Thermo-mechanically coupled modelling of cellular MgO-C refractories under thermal shock

Refractory materials such as magnesium oxide carbon (MgO-C) composites are used in the steel-making industry for furnaces, ladles or oxygen converters. A new class of composites are cellular MgO-C materials, consisting of carbon foams filled with magnesium oxide and inclusions of gas filled pores. Cellular MgO-C composites have the advantage of significantly improving the thermo-mechanical properties [1]. This contribution focuses on the FEM implementation of a fully coupled thermo-mechanical continuum model. It is based on the theory of porous media (TPM) restricted by a kinematic coupling of the displacement field of all constituents. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermo-mechanical modelling of cellular ceramic composites by a multiphase approach of porous media

Refractory materials have a wide range of applications in the steel-making industry for example as lining of furnaces, oxygen converters or for ladles. Often, magnesia carbon bricks (MgO-C) are used. These are made of a periclase phase (MgO) with carbon inclusions and pores. In their applications, refractories are subjected to thermal and mechanical loads causing damage. The thermo-mechanical behaviour of MgO-C composites and hence their thermal stability could be improved significantly using cellular MgO-C composites based on carbon foams [1, 2]. The present contribution focuses on the development of a fully coupled phenomenological thermo-mechanical continuum model based on the theory of porous media (TPM) with a new kinematic coupling of the displacement field of all constituents. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Population-scale modelling of cellular chemotaxis and aggregation

Motivated by chemotaxis of, and especially aggregation within,populations of cells, we examine an extension of the Becker–Döringaggregation equations in which monomers undergo diffusion andadvection in one spatial dimension, as well as attaching themselvesto clusters of all sizes. We restrict our attention to irreversibleaggregation, particularly for power-law rate coefficients. Weexamine the large-time behaviour of the initial-value problemon an infinite domain, both in the purely diffusive case andwith advection. We also determine the large-time behaviour ona semi-infinite domain, with a non-zero Dirichlet conditionimposed on the monomer concentration at the boundary. The asymptoticresults are confirmed by numerical simulations.     

Biomechanical modelling of cellular articular cartilage replacement tissues

The aim of the present study is to investigate the strength and damping properties of cellular articular cartilage replacement material. For this purpose, a viscoelastic-diffusion model for the acellular water-saturated condensed collagen gel type I is proposed and validated experimentally. Moreover, a remodelling law for the cell seeded collagen gel is introduced. For an experimental study of the interaction between fibre growth and mechanical stimulation, bioreactors are developed and histological investigations are carried out. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Homogenization of cellular structures for soft tissue modelling

The aim of the paper is to show how the method of homogenization can be applied in modelling of soft tissue undergoing large deformation. Simplified microstructures are considered, which consist of hyperelastic porous matrix and periodic array of fluid‐filled cells. At the microscopic level diffusion processes are described by the Darcy law, permeability of the cellular membrane is introduced. Although at the macroscopic scale the tissue is incompressible, the flow inside microscopic volumes induces viscous relaxation effects. The homogenized problem is formulated.     

Towards hybrid two-phase modelling using linear domain decomposition

The viscous flow of two immiscible fluids in a porous medium on the Darcy scale is governed by a system of nonlinear parabolic equations. If infinite mobility of one phase can be assumed (e.g., in soil layers in contact with the atmosphere) the system can be substituted by the scalar Richards model. Thus, the porous medium domain may be partitioned into disjoint subdomains where either the full two-phase or the simplified Richards model dynamics are valid. Extending the previously considered one-model situations we suggest coupling conditions for this hybrid model approach. Based on an Euler implicit discretization, a linear iterative (L-type) domain decomposition scheme is proposed, and proved to be convergent. The theoretical findings are verified by a comparative numerical study that in particular confirms the efficiency of the hybrid ansatz as compared to full two-phase model computations.     

