Band 24, Heft 3-4

Plastic deformation processes are among the most demanding processes in manufacturing because they lead to different microstructure features in the materials produced. Various dislocation patterns can be induced by plastic strain under different conditions. A serrated yielding/jerky flow in some dilute alloys, such as aluminium-magnesium alloys during plastic deformation, is a well-known phenomenon under certain regimes of strain rate and temperature, as reported in a significant number of works. The serrated features in these materials reflect the so-called Portevin-Le Chatelier effects. These undesirable effects are due to the interaction between solute atoms and mobile dislocation during the plastic deformation, which is known as dynamic strain ageing. There are a significant number of theoretical and numerical investigations that have focused on describing the serrated behaviours of these materials during plastic deformation. Hence, the fundamental objective of this paper is to provide a general review of different constitutive modelling in regards this feature. The typical material models and new constitutive models describing this feature are presented. In addition, applications of the models are provided along with their respective advantages and disadvantages.

A high-order nonlocal continuum beam model is proposed, which can be applied to study the transverse vibrations of double-walled carbon nanotubes (DWCNTs), including those that could have initial deformations due to defects or external actions. A beam element is developed adopting Hermite cubic polynomials as shape functions, and mass and elastic stiffness matrix are presented. The influence of the nonlocal parameter on the vibrational properties of DWCNTs is studied. Using the proposed model, it was found that the nonlocal parameter has a strong influence on the natural frequencies.

Vibrations of micro/nanobeams that are subjected to initial stresses due to mismatch between different materials or thermal stresses are important in some devices. The present study is an attempt to present nonlinear free vibration of simply supported size-dependent functionally graded (FG) nanobeams resting on elastic foundation and under precompressive axial force. It is assumed that the material properties of FG materials are graded in the thickness direction. The partial differential equation of motion, which is simplified into an ordinary differential equation using the Galerkin method, is derived based on Euler-Bernoulli beam theory, von Karman geometric nonlinearity, and Eringen’s nonlocal elasticity theory. The final ordinary differential equation is solved using the variational iteration method. The effects of geometrical parameters, small-scale parameter, elastic coefficient of foundation, precompressive axial force, and neutral axis location on dimensionless nonlinear natural frequencies are investigated. In this study, the buckling and postbuckling behavior of FG nanobeams and the effect of neutral axis location on buckling behavior are investigated as well. Results show that the effects of small scale on FG nanobeam frequencies change with the aspect ratio, the values of radius of gyration, and the values of compressive axial force. It is also found that the influence of neutral axis location on the nonlinear fundamental frequency of prestressed FG nanobeams is more than that of prestressed FG nanobeams resting on elastic foundation.

Plastic deformation of micro- and nanoscale samples differs from macroscopic plasticity in two respects: (i) the flow stress of small samples depends on their size, and (ii) the scatter of plastic deformation behavior increases significantly. In this work, we focus on the scatter of plastic behavior. We statistically characterize the deformation process of micropillars using results from discrete dislocation dynamics (DDD) simulations. We then propose a stochastic microplasticity model that uses the extracted information to make statistical predictions regarding the micropillar stress-strain curves. This model aims to map the complex dynamics of interacting dislocations onto stochastic processes involving the continuum variables of stress and strain. Therefore, it combines a classical continuum description of the elastic-plastic problem with a stochastic description of plastic flow. We compare the model predictions with the underlying DDD simulations and outline potential future applications of the same modeling approach.

A piezoelectric beam model with strain gradient and electric gradient effects is proposed. An energy variational principle with strain, strain gradient, electric field, and electric field gradient considered as independent variables is postulated to develop the governing equations and boundary conditions. Moreover, two strain gradient coefficients and one electric field gradient coefficient are introduced to account for higher order coupling effects of underlying microstructure. Then the bending problem of a cantilever beam is solved to illustrate the theory. It is found that the deflection of the cantilever may depend strongly on the so-introduced gradient effects. As a result of the electromechanical coupling, the generated electric field may also be affected by the strain gradient. However, electric field gradient has a limited effect on the electric field.

This paper introduces constructing convex-relaxed programs for nonconvex optimization problems. Branch-and-bound algorithms are convex-relaxation-based techniques. The convex envelopes are important, as they represent the uniformly best convex underestimators for nonconvex polynomials over some region. The reformulation-linearization technique (RLT) generates linear programming (LP) relaxations of a quadratic problem. RLT operates in two steps: a reformulation step and a linearization (or convexification) step. In the reformulation phase, the constraint and bound inequalities are replaced by new numerous pairwise products of the constraints. In the linearization phase, each distinct quadratic term is replaced by a single new RLT variable. This RLT process produces an LP relaxation. The LP-RLT yieds a lower bound on the global minimum. LMI formulations (linear matrix inequalities) have been proposed to treat efficiently with nonconvex sets. An LMI is equivalent to a system of polynomial inequalities. A semialgebraic convex set describes the system. The feasible sets are spectrahedra with curved faces, contrary to the LP case with polyhedra. Successive LMI relaxations of increasing size yield the global optimum. Nonlinear inequalities are converted to an LMI form using Schur complements. Optimizing a nonconvex polynomial is equivalent to the LP over a convex set. Engineering application interests include system analysis, control theory, combinatorial optimization, statistics, and structural design optimization.