Modelling multiphase transport in deformable cellulose based materials exhibiting internal mass exchange and swelling

A thermodynamically consistent model for porous cellulose networks is proposed. A general theory is developed based on mixture theory using chemical potentials as flow potentials. The material is decomposed into three phases, solid, liquid and gas, where the solid and gas phases are further separated into dry fiber and fiber water, water vapor and dry air, respectively. Between the phases interfaces are present and their influence on the mass exchange of water is incorporated. Emphasis is placed on the dynamics in mass exchange of water which allows for description of non-equilibrium states. The driving force for reaching equilibrium is given by the chemical potential difference. Constitutive relations relevant for paperboard are proposed and illustrative simulations are carried out to reveal the dynamics of mass exchange. The model enables analysis of transient flow accounting for effects of deformation, swelling and moisture sorption dynamics

Multiphase transport model of swelling cellulose based materials with variable hydrophobicity

A thermodynamically consistent model for multiphase flow in swelling cellulose based material is adopted. The material is decomposed into a fiber phase, a gas phase and an inter-fiber water phase, where the fiber phase consists of a fiber water and a dry fiber constituent and the gas phase is an ideal gas mixture of water vapor and dry air. The model is derived within mixture theory and includes local non-equilibrium mass exchange between inter-fiber water, fiber water and water vapor. From assumptions on the microscale structure a novel model is derived to account for spatially varying hydrophobicity. An finite element implementation is made and employed to solve boundary value problems for edge wicking to investigate the water transport in paperboard with varying hydrophobicity. The results are analysed with the aim to better understand the mechanisms of interaction between water and fiber/cellulose. Simulations with spatially varying hydrophobicity reveals different regimes of the macroscopic water uptake made accessible by the decomposition of the water into inter-fiber water and fiber water contributions

Coupled heat, mass and momentum transport in swelling cellulose based materials with application to retorting of paperboard packages

Understanding the complex interplay of mass transport, heat transport and deformation in swelling cellulose based materials is a challenging task. To aid in this endeavour a multiphysics model is developed within the mixture theory framework. The model is macroscopic and accounts for swelling, non-equilibrium mass exchange of water, elastic deformation and multiphase transport phenomena, where non-isothermal conditions are considered. The investigated material is viewed as an immiscible mixture of cellulose fibers, pore gas and inter-fiber pore water separated by interfaces. Fiber and gas are considered as miscible mixtures of dry fiber and fiber water, and dry air and water vapor, respectively. The constitutive equations are obtained in a coupled and thermodynamically consistent manner by exploitation of the dissipation inequality. As an application of the model, conditions representative of the retorting process for liquid packaging board are simulated using the proposed constitutive model. The influence of the process control parameters during the heating, cooking and cooling steps of the retorting procedure are analysed. It was found that through-plane temperature gradients and the presence of dry air in the retort had a significant impact on the moisture uptake and the moisture distribution. Spatial distribution of hydrophobicity had a great effect on the distribution of fiber water and inter-fiber water

A physically motivated modification of the strain equivalence approach

A phenomenological thermodynamic approach used for describing elasto-plasticity coupled with isotropic damage is considered. Using this approach it was recently shown by the authors that certain unwanted features exist in the plasticity-induced damage theories. This paper gives a suggestion on how to solve these issues. Based on physical arguments a simple modification of the postulate of strain equivalence is suggested. To show the effects of the modification, the von Mises plasticity model coupled with isotropic damage is used as a prototype model in the derivations. Both analytical considerations and simulations of a strain-controlled uniaxial model are performed. The results reveal that the modification of the postulate of strain equivalence gives promising results. In contrast to the postulates of strain equivalence and (complementary) energy equivalence, the present formulation predicts the elastic strain to vanish when failure takes place

Micromechanical modeling of smart composites considering debonding of reinforcements

AbstractUsing the information of the microstructure, this paper presents the development of an incremental constitutive law governing the response of an electro-magneto-thermo-mechanical smart composite. In this development, different shapes of reinforcements that have magneto-electro-thermo-elastic properties that differ from the matrix material are considered. Shapes such as ellipsoidal (spherical, prolate and oblate) particles, elliptical and circular cylindrical fibers, disk and ribbon can be treated provided that the corresponding Eshelby tensor is used. The debonding of the reinforcements from the matrix is also a part of the microscopic process considered. The developed incremental constitutive law not only predicts the macroscopic and microscopic electro-magneto-thermo-mechanical-elastic behavior of composites while considering the debonding process, but it also characterizes their different macroscopic effective properties such as permittivity, permeability, stiffness moduli, pyroelectricity, pyromagnitivity and thermal expansion coefficient in different directions. Moreover, the developed constitutive law is applicable to porous materials and composites with multiple reinforcements and porosities. In the two examples considered below, particular attention is devoted to assessing the effects of both the shape and the concentration of the inclusion and/or porosity and the damage evolution on the multiphysical microscopic and macroscopic behaviors and the effective properties. The first example sheds light on obtaining the macroscopic effective properties, taking into account the piezoelectric BaTiO3 continuous fibers embedded in the piezomagnetic CoFe2O4 matrix. While in the second example, mechanical loading is considered, epoxy is taken as the matrix material and the response of the composite is presented while the evolution of damage in terms of debonding is taking place

