An implicit integration scheme with consistent tangent modulus for Leblond’s model of transformation-induced plasticity in steels

Thermomechanical treatments involving solid-state phase transformations play an important role for the manufacturing of functional and reliable components in many engineering applications. Accordingly, numerical investigation and optimization of such processes require considering thermoelastoplasticity under the influence of ongoing transformations and in particular the impact of transformation-induced plasticity (TRIP). While a number of elaborate plasticity models have been proposed for the description of TRIP, none of them seem to have received much prevalence in applications due to their complexity or hard to determine model parameters. Instead, the overwhelming majority of applied research either relies on simplistic formulations dating back to early phenomenological approaches or neglects TRIP altogether. In this work, we therefore provide an accessible, straightforward and easy-to-implement solution scheme for the TRIP model proposed by Leblond et al. which, despite being widely recognized, is hardly ever employed in full form. Specifically, we employ implicit backward-Euler integration and an elastic–plastic operator split approach to update the stresses in order to obtain a simple and concise algorithm for which we then derive the corresponding consistent tangent modulus. Furthermore, the work contains an application of the solution scheme to a symmetrically cooled plate and an in-depth discussion of the influence of TRIP by means of this tractable numerical example. Specifically, we highlight the discrepancies arising in transient and residual stresses and strains compared to the conventional $$J_2$$ J 2 -plasticity approach where the phase transformation is accounted for merely by adapting the yield strength of the compound.

Acquisition of Abstract Knowledge in Implicit Learning of Anagram Solution Scheme

The article addresses the problem of unconscious gaining of abstract knowledge. Participants solved circular 5-letter anagram arranged by the same invariant scheme. The learned schematic invariant is not perceptive, contrary to the usual invariant acquisition technique in other studies. The possibility of implicit learning of a solution scheme is discussed. Efficiency of anagram solving is compared between the groups with constant or changed solution scheme during the test stage. The change of the solution scheme leads to a decrease of efficiency, i.e. to the lower number of the solved anagrams. The results support the possibility of gaining unconscious abstract knowledge concerning the scheme without any perceptual invariant component. Possible use of a similar stimulus material in studies of interaction between visual and verbal components of working memory is briefly discussed.

An Inverse Problem Solution Scheme for Solving the Optimization Problem of Drug-Controlled Release from Multilaminated Devices

The optimization problem of drug release based on the multilaminated drug-controlled release devices has been solved in this paper under the inverse problem solution scheme. From the viewpoint of inverse problem, the solution of optimization problem can be regarded as the solution problem of a Fredholm integral equation of first kind. The solution of the Fredholm integral equation of first kind is a well-known ill-posed problem. In order to solve the severe ill-posedness, a modified regularization method is presented based on the Tikhonov regularization method and the truncated singular value decomposition method. The convergence analysis of the modified regularization method is also given. The optimization results of the initial drug concentration distribution obtained by the modified regularization method demonstrate that the inverse problem solution scheme proposed in this paper has the advantages of the numerical accuracy and antinoise property.