The screen printing of a power-law fluid

We present a two-dimensional large-aspect-ratio model for the off-contact screen printing of a power-law fluid. We extend the work of White et al. (J Eng Math 54:49–70, 2005) by explicitly including the fluid/air free surface that is present beneath the screen ahead of the squeegee. In the distinguished parameter limit of greatest interest to industry, the process is quasi-steady on the time-scale of a print and can be analysed in three separate regions using the method of matched asymptotic expansions. This allows us to predict where the fluid transfers through the screen, the point at which it first makes contact with the substrate, and the amount of fluid deposited on the substrate during a print stroke. Finally, we show that using a shear-thinning fluid will decrease the amount of fluid transferred ahead of the squeegee, but increase the amount of fluid deposited on the substrate.     

Stability analysis of undrained adiabatic shearing of a rock layer with Cosserat microstructure

Stability of undrained shearing in a classical Cauchy continuum has been first analyzed by Rice (J Geophys Res 80(11):1531–1536, 1975) who showed that instability occurs when the underlying drained deformation becomes unstable (i.e. in the softening regime of the corresponding drained stress-strain curve). However Vardoulakis (Int J Numer Anal Methods Geomech 9:339–414, 1985; Int J Numer Anal Methods Geomech 10:177–190, 1986) has shown that Rice’s linear stability analysis, if performed at the state of maximum deviator, leads to a sharp transition from infinitely stable to infinitely unstable behaviour, which indicates that the solution of the considered initial-value problem does not exist and consequently that the corresponding problem is mathematically ill-posed. Vardoulakis (Géotechnique 46(3):441–456, 1996; Géotechnique 46(3):457–472, 1996) proposed a regularization of the ill-posed problem in the softening regime by resorting to a second grade extension of plasticity theory. In this paper, the kinetics of a granular material is described by a Cosserat continuum as first suggested by Mühlhaus and Vardoulakis (Géotechnique 37:271–283, 1987) and we incorporate the effect of shear heating due to the dissipation of the frictional work. The undrained adiabatic limit is applicable as soon as the slip event is sufficiently rapid and the shear zone broad enough to effectively preclude heat or fluid transfer as it is the case during an earthquake or a landslide. It is shown that shear heating has a destabilizing effect and that instability can occur in the hardening regime if the amount of dilatant strengthening is not sufficient as compared to the effect of thermal pressurization of the pore fluid. It is shown that the linear stability analysis with macro and micro inertia terms leads to the selection of a preferred wave length of the instability mode corresponding to the instability mode with fastest (but finite) growth coefficient.     

Dislocation dynamics by means of Lagrange formalism of irreversible processes—Complex fields and deformation processes

Conventional approaches to a phenomenological theory of plasticity suffer from the fact that they are based on the concept of a “material manifold”. In this way the dislocation dynamics are structurally eliminated from the very beginning.

We propose an alternative method within the framework of Lagrange formalism. With regard to thermodynamics of irreversible processes all degrees of freedom being involved in dissipation are associated with complex field variables. A plastically deformed crystal is modelled as a Cosserat fluid based on complex matter and vortex fields and on a real field of Cosserat triads representing the solid properties of the crystal. Using complex dislocation fields the dislocation network is described in more detail than conventionally is done by the well known dislocation density tensor. Especially the model allows for correlations within the dislocation network which is most essential for plasticity.

Our model implies a methodical unification of elasticity and plasticity. The paper is mainly concerned with the mechanical aspects of the theory.     

Stable identification of linear isotropic Cosserat parameters: bounded stiffness in bending and torsion implies conformal invariance of curvature

We describe a principle of bounded stiffness and show that bounded stiffness in torsion and bending implies a reduction of the curvature energy in linear isotropic Cosserat models leading to the so-called conformal curvature case ${\mu\,\frac{L_c^2}{2}\,\|\,{{\rm dev \, sym}\,\nabla{\rm axl}\,\overline{A}}^2\|}$ where ${\overline{A} \in \mathfrak{so}(3)}$ is the Cosserat microrotation. Imposing bounded stiffness greatly facilitates the Cosserat parameter identification and allows a well-posed, stable determination of the one remaining length scale parameter L _c and the Cosserat couple modulus μ _c .     

