This paper addresses the development of a unified framework for quantifying hysteresis and constitutive nonlinearities inherent to ferroelectric, ferromagnetic and ferroelastic materials. Because the mechanisms which produce hysteresis vary substantially at the microscopic level, it is more natural to initiate model development at the mesoscopic, or lattice, level where the materials share comm...

We consider a dichotomy for analytic families of trees stating that either there is a colouring of the nodes for which all but finitely many levels of every tree are nonhomogeneous, or else the family contains an uncountable antichain. This dichotomy implies that every nontrivial Souslin poset satisfying the countable chain condition adds a splitting real. We then reduce the dichotomy to a conj...

By virtue of its complexity, realistic approaches to describe diffusion in cellular media require the employment of computational methods. Among others, this type of studies has shown that the apparent diffusion coefficient of a macromolecular solute through a cytoplasmic-like medium exhibits a power-law dependence with the excluded volume. Power laws are ubiquitous findings in diverse systems,...

Motivated by sawmill production planning, this paper investigates multi-period, multi-product (MPMP) production planning in a manufacturing environment with nonhomogeneous raw materials, and consequently random processes yields. A two-stage stochastic linear program with recourse is proposed to address the problem. The random yields are modeled as scenarios with stationary probability distribut...

We mathematically justify a reduced piezoelectric plate model. This is achieved considering the three-dimensional static equations of piezoelectricity, for a nonhomogeneous anisotropic thin plate, and using the asymptotic analysis to compute the limit of the displacement vector and electric potential, as the thickness of the plate approaches zero. We prove that the three-dimensional displacemen...

In a system with hysteresis, the system response lags the excitation [16, 21] — for any excitation [10]. Hysteretic behavior is commonly depicted as loops in graphs (2D plots) of periodic (oscillatory) output vs. periodic input. In rate-dependent hysteresis, the size and shape of the hysteresis loop changes with the rate or frequency of the input. If the loop collapses to a function (e.g., a cu...

The problem of damping representation and measurement is investigated. Among the many parameters found in literature, the most comprehensive is loss factor 'l· Several definitions of '7 are feasible, but in linear problems they all should reduce to the ratio of the in-phase and quadrature parts of the associated complex modulus. This work surveys measuring methods for materials and structures w...

Thermoelastic simulation of functionally graded materials is practically important for engineers. Here, the extension and assembly of our two previous papers (Computational Mechanics 2006, 38, p51-60; Engineering Analysis with Boundary Elements 2008, 32, p704-712) is presented to evaluate the transient temperature and stress distributions in two-dimensional functionally graded solids. In this c...