The mixed finite element method for the quasi‐static and dynamic analysis of viscoelastic timoshenko beams

The quasi‐static and dynamic responses of a linear viscoelastic Timoshenko beam on Winkler foundation are studied numerically by using the hybrid Laplace–Carson and finite element method. In this analysis the field equation for viscoelastic material is used. In the transformed Laplace–Carson space two new functionals have been constructed for viscoelastic Timoshenko beams through a systematic procedure based on the Gâteaux differential. These functionals have six and two independent variables respectively. Two mixed finite element formulations are obtained; TB12 and TB4. For the inverse transform Schapery and Fourier methods are used. The numerical results for quasi‐static and dynamic responses of several visco‐elastic models are presented. Copyright © 1999 John Wiley & Sons, Ltd.     

Computational visco‐plasticity for kinematically constrained crystals

Crystals possessing less than five independent slip systems cannot undergo any arbitrary isochoric deformation. For these kinematically deficient crystal structures, besides incompressibility, extra constraints need to be taken into account. A visco‐plastic constitutive model, based on crystallographic slip, is formulated for these materials, incorporating the kinematic deficiency. A finite element formulation is presented that enforces these kinematic restrictions by an approximate weighting method. The procedure is applicable for large deformations. The orientation of the crystal lattice is incrementally updated. The formulation is applied to a fictitious two‐dimensional analogon of a kinematically constrained crystal. Copyright © 2000 John Wiley & Sons, Ltd.     

Fractional visco‐elastic Timoshenko beam deflection via single equation

This paper deals with the response determination of a visco‐elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco‐elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace‐transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letnikov approximation of the fractional derivative. Moreover, Timoshenko beam response is generally evaluated by solving a couple of differential equations. In this paper, expressing the equation of the elastic curve just through a single relation, a more general procedure, which allows the determination of the beam response for any load condition and type of constraints, is developed. Copyright © 2015 John Wiley & Sons, Ltd.     

Eulerian elasto‐visco‐plastic formulations for residual stress prediction

A stabilized, Galerkin finite element formulation for modeling the elasto‐visco‐plastic response of quasi‐steady‐state processes, such as welding, laser surfacing, rolling and extrusion, is presented in an Eulerian frame. The mixed formulation consists of four field variables, such as velocity, stress, deformation gradient and internal variable, which is used to describe the evolution of the material's resistance to plastic flow. The streamline upwind Petrov–Galerkin method is used to eliminate spurious oscillations, which may be caused by the convection‐type of stress, deformation gradient and internal variable evolution equations. A progressive solution strategy is introduced to improve the convergence of the Newton–Raphson solution procedure. Two two‐dimensional numerical examples are implemented to verify the accuracy of the Eulerian formulation. Copyright © 2008 John Wiley & Sons, Ltd.     

Efficient numerical implementation of pressure,time, and temperature superposition for elasto‐visco‐plastic material model by using a symbolic approach

This article is concerned with the finite element implementation of an elasto‐visco‐plastic constitutive model using a symbolic approach. The model combines the Knauss–Emri (KE) pressure, temperature, and time superposition principle in the implicit finite element scheme. The equation development and code generation was performed using the symbolic tool AceGen. The same symbolic system was applied to derive analytical sensitivities of the numerical model with respect to the material and shape parameters. To enable efficient numerical implementation of the KE model the convolution integrals were transformed into their respective incremental forms, so that radical improvements of code efficiency and computer storage requirements were achieved. The numerical examples derived for polyethylene terephthalate (PET) polymers demonstrate that symbolic systems can be applied to develop complex constitutive models capable of simulating material responses that are in good agreement with experimental measurements over a wide range of strain rates, temperatures, and loading conditions. Copyright © 2010 John Wiley & Sons, Ltd.     

