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Summary: Partial differential equations having diffusive, convective, and reactive terms appear in the modeling of a large variety of processes in several branches of science. Often, several species or components interact with each other, rendering strongly coupled systems of convection‐diffusion‐reaction equations. Exact solutions are available in extremely few cases lacking practical interest due to the simplifications made to render such equations amenable by analytical tools. Then, numerical approximation remains the best strategy for solving these problems. The properties of these systems of equations, particularly the lack of sufficient physical diffusion, cause most traditional numerical methods to fail, with the appearance of violent and nonphysical oscillations, even for the single equation case. For systems of equations, the situation is even harder due to the lack of fundamental principles guiding numerical discretization. Therefore, strategies must be developed in order to obtain physically meaningful and numerically stable approximations. Such stabilization techniques have been extensively developed for the single equation case in contrast to the multiple equations case. This paper presents a perturbation‐based stabilization technique for coupled systems of one‐dimensional convection‐diffusion‐reaction equations. Its characteristics are discussed, providing evidence of its versatility and effectiveness through a thorough assessment. [ABSTRACT FROM AUTHOR]

Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the finite element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency results from handling the kernel of this equation by the fast Fourier transform (FFT). However, the kernel is derived from an auxiliary homogeneous linear problem, which renders the extension of FFT-based schemes to nonlinear problems conceptually difficult. This paper aims to establish a link between FE-based and FFT-based methods in order to develop a solver applicable to general history-dependent and time-dependent material models. For this purpose, we follow the standard steps of the FE method, starting from the weak form, proceeding to the Galerkin discretization and the numerical quadrature, up to the solution of nonlinear equilibrium equations by an iterative Newton-Krylov solver. No auxiliary linear problem is thus needed. By analyzing a two-phase laminate with nonlinear elastic, elastoplastic, and viscoplastic phases and by elastoplastic simulations of a dual-phase steel microstructure, we demonstrate that the solver exhibits robust convergence. These results are achieved by re-using the nonlinear FE technology, with the potential of further extensions beyond small-strain inelasticity considered in this paper. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

A novel adaptive isogeometric digital height correlation (DHC) technique has been developed in which the set of shape functions, needed for discretization of the ill-posed DHC problem, is autonomously optimized for each specific set of profilometric height images, without a priori knowledge of the kinematics of the experiment. To this end, an adaptive refinement scheme is implemented, which refines the shape functions in a hierarchical manner. This technique ensures local refinement, only in the areas where needed, which is beneficial for the noise robustness of the DHC problem. The main advantage of the method is that it can be applied in experiments where the deformation mechanisms are unknown in advance, thereby complicating the choice of suitable shape functions. The method is applied to a virtual experiment in order to provide a proof of concept. A second virtual experiment is executed with stretchable electronics interconnects, which entail localized buckles upon deformation with complex kinematics. In both cases, accurate results were obtained, demonstrating the beneficial aspects of the proposed method. Moreover, the technique performance on profilometric images of a real experiment with stretchable interconnects was demonstrated. [ABSTRACT FROM AUTHOR]

ABSTRACT In this article, the thermo-mechanical time-dependent behavior of oriented polyethylene terephthalate (PET) films, which are used as a substrate material for flexible Organic Light-Emitting Diode (OLED)s, is analyzed. These films are subjected to conditions that are representative for the industrial manufacturing process. Effects of creep and thermal shrinkage are experimentally observed simultaneously. The aim of the article is to demonstrate the ability of the micromechanically-based model, which was previously used to separately describe both creep and thermal shrinkage of the polyethylene terephthalate film, to simulate experimentally observed anisotropic behavior of the film under complex loading conditions. This anisotropic behavior results from the microstructure, the internal stress state, and differences in constitutive behavior of the phases. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016, 133, 43384. [ABSTRACT FROM AUTHOR]

In digital image correlation (DIC), the unknown displacement field is typically identified by minimizing the linearized form of the brightness conservation equation, while the minimization scheme also involves a linearization, yielding a two-step linearization with four implicit assumptions. These assumptions become apparent by minimizing the non-linear brightness conservation equation in a consistent mathematical setting, yielding a one-step linearization allowing a thorough study of the DIC tangent operator. Through this analysis, eight different image gradient operators are defined, and the impact of these alternative image gradients on the accuracy, efficiency, and initial guess robustness is discussed on the basis of a number of academic examples and representative test cases. The main conclusion is that for most cases, the image gradient most common in literature is recommended, except for cases with: (1) large rotations; (2) initial guess instabilities; and (3) costly iterations due to other reasons (e.g., integrated DIC), where a large deformation corrected mixed gradient is recommended instead. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper discusses a method that provides the direct identification of constitutive model parameters by intimately integrating the finite element method (FEM) with digital image correlation (DIC), namely, directly connecting the experimentally obtained images for all time increments to the unknown material parameters. The problem is formulated as a single minimization problem that incorporates all the experimental data. It allows for precise specification of the unknowns, which can be, but are not limited to, the unknown material properties. The tight integration between FEM and DIC enables for identification while providing necessary regularization of the DIC procedure, making the method robust and noise insensitive. Through this approach, the versatility of the FE method is extended to the experimental realm, enhancing the analyses of existing experiments and opening new experimental opportunities. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The aim of this paper is to propose a continuous-discontinuous computational homogenization-localization framework to upscale microscale localization toward the onset and propagation of a cohesive discontinuity at the macroscale. The major novelty of this contribution is the development of a fully coupled micro-macro solution strategy, where the solution procedure for the macroscopic domain is based on the extended finite element method. The proposed approach departs from classical computational homogenization, which allows to derive the effective stress-strain response before the onset of localization. Upon strain localization, the microscale is characterized by a strain localization band where damage grows and by two adjacent unloading bulk regions at each side of the localization zone. The microscale localization band is lumped into a macroscopic cohesive crack, accommodated through discontinuity enriched macroscale kinematics. The governing response of the continuum with a discontinuity is obtained numerically based on proper scale transition relations in terms of the traction-separation law and the stress-strain description of the continuous surrounding material at both sides of the discontinuity. The potential of the method is demonstrated with a numerical example, which illustrates the onset and propagation of a macroscale cohesive crack emerging from microstructural damage within the underlying microstructure. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]