A continuum mechanics approach for modelling arbitrary degradation and erosion processes in polymers

Composed of rather simple components some polymers show the ability to decompose from complex structures into substances that can be easily absorbed by the surrounding environment. The responsible processes behind chain shortening and eventually the material remove are degradation and erosion. The aim of this work is to model the chemo-mechanical condition of the polymer material based on a discretised network model. Further, the influence of erosion processes on the morphology is investigated. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Minimization- and Saddle-Point-Based Modeling of Diffusion-Deformation-Processes in Hydrogels

Hydrogels have gained importance during the last years due to their wide range of synthetically fabricable elastic properties as well their increasing meaning in biomedical applications. Future exploitation of the vast prospects of hydrogels is however only feasible by establishing reliable material models that precisely capture their behavior in different environments. To this end, we propose a consistent variational framework for deformation-diffusion processes, offering a canonically compact approach to the chemo-mechanical coupling of hydrogels via a saddle-point as well as a new minimization formulation. The work depicts the construction of rate-type potentials for the chemo-mechanical evolution problem and their transformation into time-discrete incremental potentials. In terms of spatial discretization, the finite element method is employed, benefiting from the intrinsic symmetric structure of the variational foundation. While the saddle-point formulation yields the well-known LBB condition as a constraint for finite element interpolations, on the part of its minimizing counterpart H(Div, ℬ︁)-conforming elements have to be chosen. We illustrate appropriate solutions to both challenges, using mixed Taylor-Hood for the saddle-point and Raviart-Thomas elements for the minimization formulation and discuss advantages of the new approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Water uptake and mechanical characteristics of wood fiber-polypropylene composites

The influence of mixing process (in a two-roll mill, high-speed mixer, or twin-screw extruder) on the strength properties of polypropylene/wood fiber composites was studied. The best results were obtained for composites compounded in a twin-screw extruder. The water uptake and the influence of moisture on the flexural strength (σ_fl) and modulus (E_fl) were studied by immersion of the composites in water at 20, 50, and 90°C. Most strongly the moisture affected the value of E_fl, but the degree of water uptake and the change in σ_fl and E_fl also depended on temperature and the presence of a modificator—maleated polypropylene (MAH). MAH improved the strength properties of the composites both in dry and wet states and also decreased the extent of water uptake and swelling in cyclic (soaking/drying) tests. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 42, No. 1, pp. 101–114, January–February, 2006.     

Comparison of a biphasic and a multicomponent model describing viscoelastic swelling phenomena

Biological soft tissues like articular cartilage and their artificial replacement hydrogel have a multicomponent microstructure, consisting of a charged viscoelastic solid matrix saturated by a fluid, which is composed of the liquid solvent and the dissolved anions and cations. Such charged multiphasic materials exhibit a swelling behaviour under varying chemical conditions. These materials are best described by a macroscopic approach like the Theory of Porous Media (TPM). Starting from this point, a standard two-phase model is extended by dividing the fluid into the above mentioned components. Therein, the chemical relations describing the behaviour of the ions and their interaction with the other mixture constituents are incorporated. The resulting model covers mechanical as well as osmotic and electrostatic effects. For numerical and simplicity reasons, it is possible to describe the swelling phenomena by a simplified biphasic model, where the ions as a third degree of freedom and their time-dependent diffusion are neglected. Furthermore, the viscoelastic solid matrix can be replaced by an elastic material. Note that using the multicomponent model generally results in numerical problems, since the boundary conditions depend on the internal fixed charge density. It is shown that this problem can be solved by including the boundary conditions into the weak formulation. Finally, to compare the different behaviour of the above mentioned models by means of an swelling example, they are implemented into the FE tool PANDAS using stable Taylor-Hood elements for the spatial discretization. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Water absorption and swelling of glass/epoxy syntactic foams