A finite-strain elastic–plastic Cosserat theory for polycrystals with grain rotations

We investigate geometrically exact generalized continua of Cosserat micropolar type. A variational form of these models is recalled and extended to finite-strain elasto-plasticity based on the multiplicative decomposition of the deformation gradient. The stress driving the plastic evolution is the Eshelby energy momentum tensor. No plastic Cosserat rotation is introduced and the plastic spin is set to zero. It is argued that the traditional Cosserat couple modulus μ_c should be set to zero for polycrystal specimens liable to fracture in shear, still leading to a complete Cosserat theory with independent rotations in the geometrically exact case in contrast to the infinitesimal, linearized model. A geometrical linearization of the presented finite-strain plasticity model is already shown to be well posed.     

On error estimates and adaptivity in elastoplastic solids: Applications to the numerical simulation of strain localization in classical and Cosserat continua

The a posteriori error estimates based on the post-processing approach are introduced for elastoplastic solids. The standard energy norm error estimate established for linear elliptic problems is generalized here to account for the presence of internal variables through the norm associated with the complementary free energy. This is known to represent a natural metric for the class of elastoplastic problems of evolution. In addition, the intrinsic dissipation functional is utilized as a basis for a complementary a posteriori error estimates. A posteriori error estimates and adaptive refinement techniques are applied to the finite element analysis of a strain localization problem. As a model problem, the constitutive equations describing a generalization of standard J₂-elastoplasticity within the Cosserat continuum are used to overcome serious limitations exhibited by classical continuum models in the post-instability region. The proposed a posteriori error estimates are appropriately modified to account for the Cosserat continuum model and linked with adaptive techniques in order to simulate strain localization problems. Superior behaviour of the Cosserat continuum model in comparison to the classical continuum model is demonstrated through the finite element simulation of the localization in a plane strain tensile test for an elastopiastic softening material, resulting in convergent solutions with an h-refinement and almost uniform error distribution in all considered error norms.     

TRACI 2.0: the tool for the reduction and assessment of chemical and other environmental impacts 2.0

TRACI 2.0, the Tool for the Reduction and Assessment of Chemical and other environmental Impacts 2.0, has been expanded and developed for sustainability metrics, life cycle impact assessment, industrial ecology, and process design impact assessment for developing increasingly sustainable products, processes, facilities, companies, and communities. TRACI 2.0 allows the quantification of stressors that have potential effects, including ozone depletion, global warming, acidification, eutrophication, tropospheric ozone (smog) formation, human health criteria-related effects, human health cancer, human health noncancer, ecotoxicity, and fossil fuel depletion effects. Research is going on to quantify the use of land and water in a future version of TRACI. The original version of TRACI released in August 2002 (Bare et al. J Ind Ecol 6:49–78, 2003) has been used in many prestigious applications including: the US Green Building Council’s LEED Certification (US Green Building Council, Welcome to US Green Building Council, 2008), the National Institute of Standards and Technology’s BEES (Building for Environment and Economic Sustainability) (Lippiatt, BEES 4.0: building for environmental and economic sustainability technical manual and user guide, 2007) which is used by US EPA for Environmentally Preferable Purchasing (US Environmental Protection Agency, Environmentally Preferable Purchasing (EPP), 2008d), the US Marine Corps’ EKAT (Environmental Knowledge and Assessment Tool) for military and nonmilitary uses (US Marine Corps, Environmental knowledge and assessment tool (EKAT): first time user’s guide, 2007), and within numerous college curriculums in engineering and design departments.     

Computation of transient hygroscopic stresses in unidirectional laminated composite plates with cyclic and asymmetrical environmental conditions

External variations in temperature and moisture are of primary importance for the long term behaviour of structures made of polymer matrix composites, because they induce residual stresses within laminated composite plates. It was shown (Hahn et al., 1978; Benkeddad et al., 1995, 1996; Tounsi et al., 2000, 2002, 2004; Adda-Bedia et al., 2001; Tounsi and Adda-Bedia, 2003a, b) that the heterogeneity and the anisotropy of such plates, have an influence on the distribution of transient hygroscopic stresses through the thickness of composite plates. The aim of the present paper is to present a simplified approach for the calculation of transient hygroscopic stresses within unidirectional laminates in the case where these latter are exposed to the cyclic and unsymmetric environmental conditions. Several examples are presented to assess such stresses and to demonstrate the efficiency of the used method. These stresses have to be taken into consideration for the design of composite structures submitted to a moist environment.     

