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Abstract Fast computation of demagnetization curves is essential for the computational design of soft magnetic sensors or permanent magnet materials. We show that a sparse preconditioner for a nonlinear conjugate gradient energy minimizer can lead to a speed up by a factor of 3 and 7 for computing hysteresis in soft magnetic and hard magnetic materials, respectively. As a preconditioner an approximation of the Hessian of the Lagrangian is used, which only takes local field terms into account. Preconditioning requires a few additional sparse matrix vector multiplications per iteration of the nonlinear conjugate gradient method, which is used for minimizing the energy for a given external field. The time to solution for computing the demagnetization curve scales almost linearly with problem size. [ABSTRACT FROM AUTHOR]

The present paper demonstrates how a natural crack mosaic resembling a random tessellation evolves with repeated 'wetting followed by drying' cycles. The natural system here is a crack network in a drying colloidal material, for example, a layer of mud. A spring network model is used to simulate consecutive wetting and drying cycles in mud layers until the crack mosaic matures. The simulated results compare favourably with reported experimental findings. The evolution of these crack mosaics has been mapped as a trajectory of a 4-vector tuple in a geometry-topology domain. A phenomenological relation between energy and crack geometry as functions of time cycles is proposed based on principles of crack mechanics. We follow the crack pattern evolution to find that the pattern veers towards a Voronoi mosaic in order to minimize the system energy. Some examples of static crack mosaics in nature have also been explored to verify if nature prefers Voronoi patterns. In this context, the authors define new geometric measures of Voronoi-ness of crack mosaics to quantify how close a tessellation is to a Voronoi tessellation, or even, to a Centroidal Voronoi tessellation. • Simulation of evolution of crack mosaics in mud due to wetting–drying cycles. • Spring network model is based on principles of fracture mechanics. • Crack junctions evolve from T to Y junctions with time cycles. • Energy minimization is shown at crack maturation. • Show that natural complex networks prefer Voronoi diagrams at equilibrium. [ABSTRACT FROM AUTHOR]

This paper deals with the thermomechanical coupling in dissipative materials. The focus lies on finite strain plasticity theory and the temperature increase resulting from plastic deformation. For this type of problem, two fundamentally different modeling approaches can be found in the literature: (a) models based on thermodynamical considerations and (b) models based on the so-called Taylor–Quinney factor . While a naive straightforward implementation of thermodynamically consistent approaches usually leads to an over-prediction of the temperature increase due to plastic deformation, models relying on the Taylor–Quinney factor often violate fundamental physical principles such as the first and the second law of thermodynamics. In this paper, a thermodynamically consistent framework is elaborated which indeed allows the realistic prediction of the temperature evolution. In contrast to previously proposed frameworks, it is based on a fully three-dimensional, finite strain setting and it naturally covers coupled isotropic and kinematic hardening — also based on non-associative evolution equations. Considering a variationally consistent description based on incremental energy minimization, it is shown that the aforementioned problem (thermodynamical consistency and a realistic temperature prediction) is essentially equivalent to correctly defining the decomposition of the total energy into stored and dissipative parts. Interestingly, this decomposition shows strong analogies to the Taylor–Quinney factor. In this respect, the Taylor–Quinney factor can be well motivated from a physical point of view. Furthermore, certain intervals for this factor can be derived in order to guarantee that fundamental physically principles are fulfilled a priori. Representative examples demonstrate the predictive capabilities of the final constitutive modeling framework. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fast local image inpainting algorithm based on the Allen–Cahn model. The proposed algorithm is applied only on the inpainting domain and has two features. The first feature is that the pixel values in the inpainting domain are obtained by curvature-driven diffusions and utilizing the image information from the outside of the inpainting region. The second feature is that the pixel values outside of the inpainting region are the same as those in the original input image since we do not compute the outside of the inpainting region. Thus the proposed method is computationally efficient. We split the governing equation into one linear equation and one nonlinear equation by using an operator splitting technique. The linear equation is discretized by using a fully implicit scheme and the nonlinear equation is solved analytically. We prove the unconditional stability of the proposed scheme. To demonstrate the robustness and accuracy of the proposed method, various numerical results on real and synthetic images are presented. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the analysis of homogenization assumptions within phase field theories in a finite strain setting. Such homogenization assumptions define the average bulk׳s energy within the diffusive interface region where more than one phase co-exist. From a physical point of view, a correct computation of these energies is essential, since they define the driving force of material interfaces between different phases. The three homogenization assumptions considered in this paper are: (a) Voigt/Taylor model, (b) Reuss/Sachs model, and (c) Khachaturyan model. It is shown that these assumptions indeed share some similarities and sometimes lead to the same results. However, they are not equivalent. Only two of them allow the computation of the individual energies of the co-existing phases even within the aforementioned diffusive interface region: the Voigt/Taylor and the Reuss/Sachs model. Such a localization of the averaged energy is important in order to determine and to subsequently interpret the driving force at the interface. Since the Voigt/Taylor and the Reuss/Sachs model are known to be relatively restrictive in terms of kinematics (Voigt/Taylor) and linear momentum (Reuss/Sachs), a novel homogenization approach is advocated. Within a variational setting based on (incremental) energy minimization, the results predicted by the novel approach are bounded by those corresponding to the Voigt/Taylor and the Reuss/Sachs model. The new approach fulfills equilibrium at material interfaces (continuity of the stress vector) and it is kinematically compatible. In sharp contrast to existing approaches, it naturally defines the mismatch energy at incoherent material interfaces. From a mathematical point of view, it can be interpreted as a partial rank-one convexification. [Copyright &y& Elsevier]