The results of experimental and theoretical investigation of glass/epoxy syntactic foams at a long-term (10 years) exposure in water are presented. Specimens for experimental investigation were made from EDT-10 epoxy filled with MSO-779 hollow glass spheres. Seven types of specimens with filler volume fraction varying from 0 to 0.6 were tested. The curves of long-term water absorption and swelling were determined. It was expected that the addition of hollow glass spheres must substantially reduce the sorptional capacity of material because of the reduction of the volume content of the matrix and, therefore, because of reduction of the part of the volume where the molecules of water can diffuse. However, the water absorption process in syntactic foams was found to continue during the total term of the experiments without a tendency to stop. After ten years the limiting equilibrium state was not achieved and the concentration of water in composite specimens became higher than the equilibrium concentration of water in unfilled EDT-10 epoxy. In long-term tests the swelling strain was found to be a nonlinear function of water content. The degree of nonlinearity increased when the volume content of the filler was increased. The calculational prediction of absorption and swelling curves of syntactic foams with different volume contents of the filler was done using the experimentally determined characteristics of absorption of the matrix. The water transport process in the matrix was considered to obey Fick's law. It was found that the initial parts of the experimental curves (during the first year of exposure) show a good enough agreement with calculated data for engineering applications. Subsequently, the discrepancy between the experimental results and calculated data increased and reached such large values that the predicted results became unacceptable. The possible reasons of such discrepancy (breaking of adhesion bonds between the matrix and the filler with subsequent sorption of water at the glass sphere surface, and diffusional filling by water of the inner parts of the damaged glass spheres, etc.) are discussed.Presented at the Ninth International Conference on the Mechanics of Composite Materials, Riga, October, 1995. University of Colima, Colima City, Colima, Mexico. Institute of Polymer Mechanics, Latvian Academy of Sciences, Riga, LV-1006, Latvia. Published in Mekhanika Kompozitnykh Materialov, No. 1, pp. 83–97, January–February, 1996.     

Experimental validation of a viscoelastic material model for numerical simulation of the extrusion process of rubber blends

The goal of this contribution is the validation of a viscoelastic material model, which allows consideration of the interaction of the typical swelling behavior of viscoelastic fluids and the shear rate dependent viscosity of industrial used rubber blends in the context of an extrusion process. With this knowledge more realistic numerical simulations of the die swell phenomenon and its influence on the resulting profile geometry are possible. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of Swelling Phenomena in Charged Hydrated Porous Media

Biological tissues like articular cartilage and geomaterials like clay have a multicomponent microstructure. The charged solid is saturated by a viscous fluid, which itself is composed of several components: the liquid solvent and the dissolved ions, namely, water, anions and cations. These charged multiphase materials exhibit a swelling behaviour under varying chemical conditions. The model describing such materials combines electrochemical and mechanical effects like osmosis and electrostatics within a macroscopic formulation. Starting from the Theory of Porous Media (TPM), a four component model is presented, wherein all constituents are materially incompressible and mass exchanges are excluded. This isothermal model leads to a set of equations which consists of three primary variables: the solid displacement u _S, the pore‐pressure p and the molar ion concentration c_m, since the ion concentrations always depend on each other because of the electroneutrality condition. For the numerical treatment, the weak formulations of governing equations are implemented in the FE tool PANDAS, wherein Taylor‐Hood elements are used for the spatial discretization. Finally, a simulation of a 3‐d swelling experiment is shown. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of a PDE model of the swelling of mitochondria accounting for spatial movement

We analyze existence and asymptotic behavior of a system of semilinear diffusion‐reaction equations that arises in the modeling of the mitochondrial swelling process. The model itself expands previous work in which the mitochondria were assumed to be stationary, whereas now their movement is modeled by linear diffusion. While in the previous model certain formal structural conditions were required for the rate functions describing the swelling process, we show that these are not required in the extended model. Numerical simulations are included to visualize the solutions of the new model and to compare them with the solutions of the previous model.     

Water absorption and its effect on rubber strength

The effect of the swelling of rubbers in water and their recovery on the tear strength of the material has been investigated and a mechanism of water absorption is proposed. It is shown that there is a fundamental difference between the mechanism of water absorption and swelling in solvents. The strength of a rubber dried after being kept in water is anomalously high. This effect is explained in terms of the proposed polymer-nonsolvent interaction mechanism.É. A. Ter-Gazaryan State Scientific-Research and Design Institute of Polymer Adhesives, Kirovakan. Moscow Technological Institute of the Meat and Dairy Industry. Translated from Mekhanika Polimerov, No. 1, pp. 136–138, January–February, 1970.     

Finite Swelling with Weakly Fulfilled Boundary Conditions

Biological soft tissues exhibit a swelling behaviour and consist of multiple phases, a solid phase composed of collgagen fibers and charged PGA chains and a fluid phase composed of the liquid solvent and the ions of dissolved salt. In this contribution, the Theory of Porous Media (TPM) model consists of four constituents, a charged solid and an aqueous solution composed of water and the ions of dissolved salt. The solid is modelled by a finite elasticity law accounting for the multiphasic micro structure, whereas the fluid is considered as a viscous Newtonian fluid. One finally ends up with the volume balance of the fluid, the concentration balance of the cations, the momentum balance of the overall mixture. The resulting set of partial differential equations is solved within the framework of the FEM. Therefore, the weak forms are derived and the resulting set of equations for the primary variables pore pressure p, cation concentration c and solid displacement u _S , is implemented into the FE tool PANDAS. Finally, a three dimensional example of a swelling hydrogel disc is shown. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magneto-Sensitive Elastomers: An Experimental Point of View