Comparative analysis of asynchronous cellular automata in stochastic pharmaceutical modelling

In pharmaceutical modelling, cellular automata have been used as an established tool to represent molecular changes through discrete structural interactions. The data quality provided by such modelling is found suitable for the early drug design phase where flexibility is paramount. While both synchronous (CA) and asynchronous (ACA) types of automata have been used, analysis of their nature and comparative influence on model outputs is lacking. In this paper, we outline a representative probabilistic CA for modelling complex controlled drug formulations and investigate its transition from synchronous to asynchronous update algorithms. The key investigation points include quantification of model dynamics through three distinct scenarios, parallelisation performance and the ability to describe different release phenomena, namely erosion, diffusion and swelling. The choice of the appropriate update mechanism impacts the perceived realism of the simulation as well as the applicability of large-scale simulations.     

Mathematical modelling of a hydraulic accumulator for hydraulic hybrid drives

ABSTRACT

Hydraulic accumulators are used as energy storages in a wide area of applications. In particular, in automotive hybrid drive-trains, this type of energy storage is an interesting alternative to today’s common strategies like chemical batteries or flywheels. This article deals with the mathematical modelling of a hydraulic accumulator for passenger vehicles, which comprises a carbon fibre reinforced plastic (CFRP) body and aluminium piston. The thermodynamical behaviour of the oil and gas as well as the interaction with the CFRP body is investigated in detail. Starting from a complex model, two models of reduced complexity are derived. The validation of these models with measurement data from a test drive with a prototype series hydraulic hybrid drive-train proves their high accuracy.     

A cellular automaton technique for modelling of a binary dendritic growth with convection

A two-dimensional model for the simulation of a binary dendritic growth with convection has been developed in order to investigate the effects of convection on dendritic morphologies. The model is based on a cellular automaton (CA) technique for the calculation of the evolution of solid/liquid (s/l) interface. The dynamics of the interface controlled by temperature, solute diffusion and Gibbs–Thomson effects, is coupled with the continuum model for energy, solute and momentum transfer with liquid convection. The solid fraction is calculated by a governing equation, instead of some approximate methods such as lever rule method [A. Jacot, M. Rappaz, Acta Mater. 50 (2002) 1909–1926.] or interface velocity method [L. Nastac, Acta Mater. 47 (1999) 4253; L. Beltran-Sanchez, D.M. Stefanescu, Mat. and Mat. Trans. A 26 (2003) 367.]. For the dendritic growth without convection, mesh independency of simulation results is achieved. The simulated steady-state tip velocity are compared with the predicted values of LGK theory [Lipton, M.E. Glicksmanm, W. Kurz, Metall. Trans. 18(A) (1987) 341.] as a function of melt undercooling, which shows good agreement. The growth of dendrite arms in a forced convection has been investigated. It was found that the dendritic growth in the upstream direction was amplified, due to larger solute gradient in the liquid ahead of the s/l interface caused by melt convection. In the isothermal environment, the calculated results under very fine mesh are in good agreement with the Oseen–Ivanstov solution for the concentration-driven growth in a forced flow.     

Thermo-mechanical post-critical analysis of nonlocal orthotropic plates

A closed-form analytical solution for critical temperature and nonlinear post-critical temperature-deflection behaviour for nonlocal orthotropic plates subjected to thermal loading is presented. The long-range molecular interactions are represented by a nonlocal continuum framework, including orthotropy. The Von-Karman nonlinear strains are employed in deriving the governing equations. An approximate solution to the system of nonlinear partial differential equations is obtained using a perturbation type method. Series expansions up to second order of the associated field variables and the load parameter, dictating nonlinearity are employed. The behaviour in the post-critical regime is illustrated numerically by adopting an example of orthotropic Single Layer Graphene Sheet (SLGS), a widely acclaimed nano-structure, often modelled as plate. Post-critical temperature-deflection paths are presented with special emphasis on their post-critical reserve in strength and stiffness. Influence of aspect ratio and behaviour in higher modes are demonstrated. Implications of nonlocal interactions on the redistribution of in-plane forces are presented to show striking disparity with the classical plates. The obtained solution may serve as benchmark for verification of numerical solutions and may be useful in formulating simple design guidelines for plate type nanostructures liable to the thermal environment.     