Modeling of creep and stress relaxation of the nickel‐base alloy NiCr20TiAl at isothermal and non‐isothermal loading conditions

The design and dimensioning of new as well as the assessment of operating high‐temperature components in service require a precise prediction of creep and stress relaxation. The increasing share of renewable energies forces fossil‐fired power plants for increasing numbers of start‐ups and shut‐downs. Consequently, transient loading conditions need to be taken into account. In order to meet this demand, non‐isothermal creep equations are necessary, which enables a consistent prediction of creep strain and stress relaxation in a wide range of temperatures and stresses. In this paper, an approach for the visco‐plastic modeling of creep and stress relaxation for non‐isothermal loading conditions is presented. The strain portions creep, “negative creep” and initial plasticity, occurring at elevated temperatures are described by temperature‐dependent phenomenological equations. Within this paper, the adjustment of the parameters is based on a wide database of hot tensile tests, creep and annealing experiments. The nickel‐base alloy NiCr20TiAl has been examined in a temperature range from 450 °C to 650 °C. The developed material models have been successfully validated with isothermal and non‐isothermal relaxation experiments. Further, the recalculation of a staged relaxation test demonstrates the capability of the defined material laws in a wide stress range under isothermal and non‐isothermal loading conditions.     

A numerical model for the time‐dependent cracking of cementitious materials

A unified finite element formulation is presented for the analysis of the time‐dependent cracking of cementitious materials. The rate‐type constitutive law incorporates linear visco‐elasticity and continuum plasticity. The former accounts for the bulk creep via a Maxwell chain, while the latter describes crack initiation and propagation via a softening, anisotropic Rankine yield criterion. The rate dependence of bond ruptures leading to fracture is accounted for by considering the viscosity of the cracking process. This contribution to the cracking resistance also regularises the localisation process. It is demonstrated how other important phenomena in cementitious materials, such as stress‐dependent hygral and thermal shrinkage, can be incorporated into the computational framework. Copyright © 2001 John Wiley & Sons, Ltd.     

Finite elements in space and time for the analysis of generalised visco‐elastic materials

Numerical analysis of linear visco‐elastic materials requires robust and stable methods to integrate partial differential equations in both space and time. In this paper, symmetric space–time finite element operators are derived for the first time for elementary linear elastic spring and linear viscous dashpot. These can thereafter be assembled in parallel and in series to simulate an arbitrarily complex linear visco‐elastic behaviour. The flexibility of the proposed method allows the formulation of the behaviour, which closely reflects physical processes. An efficient algorithm is proposed to use the generated elementary matrices in a way that is comparable with finite difference schemes, in terms of both processor and memory costs. This unconditionally stable and convergent procedure is equally valid for space domains in which geometry or material properties evolve with time. Copyright © 2013 John Wiley & Sons, Ltd.     

Contact with friction in multi‐material arbitrary Lagrangian‐Eulerian formulations using X‐FEM

A contact method with friction for the multi‐dimensional Lagrangian step in multi‐material arbitrary Lagrangian–Eulerian (ALE) formulations is presented. In our previous research, the extended finite element method (X‐FEM) was used to create independent fields (i.e. velocity, strain rate, force, mass, etc.) for each material in the problem to model contact without friction. The research presented here includes the extension to friction and improvements to the accuracy and robustness of our previous study. The accelerations of the multi‐material nodes are obtained by coupling the material force and mass fields as a function of the prescribed contact; similarly, the velocities of the multi‐material nodes are recalculated using the conservation of momentum when the prescribed contact requires it. The coupling procedures impose the same nodal velocity on the coupled materials in the direction normal to their interface during the time step update. As a result, the overlap of materials is prevented and unwanted separation does not occur. Three different types of contacts are treated: perfectly bonded, frictionless slip, and slip with friction. Example impact problems are solved and the numerical solutions are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Dielectric elastomers – numerical modeling of nonlinear visco‐electroelasticity