Magneto-sensitive elastomers (MSEs) are smart materials changing their shape and mechanical properties in the presence of a magnetic field. Focussing on model systems, silicone based MSEs are prepared by a multi-step mixing process and characterised using a rotational rheometer (plate-plate). Data obtained by relaxation tests is used to set-up a material model coupling the theories of viscoelasticity and magnetoelasticity. The behaviour of MSEs in quasi-static and dynamic mechanical shear experiments can be successfully predicted by the analytical model using parameters received by fitting the transient experiments. The model is validated for small shear deformations (γ = 0.02) and low magnetic fields (𝔹 = 0.2 T). (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On coupled problems in geomechanics

Geomechanical problems are generally based on the category of granular, cohesive-frictional materials with a fluid pore content. At the macroscopic scale of continuum mechanics, these materials can be successfully described on the basis of the well-founded Theory of Porous Media (TPM) [1]. The present contribution touches fundamental problems of coupled media by investigating the interacting behaviour of an elasto-viscoplastic porous solid skeleton, the soil, and two pore fluids, water and air. Furthermore, electro-chemical reactions are considered in order to include the swelling behaviour of active soil. In conclusion, this leads to a system of strongly coupled partial differential equations (PDE) that can be solved by use of the finite element method (FEM). In particular, the presentation includes fluid-flow situations in the fully or the partially saturated range, swelling phenomena of active clay [3] as well as localisation phenomena [2] as a result of fluid flow or heavy rainfall events. The computations are carried out by use of the single-processor FE tool PANDAS [4] and, in case of large 3-d problems, by coupling PANDAS with the multi-processor solver M++. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling of macroscopical transient frost processes and microscopical driving forces

The artificial saturation phenomenon due to freeze-thaw cycles is described by a multi-phase and multiscale model (1; 2; 3) formulated within the Theory of Porous Media, (4). It represents partially saturated concrete as a mixture of 5 interacting constituents φ^a, namely the solid skeleton φ^s, the bulk water φ^l, the pore volume occupied by vapour φ^v, the ice φⁱ and the gel water phase φ^p. Most relevant for the model is the distinction between two length scales and their characteristic time scales. The boundary is marked where macroscopic bulk conditions change to surface physics and chemistry. Surface physics and chemistry acting on the nano-scale affect fundamental properties of concrete and consequently the durability of concrete against freeze-thaw. At the macroscopic scale the model describes transient conditions (i.e. water-uptake, heat transport, volume dilatation of 9 %, phase change of first order considering hysteresis) which are characterized by a relatively long time period to reach equilibrium in contrast to the processes modelled on the microstructure. At the microscopic scale the model represents the nanoscopic CSH-gel system consisting of solid CSH and water as a linked system of both components basing on the concept of the “Solid-Liquid Gel System” (5). In the constribution the numerical results of the model are presented with focus on the evaluation of the process zone during the penetration of the melting front into the matrix. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Modelling and simulation of heat exchange and transport in a geothermal plant

The production of energy by use of the high temperature in the earth's mantle has played an increasingly important role in recent years. However, large uncertainties concerning the conditions in the subsurface make it difficult to use power plants efficiently. An appropriate modelling and simulation of the heat exchange and transport provides a promising tool for further investigations of the process and optimisation of the productivity. Starting from the isothermal state at high temperatures, a cold fluid is injected through a borehole into a porous rock by applying a pressure difference between at least two wells. Passing the fractured rock, the water is heated at the crack interfaces. In addition to the convection of the temperature due to the water flow, the conduction of heat in the rock and the water has to be considered. The modelling approach of this coupled process is based on the Theory of Porous Media (TPM). Both, the rock and the water, are assumed to be materially incompressible and the thermal expansion is solely considered for the fluid, since the expansion of the rock is negligible for the occurring temperature differences. Furthermore, it is assumed that the subsurface is saturated with water. To solve the generated initial-boundary-value problem, the governing primary variables of the coupled model are spatially approximated by mixed finite elements and the time discretisation is carried out by an implicit Euler time-integration scheme. Since in the considered problem the convective transport is dominant, a streamline upwinding scheme is used for the numerical stabilisation to obtain non-oscillatory solutions. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Model development in discrete-event simulation and system dynamics: An empirical study of expert modellers