Design of hybrid genetic- SVD ANFIS networks for fatigue life modelling of GRP composites

Genetic algorithm (GA) and singular value decomposition (SVD) are deployed for the optimal design of both Gaussian membership functions of antecedents and the vector of linear coefficients of consequents, respectively, of adaptive neurofuzzy inference systems (ANFIS) networks that are used for fatigue life modelling and prediction of unidirectional GRP Composites. The aim of such modelling is to show how the fatigue life varies with the variation of important parameters namely, maximum stress, stress ratio, fiber angle. It is demonstrated that SVD can be effectively used to optimally find the vector of linear coefficients of conclusion parts in ANFIS models and their Gaussian membership functions in premise parts are determined by GA.     

Integrated production scheduling and distribution planning in dairy supply chain by hybrid modelling

In this paper we address the production scheduling and distribution planning problem in a yoghurt production line of the multi-product dairy plants. A mixed integer linear programming model is developed for the considered problem. The objective function aims to maximize the benefit by considering the shelf life dependent pricing component and costs such as processing, setup, storage, overtime, backlogging, and transportation costs. Key features of the model include sequence dependent setup times, minimum and maximum lot sizes, overtime, shelf life requirements, machine speeds, dedicated production lines, typically arising in the dairy industry. The model obtains the optimal production plan for each product type, on each production line, in each period together with the delivery plan. The hybrid modelling approach is adopted to explore the dynamic behavior of the real world system. In the hybrid approach, operation time is considered as a dynamic factor and it is adjusted by the results of the simulation and optimization model iteratively. Thus, more realistic solutions are obtained for the scheduling problem in yoghurt industry by using the iterative hybrid optimization-simulation procedure. The efficiency and applicability of the proposed model and approach are demonstrated in a case study for a leading dairy manufacturing company in Turkey.     

A two-stage hybrid optimization for honeycomb-type cellular structures under out-of-plane dynamic impact

Honeycomb structures with better balance between lightweight and crashworthiness have aroused growing attentions. However, structural parameters design by traditional optimization algorithm in small design space is not sufficient to significantly enhance the specific energy absorption (SEA) with the lower peak acceleration (a_max). In this paper, a two-stage hybrid optimization for honeycomb-type cellular parameters is proposed to achieve rapid positioning of design space and significantly increase crashworthiness in a larger variable domain under out-of-plane dynamic impact. In stage I, a Taguchi-based grey correlation discrete optimization, combining Taguchi analysis, grey relational analysis, analysis of variance (ANOVA) with grey entropy measurement, is performed to determine the initial optimal value with a higher robustness and the significant influence variables. In stage II, a multi-objective design technique, namely non-nominated sorting genetic algorithm II based on surrogated model, is adopted to maximize the SEA and minimize the a_max in a relatively small design domain. And it is found that the proposed two-stage hybrid method can broaden the optimal design space compared to that of traditional method attributable to its center point positioned by stage I. And the final optimization based on the proposed strategy is superior to the original structure, i.e., the SEA is increased by 47.55% and the a_max is decreased by 80.8%. Therefore, the proposed algorithm can also be used to solve other more complicated engineering problems in a large design space with insightful design data.     

Estimations on Thermo-mechanical Dynamics of Vibration Elastomeric Isolators

This analysis deals with one of the basic problem category of vibratory systems, means the complete and complex characterization of elastic and viscous isolators behaviour under dynamic loads such as vibrations, seismic waves, shocks, etc. Usually, the dynamic characteristics of vibration isolators made by elastomeric materials are considered to have a constant shape for a certain practical case. It is ignored the thermal phenomenon inside the isolator block during the exploitation cycles and its influences on the proper characteristic parameters. This usual approximation leads to more or less significant differences between simulation and practical evolution of a vibration isolator subjected to the same dynamic load. Continuous changes of rigidity modulus and/or dissipative characteristics due to internal thermal effects imply aleatory evolution of the isolated system, unstable movements and resonance imminence danger. The partial results of this analysis dignify the linkage between thermal effects into the elastomeric isolator and its essential dynamic parameters. Using of these correlations frames the seismic shock and vibration protective devices designing and deployment areas. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)