STABILITY CONSIDERATIONS FOR ELASTIC-PLASTIC PROCESSES WITH DAMAGE

Classical theory of plasticity is fairly complete with flow rules, convexity of yield surfaces, extremum principles, and the uniqueness theorem. For the strain-hardening plasticity, Drucker’s postulates are established and proven based on the plastic-work and energy principles. Plasticity models have been further applied to heterogeneous and cementitious materials with certain degrees of success. In this paper, the stability statements of strain-hardening and strain-softening processes in concrete are examined by utilizing thermodynamic potential functions in the stress space and by applying Euler’s theorem of homogenous functions. It is shown that by specifying a strain-hardening parameter to account for the plastic strains and a damage parameter to represent the effect of microcracking, the dissipation inequality can be used to establish the Drucker’s stability postulate for the plastic flow within the framework of the internal variable theory of thermodynamics. Using the same approach and assuming uncoupling between plastic flow and microcracking, the formation leads to a softening stability statement for damage processes in concrete.

IMPROVEMENT OF CROSS SECTION OF COMPRESSED ELEMENTS BY TOPOLOGICAL RATIONALIZATION

The article describes the procedure of direct (rational) design of vertical compressed elements (columns, pylons, stiffening diaphragms, retaining walls). This technology is an exclusive modification of topological (bionic) rationalization. It is based on new energy principles and algorithms for sequential construction of geometric and / or physical-mechanical "image" of the structure. The example of the formation of energy-equivalent columns shows the sequence of computational operations of the method. The solution is built analytically in order to show the nuances of the necessary operations. At the same time, these examples show that the introduced optimization criteria in the form of en → const and U → inf U (here en is the value of the normalized density of potential deformation energy, and U is the potential energy of deformation) determine, including the minimum volume of constructs, as well as their minimum deflections. A fundamental element of the approach is the use of a new criterion of the limit state, which provides an estimate of the intensity of the element. In this case, the properties of the material and the type of stress-strain state are taken into account. The obtained analytical solution was used as a control test for the general computational procedure of the method. In this regard, the article presents the results of the analytical and numerical solution. The efficiency of the computational procedure is confirmed by the speed of its convergence and the minimum difference of geometric parameters (topology) of the structure with test examples. The technological sequence of computational operations of the method is completed by the construction of elements (pylons) with a simple external and complex internal geometry. Keywords: deformation, energy, iteration, voids, cavity, rationalization.

Minimum energy bounds on longitudinal elastic constants of transversely isotropic unidirectional composites

We consider the n -component transversely isotropic unidirectional elastic composites, the longitudinal axis of which is parallel to those of the transversely isotropic components as well as the generators of the cylindrical phase boundaries between them. From the minimum energy and complementary energy principles, with appropriate constant strain and piece-wise constant stress trial fields, optimization and iteration techniques, a set of bounds for the macroscopic (effective) longitudinal elastic constants of the composites (including the simple lower arithmetic average estimate for longitudinal Young modulus E eff ≥ E V ) are constructed. Numerical examples are provided to illustrate the obtained results.

The multicultural mind as an epistemological test and extension for the thinking through other minds approach

The multicultural experience (i.e., multicultural individuals and cross-cultural experiences) offers the intriguing possibility for (i) an empirical examination of how free-energy principles explain dynamic cultural behaviors and pragmatic cultural phenomena and (ii) a challenging but decisive test of thinking through other minds (TTOM) predictions. We highlight that TTOM needs to treat individuals as active cultural agents instead of passive learners.