An empirical study comparing the model development process followed by experts in discrete-event simulation (DES) and system dynamics (SD) modelling is undertaken. verbal protocol analysis (VPA) is used to study the modelling process followed by ten expert modellers (5 SD and 5 DES). Participants are asked to build simulation models based on a case study and to think aloud while modelling. The generated verbal protocols are divided into seven modelling topics: problem structuring, conceptual modelling, data inputs, model coding, verification & validation, results & experimentation and implementation and then analyzed. Our results suggest that all modellers switch between modelling topics, however DES modellers follow a more linear progression. DES modellers focus significantly more on model coding and verification & validation, whereas SD modellers on conceptual modelling. Observations are made revealing some interesting differences in the way the two groups of modellers tackle the case. This paper contributes towards the comparison of DES and SD.     

Applying stochastic goal programming: A case study on water use planning

A decision support model to help public water agencies allocate surface water among farmers and authorize the use of groundwater for irrigation (especially in Mediterranean dry regions) is developed. This is a stochastic goal programming approach with two goals, the first concerning farm management while the other concerns environmental impact. Targets for both goals are established by the agency. This model yields three reduction factors to decide the different reductions in available surface water, standard groundwater and complementary groundwater that the agency should grant/authorize for irrigation, this depending on if it is a dry or wet year. In drought periods, the model recommends using more groundwater (in percentage) than in wet periods. A case study using year-to-year statistical information on available water over the period 1941–2005 is developed through numerical tables. A step-by-step computational process is presented in detail.     

Nonlinear moisture deformation of a composite with a densified reinforcement

Conclusion An analytical method is presented for estimation moisture deformation of densified in technological pressing wood-based composite material with nonlinear swelling properties. This includes modelling of the processing effects as well as interfacial bonding. By using the multilayer model supported on the laminate analogy the optimum particle alignment has been estimated for a real composite production process.Published in Mekhanika Kompozitnykh Materialov, Vol. 30, No. 3, pp. 314–320, May–June, 1994.     

Modeling and analysis of the removal of an organic pollutant from a water body using fungi

In this paper, a non linear mathematical model for removing an organic pollutant such as a dye from a water body is proposed and analyzed. In the modeling process four variables are considered, namely, (i) the concentration of the dye, (ii) the density of fungus population, (iii) the concentration of a nutrient and (iv) the concentration of dissolved oxygen (DO). It is assumed that an organic pollutant is present in water with given concentration or discharged with a constant rate in water. It is assumed further that fungus population is kept alive and active due to supply of a nutrient. It is considered that nutrient and oxygen are supplied to the water body from outside with constant rates. The model is analyzed by using the stability theory of differential equations. The model analysis shows that organic pollutant can be removed from the water body by fungus population and the level of degradation depends upon the concentration of organic pollutant, the density of fungal population and the interaction processes involved.The simulation analysis of the proposed model confirms the analytical results. It is also found that these results are qualitatively in line with the experimental observations of one of the authors (Sanghi).     

Effect of hydrostatic pressure combined with uniaxial tension on certain physical properties of polymers

The residual changes in the density and swelling properties of high-density polyethylene, teflon, PVC, and ebonite after extension under hydrostatic pressure have been investigated. It is shown that in this case the density of all the materials tested is higher and the swelling lower than in the case of uniaxial tension alone. This effect of hydrostatic pressure is attributable to the creation of favorable conditions for the healing of cracks formed in the deformation process.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1018–1023, 1967     

Deformability of thermoplastics in physiological salt solution

Conclusions 1. The creep of thermoplastics in physiological salt solution is characterized by change in the rate of creep deformation relative to the creep in air. The bending creep deformations of HMWPE and phenylone and the compressive creep deformation of HMWPE are described by a binomial equation [Eq. (5)] and the compressive creep deformation of phenylone is described by Eq. (6).2. The lifetime of the thermoplastics studied under static compression and bending determined relative to limiting deformations is described by Eq. (7). Under the same stresses and limiting deformations, the lifetime of phenylone in physiological salt solution is greater than the lifetime of HMWPE.3. After the simultaneous action of physiological salt solution and static stress over one month, most of the characteristics of short-term strength in phenylone are significantly reduced due to swelling in the model medium.Paper presented at the Third All-Union Conference on Polymer Mechanics, Riga, 1976.N. N. Priorov Central Scientific-Research Institute of Traumatology and Orthopedics, Moscow. Kazan Construction Engineering Institute. Translated from Mekhanika Polimerov, No. 2, pp. 325–331, March–April, 1978.