Cosserat point element (<Emphasis Type="Italic">CPE</Emphasis>) for finite deformation of orthotropic elastic materials

An eight node brick Cosserat point element (CPE) has been developed for the numerical solution of three-dimensional problems of hyperelastic nonlinear orthotropic elastic materials. In the Cosserat approach, a strain energy function for the CPE is proposed which satisfies restrictions due to a nonlinear form of the patch test. Part of the strain energy of the CPE is characterized by a three-dimensional strain energy function that depends on physically based nonlinear orthotropic invariants. Special attention has been focused on developing closed form expressions for constitutive coefficients in another part of the strain energy that characterizes the response to inhomogeneous deformations appropriate for orthotropic material response. A number of example problems are presented which demonstrate that the CPE is a robust user friendly element for finite deformations of orthotropic elastic materials, which does not exhibit unphysical locking or hourglassing for thin structures or nearly incompressible materials.     

Stress and couple stress in foams

Even in the range of small elastic deformations the behavior of foams is not well described by only two elastic constants. Usually the manufacturers give values of the material parameters depending on the loading conditions. This problem is investigated on a microscopic scale by a simple beam model. It has been found that this approach shows the size effect that cannot be described within the framework of the standard continuum mechanical setting. The size effect within this model can be explained by independent rotations which do not scale with the displacement field.

A homogenization procedure is proposed that allows for the determination of macroscopic quantities like stress and couple stress in terms of volumetrical averages. The homogenized results of the microscopic model are compared to the results obtained by an enhanced macroscopic model, namely a Cosserat model. Both approaches show good agreement.     

Transverse Ultrasound Measurements in 4He Single Crystals

Recently, Kim and Chan (Science 305:1941, 2004; Phys. Rev. Lett. 97:115302, 2006) have reported an anomalous decoupling transition of solid ⁴He in a torsional oscillator measurement, and interpret their results as evidence for non-classical rotational inertia and a possible supersolid phase of ⁴He. The detailed nature and properties of such a “supersolid” state in ⁴He are still far from being clear, although there are clues from experiments involving ³He impurities, different sample cell geometries, annealing effects and grain boundary flow. Defects produced during crystal growth or deformation (e.g. dislocations) may affect supersolidity, or even produce it, and they are expected to have significant impact on the elastic properties of the solid. The supersolid fraction could also decouple from the lattice and produce a decrease in the transverse sound speed. We have begun the experiments in this laboratory to study such effects, measuring the velocity and attenuation of transverse ultrasound at 10 MHz in ⁴He single crystals grown at constant pressure.      

Competition between recovery and recrystallization in two tungsten supplies according to ITER specifications

In thermonuclear fusion devices, tungsten, implemented as armour material of plasma facing components, is in direct contact with the plasma. Due to high heat flux (20 MW/m\(^{2}\) ), a premature cracking can be observed in relation with the loss of tungsten mechanical properties. It is usually attributed to two competing restoration processes: recovery and recrystallization. A recent investigation on two tungsten supplies according to ITER specifications has highlighted that hardness abatement at high temperature leads to overestimate the recrystallization fraction, which may be a consequence of the significant contribution of recovery during annealing. The present article aims at investigating this phenomenon through the use of a dedicated mean field recrystallization model that, unlike JMAK models, accounts for physical parameters at the microstructure scale such as recovery parameter or grain boundary mobility. The methodology is applied on the two tungsten supplies for ITER. It allows discriminating, for the first time, the respective contributions of recovery and recrystallization to the macroscopic softening in the high temperature range (from 1450 to \(1800\,^{\circ }{\text {C}}\)) and annealing times (0–3500 s). The approach has led to the conclusions that the two supplies merely differ from their initial (delivery) state through the stored energy, the initial recrystallized fraction and the grain size but not from intrinsic physical parameters such as recovery parameter or grain boundary mobility.