Dielectric elastomer actuators that can directly turn electrical energy into mechanical energy belong to the group of electroactive polymers. This type of electroelastic material exhibits large displacement characteristics and is able to change its mechanical behavior in response to the application of an electric field. Dielectric actuators are made out of elastomers which in general show viscoelastic behavior. To take this time dependent effect into account, the deformation gradient is multiplicatively decomposed. The paper is focused on the numerical modeling of soft dielectric elastomers. The theoretical foundation and the consistent finite element implementation is outlined based on the laws of electricity and elasticity. Furthermore, numerical examples of the nonlinear visco‐electroelasticity model are shown. Copyright © 2012 John Wiley & Sons, Ltd.     

Solving inverse electromagnetic problems using FDTD and gradient‐based minimization

We address time‐domain inverse electromagnetic scattering for determining unknown characteristics of an object from observations of the scattered field. Applications include non‐destructive characterization of media and optimization of material properties, for example, the design of radar absorbing materials. Another application is model reduction where a detailed model of a complex geometry is reduced to a simplified model. The inverse problem is formulated as an optimal control problem where the cost function to be minimized is the difference between the estimated and observed fields, and the control parameters are the unknown object characteristics. The problem is solved in a deterministic gradient‐based optimization algorithm using a parallel 2D FDTD scheme. Highly accurate analytical gradients are computed from the adjoint formulation. The inverse method is applied to the characterization of layered dispersive media and the determination of parameters in subcell models for thin sheets and narrow slots. Copyright © 2006 John Wiley & Sons, Ltd.     

Pyrrolic‐Type Nitrogen‐Doped Hierarchical Macro/Mesoporous Carbon as a Bifunctional Host for High‐Performance Thick Cathodes for Lithium‐Sulfur Batteries

Lithium‐sulfur (Li‐S) batteries are highly considered as a next‐generation energy storage device due to their high theoretical energy density. For practical viability, reasonable active‐material loading of >4.0 mg cm^?2 must be employed, at a cost to the intrinsic instability of sulfur cathodes. The incursion of lithium polysulfides (LiPS) at higher sulfur loadings results in low active material utilization and poor cell cycling capability. The use of high‐surface‐area hierarchical macro/mesoporous inverse opal (IOP) carbons to investigate the effects of pore volume and surface area on the electrochemical stability of high‐loading, high‐thickness cathodes for Li‐S batteries is presented here. The IOP carbons are additionally doped with pyrrolic‐type nitrogen groups (N‐IOP) to act as a polar polysulfide mediator and enhance the active‐material reutilization. With a high sulfur loading of 6.0 mg cm^?2, the Li‐S cells assembled with IOP and N‐IOP carbons are able to attain a high specific capacity of, respectively, 1242 and 1162 mA h g^?1. The N‐IOP enables the Li‐S cells to demonstrate good electrochemical performance over 300 cycles.     

Inverse finite element method for large‐displacement beams

A finite element model for the inverse analysis of large‐displacement beams in the elastic range is presented. The model permits determining the initial shape of a beam such that it attains the given design shape under the effect of service loads. This formulation has immediate applications in various fields such as compliant mechanism design where flexible links can be modeled as large‐displacement beams. Numerical tests for validation purposes are given, together with two design applications of flexible mechanisms with distributed compliance: a flexible gripper and a flexible S‐type clutch. Copyright © 2010 John Wiley & Sons, Ltd.     

Towards Eliminating the Displacement Bias Due to Out‐Of‐Plane Motion in 2D Inverse Problems: A Case of General Rigid‐Body Motion