Model Describing Material-Dependent Deformation Behavior in High-Velocity Metal Forming Processes

A constitutive model for rate-dependent and thermomechanically coupled plasticity at finite strains is presented. The plasticity model is based on a J(2) model and rate-dependent behavior is included by use of a Perzyna-type formulation. Adiabatic heating effects are handled in a consistent way and not, as is a common assumption, through a constant conversion of the internal work rate into rate of heating. The conversion factor is instead derived from thermodynamic considerations. The stored energy is assumed to be a function of a single internal variable which differs from the effective plastic strain. This allows a thermodynamically consistent formulation to be obtained which, as shown, can be calibrated by use of simple procedures. Choosing 100Cr6 steel in two differently heat treated conditions as prototype material, experimental tests are performed, enabling the model to be calibrated. Significant differences in deformation behavior are noted as the differently heat treated specimens are compared. In addition, the local stress-updating procedure is reduced to a single scalar equation, permitting a very efficient numerical implementation of the model. The constitutive formulation proposed was employed in an explicit finite element solver, illustrative simulations of a high-velocity metal forming process being performed to demonstrate the capabilities of the model and certain characteristic traits of the materials that were studied

Recrystallization and texture evolution during hot rolling of copper, studied by a multiscale model combining crystal plasticity and vertex models

A multiscale modeling framework, combining a graph-based vertex model of microstructure evolution with a GPU-parallelized crystal plasticity model, was recently proposed by the authors. Considering hot rolling of copper, the full capabilities of the model are demonstrated in the present work. The polycrystal plasticity model captures the plastic response and the texture evolution during materials processing while the vertex model provides central features of grain structure evolution through dynamic recrystallization, such as nucleation and growth of individual crystals. The multiscale model makes it possible to obtain information regarding grain size and texture development throughout the workpiece, capturing the effects of recrystallization and heterogeneous microstructure evolution. Recognizing that recrystallization is a highly temperature dependent phenomenon, simulations are performed at different process temperatures. The results show that the proposed modeling framework is capable of simultaneously capturing central aspects of material behavior at both the meso- and macrolevel. Detailed investigation of the evolution of texture, grain size distribution and plastic deformation during the different processing conditions are performed, using the proposed model. The results show a strong texture development, but almost no recrystallization, for the lower of the investigated temperatures, while at higher temperatures an increased recrystallization is shown to weaken the development of a typical rolling texture. The simulations also show the influence of the shear deformation close to the rolling surface on both texture development and recrystallization

A comparison of viscoplasticity formats and algorithms

Algorithmic issues for the two thermodynamically consistent viscoplastic formulations of Perzyna and Duvaut–Lions are discussed. It is shown that it is simple to avoid the numerical problems associated with a small relaxation time without resorting to elaborate perturbation techniques, as suggested in the literature. A systematic numerical investigation of the efficiency of Newton iterations, that employ the Algorithmic Tangential Stiffness (ATS) tensor, as compared to various approximations, is carried out for a cohesive-frictional model with non-linear isotropic hardening. Generally, the ATS-tensor is formulated in such an explicit fashion that its tensorial structure resembles that of the underlying rate-independent continuum stiffness. For both the Perzyna and the Duvaut–Lions format, it appears that the ATS-tensor is obtained by a proper augmentation of the corresponding rate-independent ATS-tensor

Multi-scale plasticity modeling: Coupled discrete dislocation and continuum crystal plasticity

A hierarchical multi-scale model that couples a region of material described by discrete dislocation plasticity to a surrounding region described by conventional crystal plasticity is presented. The coupled model is aimed at capturing non-classical plasticity effects such as the long-range stresses associated with a density of geometrically necessary dislocations and source limited plasticity, while also accounting for plastic flow and the associated energy dissipation at much larger scales where such non-classical effects are absent. The key to the model is the treatment of the interface between the discrete and continuum regions, where continuity of tractions and displacements is maintained in an average sense and the flow of net Burgers vector is managed via "passing" of discrete dislocations. The formulation is used to analyze two plane strain problems: (i) tension of a block and (ii) crack growth under mode I loading with various sizes of the discrete dislocation plasticity region surrounding the crack tip. The computed crack growth resistance curves are nearly independent of the size of the discrete dislocation plasticity region for region sizes ranging from 30 mu m x 30 mu m to 10 mu m x 5 mu m. The multi-scale model can reduce the computational time for the mode 1 crack analysis by a factor of 14 with little or no loss of fidelity in the crack growth predictions. (c) 2008 Elsevier Ltd. All rights reserved