     

High density polyethylene (HDPE): Experiments and modeling

The uniaxial tension (loading and unloading), creep and relaxation experiments on high density polyethylene (HDPE) have been carried out at room temperature. The stress–strain behavior of HDPE under different strain rates, creep (relaxation) behavior at different stress (strain) levels have been investigated. These experimental results are used to compare the simulation results of a unified state variable theory, viscoplasticity theory based on overstress (VBO) and a macro-mechanical constitutive model for elasto-viscoplastic deformation of polymeric materials developed by Boyce et al. (Polymer 41:2183–2201, 2000). It is observed that elasto-viscoplasticity model by Boyce et al. (Polymer 41:2183–2201, 2000) is not good enough to simulate stress–strain, creep and relaxation behaviors of HDPE. However, the aforementioned behaviors can be modeled quantitatively by using VBO model.     

Influence of Membrane Stresses on Postbuckling of Rectangular Plates Using a Nonlinear Elastic 3-D Cosserat Brick Element

This paper has two main objectives. The first is to examine the influence of membrane stresses on postbuckled deformations of nonlinear elastic isotropic rectangular plates. The second is to further examine the accuracy of a new 3-D Cosserat eight noded brick element (Nadler and Rubin in Int J Solids Struct 40: 4585–4614, 2003) which was developed within the context of the theory of a Cosserat point. The equations of the Cosserat element include both material and geometric nonlinearities. A number of example problems are considered which examine predictions of the Cosserat element for beams and plates and comparison has been made with results from the commercial codes ANSYS and ADINA. Also, the approximate nonlinear postbuckling solution described in Timoshenko and Gere (Theory of elastic stability, Mc Graw-Hill, New York) is shown to be more limited than originally expected. These results suggest that the Cosserat element is robust, can perform well under extreme conditions and is capable of modeling combinations of three-dimensional bodies with attached thin structures.     

Micromechanics-based viscoelastic damage model for particle-reinforced polymeric composites

The objective of this study is to develop a micromechanics-based viscoelastic damage model that can predict the overall viscoelastic behavior of particle-reinforced polymeric composites undergoing damage. The emphasis here is that the present model successfully combines a rate-dependent viscoelastic constitutive model and a damage model. The Laplace transform based on the Boltzmann superposition principle and the ensemble-volume averaged method suggested by Ju and Chen (Acta Mech 103:103–121, 1994a; Acta Mech 103:123–144, 1994b) are extended toward effective viscoelastic properties. Further, the probability of the distribution function of Weibull (J Appl Mech 18:293–297, 1951) is adopted to describe a damage model that is dependent on damage parameters. A series of numerical simulations including parametric studies, and experimental comparisons are carried out to give insight into the potential capacity of the present micromechanics-based viscoelastic damage framework.     

Behaviour of granular bodies in induced shear zones

This paper deals with the behaviour of granular bodies in induced shear zones. Shearing of an infinite narrow layer of sand between two very rough boundaries under conditions of free dilatancy is numerically modelled with a finite element method and a hypoplastic constitutive relation within a polar (Cosserat) continuum. The relation can reproduce the essential features of granular bodies during shear localisation. The material constants are easily determined from element test results and can be estimated from granulometric properties. The attention is laid on the influence of the initial void ratio, mean grain diameter, layer height, pressure level and grain roughness on the thickness of induced shear zones. In addition, the effect of dilatancy constraint on shear localisation is investigated. The results are also compared to solutions within a non-polar continuum. The FE-calculations demonstrate that polar effects manifested by the appearance of grain rotations and couple stresses are significant in shear zones and their thickness is mainly affected by the initial void ratio, the mean grain diameter and the layer height. Received: 16 November 1999     