Abstract: This paper addresses the theoretical prediction of the quasiconvex hull of energy-minimizing (or stress-free) strains that can be realized by martensitic microstructure. Polyconvexification and related notions are used to derive some upper bounds (in the sense of inclusion) on the quasiconvex hull. Lower bounds are obtained from lamination techniques. The geometrically linear setting (infinitesimal strains) is considered in the present Part 2. Three-, four-, and twelve-well problems are considered. In particular, the structure of the set of energy-minimizing strains in cubic to monoclinic transformations is investigated in detail. That investigation is notably supported by three-dimensional vizualisations obtained by considering four-well restrictions. [Copyright &y& Elsevier]

Near/sub-threshold operation is promising to achieve energy minimization when high performance is not required. The device sizing in sub-threshold region is different from super-threshold region due to significantly different IV characteristics and impact of parasitic effects in these two regions. We have investigated the impact of the inverse narrow width effect (INWE) on transistor drain current in the near/sub-threshold region at three different technology nodes (90 nm, 65 nm, and 40 nm) and proposed an INWE-aware sub-threshold device sizing method to mitigate the impact of INWE to reduce delay, power consumption and area. We applied the proposed device sizing method to designing an INWE-aware standard cell library and achieved up to 20% less delay, 34% less power consumption and 47% less area, compared with the sub-threshold library designed using conventional sizing method. For further optimization, we proposed a dual-width library by combining the INWE-aware library and the minimum sized library. A near-threshold baseband processor designed with the dual width library achieved a total power consumption of ~ 4 μW with 6 MHz at 0.5 V, which is 30% better than the counterpart design. [ABSTRACT FROM PUBLISHER]

Abstract: We introduce and study a variational model for the formation of patterns induced by bringing the surface of a rigid plate into contact proximity with the surface of a polymeric film strongly bonded to a substrate. We treat the film as a homogeneous, isotropic, hyperelastic solid and account for both attractive and repulsive van der Waals interactions between the film surface and the proximate contractor. Aside from confirming the intuitive expectation that the presence of a repulsive contribution to the van der Waals potential should stabilize patterns that form on the film surface, we elucidate the role of repulsive interactions at the onset of instability. For a recently proposed van der Waals potential involving two parameters, the Hamaker constant A and the equilibrium spacing , our results include estimates for the critical gap at which undulations appear on the film surface, the corresponding wavenumber of the undulations, and a lower bound for the attractive force needed to induce the undulations. To leading order, , , and , where h and μ denote the thickness and infinitesimal shear modulus of the film. Correction terms due to repulsive interactions indicate that, while may be influenced by and A, may also be influenced by . Granted knowledge of and A, our results also suggest a simple experimental protocol for determining . [Copyright &y& Elsevier]

Abstract: This paper offers a treatment for investigating the role of the interplay between mechanics and the absorption of a swelling agent on the equilibrium and cavitation of a spherical specimen. This treatment is then applied, within the context of the classical theory of swelling of a rubber by a liquid, to establish, among other things, necessary conditions for the existence of multiphase equilibria and the occurrence of cavitation. These conditions involve the parameters entering the theory, namely the number c S of polymer chains per unit reference volume, the volume occupied by a swelling-agent molecule, and the Flory–Huggins interaction parameter . [Copyright &y& Elsevier]

Abstract: A novel class of cohesive constitutive models suitable for the analysis of material separation such as that related to cracks, shear bands or delamination processes is presented. The proposed framework is based on a geometrically exact description (finite deformation) and it naturally accounts for material anisotropies. For that purpose, a Helmholtz energy depending on evolving structural tensors is introduced. In sharp contrast to previously published anisotropic cohesive models with finite strain kinematics based on a spatial description, all models belonging to the advocated class are thermodynamically consistent, i.e., they are rigorously derived by applying the Coleman and Noll procedure. Although this procedure seems nowadays to be standard for stress–strain-type constitutive laws, this is not the case for cohesive models at finite strains. An interesting new finding from the Coleman and Noll procedure is the striking analogy between cohesive models and boundary potential energies. This analogy gives rise to the introduction of additional stress tensors which can be interpreted as deformational surface shear. To the best knowledge of the authors, those stresses which are required for thermodynamical consistency at finite strains, have not been taken into account in existing models yet. Furthermore, the additional stress tensors can result in an effective traction-separation law showing a non-trivial stress-free configuration consistent with the underlying Helmholtz energy. This configuration is not predicted by previous models. Finally, the analogy between cohesive models and boundary potential energies leads to a unique definition of the controversially discussed fictitious intermediate configuration. More precisely, traction continuity requires that the interface geometry with respect to the deformed configuration has to be taken as the average of both sides. It will be shown that the novel class of interface models does not only fulfill the second law of thermodynamics, but also it shows an even stronger variational structure, i.e., the admissible states implied by the novel model can be interpreted as stable energy minimizers. This variational structure is used for deriving a variationally consistent numerical implementation. [Copyright &y& Elsevier]

This paper examines the engineered domain configurations and the macroscopic properties of ferroelectric crystals using an energy minimization theory. The energy minimizing domain configurations have been constructed, and their macroscopic properties have been calculated and compared well with experiments. The optimal domain configurations have also been identified. [Copyright &y& Elsevier]

The present work is concerned with the formulation of a continuum theory of viral DNA packaging based on a director field representation of the encapsidated DNA. The point values of the director field give the local direction and density of the DNA. The continuity of the DNA strand requires that the director field be divergence-free and tangent to the capsid wall. The energy of the DNA is defined as a functional of the director field which accounts for bending, torsion, and for electrostatic interactions through a density-dependent cohesive energy. The operative principle which determines the encapsidated DNA conformation is assumed to be energy minimization. We show that torsionless toroidal solenoids, consisting of planar coils contained within meridional planes and wrapped around a spool core, and fine mixtures of the solenoid and spool phase, beat the inverse spool construction. [Copyright &y& Elsevier]