinforcement can be directly used in standard programs used for designing road pavements with mechanistic methods.

A New Concept of the Non-Associative Plastic Flow

The new concept of a “fuzzy” departure from the associative flow rule is formulated following the basic concept of the classical theory of hardening plasticity. General constitutive relations are derived to describe elastic hardening/softening plastic behaviour. The second law of thermodynamics for plastic deformation is used. As an example, constitutive equations are proposed for a plain concrete under short-term monotonic loading. Only one additional material parameter due to dilatancy is involved. The obtained numerical results are compared to existing experimental evidence. Good agreement has been observed.