A time-discrete model for dynamic fracture based on crack regularization

We propose a discrete time model for dynamic fracture based on crack regularization. The advantages of our approach are threefold: first, our regularization of the crack set has been rigorously shown to converge to the correct sharp-interface energy Ambrosio and Tortorelli (Comm. Pure Appl. Math., 43(8): 999–1036 (1990); Boll. Un. Mat. Ital. B (7), 6(1):105–123, 1992); second, our condition for crack growth, based on Griffith’s criterion, matches that of quasi-static settings Bourdin (Interfaces Free Bound 9(3): 411–430, 2007) where Griffith originally stated his criterion; third, solutions to our model converge, as the time-step tends to zero, to solutions of the correct continuous time model Larsen (Math Models Methods Appl Sci 20:1021–1048, 2010). Furthermore, in implementing this model, we naturally recover several features, such as the elastic wave speed as an upper bound on crack speed, and crack branching for sufficiently rapid boundary displacements. We conclude by comparing our approach to so-called “phase-field” ones. In particular, we explain why phase-field approaches are good for approximating free boundaries, but not the free discontinuity sets that model fracture.     

Effect of a temperature change from 20 to 50°C on the basic creep of HPC and HPFRC

This research was performed in order to study the basic creep of High Performance Concretes (HPC) under uniaxial compression at 20 and 50°C. The aim of this work is to contribute to a better understanding of the basic creep phenomena of HPC at moderate temperature and to provide experimental data which will be used in Thermo-Hydro-Mechanical models such as those necessary for the National project CEOS.FR (Sellier, Thermo hydro mechanical numerical modelling, invited paper at the CEOS International workshop on Control of cracking in R.C. structures: a major step towards serviceability, 2009). The article also presents the fitting of a model considering the effect of temperature via an Arrhenius law affecting its viscous modules (Sellier and Buffo-Lacarriere, Eur J Environ Civ Eng 10:1161–1182, 2009). The concretes are those envisioned for future storage structures of Intermediate Level Long-Life Nuclear Wastes. The research programme has been established with four HPC, two non fibrous and two fibrous; the kinetics and amplitude of basic creep under uniaxial compression are measured during several months at 50°C and compared to those obtained at 20°C for the same materials (Camps, PhD thesis, 2008). Experimental results show that the average creep at 50°C is about twice the creep at 20°C. Besides, results show that this amplification depends on the binder type; the sensitivity to the temperature rise is greater for blended cement based concretes than for OPC based ones. The creep increase due the temperature rise is higher for the HPC under study than for ordinary concretes inventoried in a literature survey. The creep amplitude of HPC seems correlated to their amount of secondary C–S–H. At last, the fitting of the model parameters on the experimental results shows that the values of activation energy are quite close to those obtained by other authors on ordinary concretes (Bazant et al., J Eng Mech ASCE 130(6): 691–699, 2004).     

Oxidation behaviour of synthetic stainless steel interdiffusion layers

Abstract

The possibility of creating an oxidation-protection layer system composed of Fe, Ni and Cr on top of a plain carbon steel substrate by means of electroplating is investigated within this study. It is shown that by applying an appropriate heat treatment, interdiffusion takes place transforming the individual layers into a gradient structure with stainless-steel-like properties. The layering process combined with the interdiffusion heat treatment allows numerous stainless-steel-like compositions to be produced. The proposed layer-by-layer electrodeposition process is followed by vacuum annealing, where interdiffusion of the various elements causes a redistribution of the phase composition, leading to a gradient corrosion-resistant layer. The samples were vacuum-annealed at 1030 °C for 24 hours and oxidized in air at 700 °C for various time periods afterwards. The respective oxidation behaviour of the interdiffusion layers was characterized by applying analytical SEM to ground and polished cross sections.     

Self-accommodation in polycrystalline 10M Ni–Mn–Ga martensite

10M Ni–Mn–Ga polycrystals show a typical self-accommodated microstructure consisting of macro and micro twins. The macro twin lamellae separate micro twins creating a so-called “twins within twins” microstructure. Such a configuration allows the distribution of martensitic variants with no net change in shape of the sample. The arrangement of variants can occur on different length scales, from a few nanometers up to a few millimeters, not only depending on grain size but also on processing condition (e.g., extrusion, torsion). Small austenite grains do not completely transform to martensite giving rise to some residual austenite. Furthermore, characteristic branching of macro and micro twins is observed due to lowering of the elastic energy at grain and macro twin boundaries, respectively.