This article reports an important development related to the inverse characterization of material constitutive parameters using 2D optical displacement field measurements. The out‐of‐plane motion of the specimen, which has traditionally been considered detrimental to the accuracy of these experiments, is generally of two types: (a) a global out‐of‐plane rigid‐body motion of the specimen relative to the camera and (b) out‐of‐plane deformations resulting from material heterogeneity or out‐of‐plane loads. In an earlier article, we proposed to partially relax the condition of no out‐of‐plane motion by allowing for (b) in 2D inverse procedures, in the context of finite element update method, and introduced a compensation strategy by redefining the cost function on the object plane of the acquisition system. The experimental errors due to (a) were assumed negligible. Here, we propose that the global rigid‐body motion (a) may also be recovered within the inverse procedures, hence completely waiving the condition of strictly in‐plane displacements for inverse problems. The recovery is achieved by identifying and including the possible modes of global rigid‐body motion within the cost function together with careful selection of test configuration. The effects of individual rigid‐body modes on the computed displacement fields are studied in detail and utilized as a guideline for selection of test configuration. The approach is fully demonstrated and validated by simulated as well as real experiments for determining elastic constants of isotropic and orthotropic materials using different experimental setups. Effects of improving the optimization routine, for cost function minimization, and experimental noise are also presented.     

One‐Step Fabrication of Unique Mesoporous NiO Hollow Sphere Film on FTO for High‐Performance P‐Type Dye‐Sensitized Solar Cells

P‐type dye sensitized solar cells (p‐DSCs) deliver much lower overall efficiency than their inverse model, n‐DSCs. However, they have fundamental and practical significance, in particular, their tandem structured solar cells with both p‐ and n‐photoelectrodes could offer great potential to significantly improve the efficiency of existing solar cells. A facile and environmentally friendly method is developed to directly one‐step grow hollow NiO spherical structures on fluorine‐doped tin oxide (FTO) substrate, in which a Ni²⁺ and polymer complex spherical structure is self‐constructed through a controlled solvent evaporation process, followed by calcination‐converting to a unique NiO hollow sphere film. The prepared material is further used as a photocathode in p‐type dye sensitized solar cells, resulting in 41% increase of an open‐circuit voltage and 18% enhancement of power conversion efficiency than NiO nanoparticles photocathode. The improved performance can be ascribed to suppressed charge recombination at the photocathode/electrolyte interface. This template‐free approach could be universally used to fabricate other nanostructured hollow spheres for a wide range of energy conversion applications such as electrochemical capacitors, chemical sensors, and electrochromic devices.     

Non‐Gaussian positive‐definite matrix‐valued random fields with constrained eigenvalues: Application to random elasticity tensors with uncertain material symmetries

This paper is devoted to the construction of a class of prior stochastic models for non‐Gaussian positive‐definite matrix‐valued random fields. The proposed class allows the variances of selected random eigenvalues to be specified and exhibits a larger number of parameters than the other classes previously derived within a nonparametric framework. Having recourse to a particular characterization of material symmetry classes, we then propose a mechanical interpretation of the constraints and subsequently show that the probabilistic model may allow prescribing higher statistical fluctuations in given directions. Such stochastic fields turn out to be especially suitable for experimental identification under material symmetry uncertainties, as well as for the development of computational multi‐scale approaches where the randomness induced by fine‐scale features may be taken into account. We further present a possible strategy for inverse identification, relying on the sequential solving of least‐square optimization problems. An application is finally provided. Copyright © 2011 John Wiley & Sons, Ltd.     

Multiaxial creep–fatigue under anisothermal conditions

Because creep–fatigue is mainly studied in uniaxial tension, it is shown here how to proceed to perform both experiments and calculations under multiaxial loading and when the temperature varies both in time and space. The constitutive equations used are those of elasto‐visco‐plasticity coupled or not, to damage, with isotropic and kinematic hardening. It is shown that the unified damage law first proposed for ductile failure and then for fatigue may also be applied to multiaxial creep–fatigue interactions with a new expression for the damage threshold. The procedure for the identification of material parameters is described in detail. Finally, it is shown that the uncoupled calculation procedure, where damage is calculated as a post‐processing of an elasto‐visco‐plastic computation, gives satisfactory results in comparison to the fully coupled analysis; the latter being more accurate but very expensive in computer time.