Thermo-mechanical modelling of cellular hybrid refractories

Refractory materials are subjected to both quasi-static and dynamic thermal loading (thermal shock) causing damage up to mechanical failure. Typical refractories are magnesia carbon bricks consisting of periclase (MgO) and carbon inclusions. Recently, a significant improvement of the thermo-mechanical behaviour could be achieved by cellular hybrid composites made of periclase-filled carbon foams. The present contribution focuses on MgO-filled carbon foams and the investigation and optimisation of the structure-property relationship with respect to a reduction of thermally induced stresses and damage. It is a transient as well as static, fully coupled thermo-mechanical problem. According to the fact that, in general, refractories are brittle materials a linear elastic model, with a damage criterion was used. To optimise the structural morphology of the cellular refractories, the effect of micro structural changes has been determined. For the investigation of the thermal shock! behaviour, the results correlate very well with the experimentally motivated Hasselman relation. There is a significant size effect depending on the pore size. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Generalized thermoelasticity of beams under partial thermal shock

In this paper, the generalized thermoelastic response of a beam subjected to a partial lateral thermal shock is analysed. The beam is made of homogeneous and isotropic material and is assumed to follow the Hooke law for its constitutive material. The displacement gradient is small and the linear form of strain-displacement relations is used for the beam. The equations of motion and the boundary conditions of the beam are derived based on Hamilton’s principle. According to the first and second laws of thermodynamics, a non-Fourier constitutive equation is employed to derive the energy equation of the beam. The non-Fourier effects lead to the constitutive equation of the hyperbolic type and thus the thermal and mechanical waves can be observed. The propagation of waves in the beam are simulated by finite element model and the wave reflections for different types of boundary conditions are studied. The relaxation time is considered as a significant parameter and results show that energy absorption of the structure and the wave propagation speed depend upon this parameter.     

Whirl characteristics of a flexible liquid-filled rotor under thermal shock

In this paper, the whirl characteristics of a flexible liquid-filled rotor subjected to thermal shock are investigated. On the basis of the Hamilton principle, the whirl frequency equation of the rotor system is derived. Using Laplace transform, the analytical model of the temperature field of the rotor is obtained. The validity of the developed temperature model is demonstrated by comparing with the finite element results. Then, the thermal axial force exerted on the rotor is calculated and the influence factors are studied. The system stability is analyzed in terms of the whirl frequency equation. The reasonability of the predict model for system stability is verified, and a good agreement can be seen in the comparison of the obtained results based on the presented analytical method with published data. Finally, the critical spinning speed of the rotor system is analyzed, and the effects of some main parameters on system critical speed are investigated.     

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.     

Stability analysis of coupled structural acoustics PDE models under thermal effects and with no additional dissipation

In this study we consider a coupled system of partial differential equations (PDE's) which describes a certain structural acoustics interaction. One component of this PDE system is a wave equation, which serves to model the interior acoustic wave medium within a given three dimensional chamber Ω. This acoustic wave equation is coupled on a boundary interface Γ₀ to a two dimensional system of thermoelasticity: this thermoelastic PDE is composed in part of a structural beam or plate equation, which governs the vibrations of flexible wall portion Γ₀ of the chamber Ω. Moreover, this elastic dynamics is coupled to a heat equation which also evolves on Γ₀, and which imparts a thermal damping onto the entire structural acoustic system. As we said, the interaction between the wave and thermoelastic PDE components takes place on the boundary interface Γ₀, and involves coupling boundary terms which are above the level of finite energy. We analyze the stability properties of this coupled structural acoustics PDE model, in the absence of any additive feedback dissipation on the hard walls Γ₁ of the boundary . Under a certain geometric assumption on Γ₁, an assumption which has appeared in the literature in connection with structural acoustic flow, and which allows for the invocation of a recently derived microlocal boundary trace estimate, we show that classical solutions of this thermally damped structural acoustics PDE decay uniformly to zero, with a rational rate of decay.     

On a symplectic analytical singular element for cracks under thermal shock considering heat flux singularity

In a precise numerical modelling of cracks under thermal shock, the singularity issue resulted from heat flux should also be considered in addition to the one resulted from stress. The assumptions of constant temperature distribution usually adopted in the existing studies may lead to significant error. The concerned problem involves the discretization in both space and time domains. Numerical error resulted from the singularity issues in the space domain may be accumulated in the time domain. Hence, a unified framework which integrates reliable methods for both space and time domains are desired. In the present contribution, the classic thermal stress problem is restudied under the Hamiltonian system and the eigen functions are obtained analytically. A symplectic analytical singular element (SASE) for thermal stress analysis is reformulated based on the existing ones for thermal conduction and stress analyses. The singularity issues of both stress and heat flux are considered. A unified framework is formed with the precise time domain expanding algorithm (PTDEA) for the time domain and the formulated SASE for the space domain. A self-adaptive technique is used for the PTDEA to improve the numerical efficiency. The time dependent fracture parameters i.e., heat flux intensity factors (HFITs) and the mixed mode thermal stress intensity factors (TSIFs) can be solved accurately without any post-processing. Numerical examples are given for verification and validation of the proposed method.     

Electromagnetic and thermal modelling of axisymmetric induction furnaces

A numerical method to describe the thermo-electric behavior of an induction heating furnace is introduced. It is obtained by using an enthalpy formulation concerning the thermal model and an integral representation of the electromagnetic potential in an unbounded domain. A BEM-FEM method is used and an iterative algorithm together with numerical results for an industrial heating system are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multivariate reliability modelling based on dependent dynamic shock models

In this paper, we stochastically model positively dependent multivariate reliability distributions based on stochastically dependent dynamic shock models. In the first part, we consider a shock model with delayed failures. This shock model will be used to construct a class of absolutely continuous multivariate reliability distributions. Explicit parametric forms for the multivariate reliability functions are suggested. Multivariate ageing properties and dependence structures of the class are discussed as well. In the second part, we obtain two types of absolutely continuous multivariate exponential distributions based on further generalized shock models.     

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.     

Stochastic thermal shock problem in generalized thermoelasticity

In this work, we consider the problem of a half space in the context of the theory of generalized thermoelasticity with one relaxation time. Realistically, the boundary conditions of the problem are considered to be stochastic. Laplace transform technique is used to solve the problem. The boundary conditions are considered to be of a type white noise. The inverse transforms are obtained in an approximate manner using asymptotic expansions valid for small values of time. Numerical results are given and represented graphically. Finally, a comparison with the ideal case when the boundary conditions are deterministic is carried out.     

Three-dimensional thermal shock problem of generalized thermoelastic half-space

A three-dimensional model of the generalized thermoelasticity with one relaxation time is established. The resulting non-dimensional coupled equations together with the Laplace and double Fourier transforms techniques are applied to a specific problem of a half space subjected to thermal shock and traction free surface. The inverses of Fourier transforms and Laplace transforms are obtained numerically by using the complex inversion formula of the transform together with Fourier expansion techniques. Numerical results for the temperature, thermal stress, strain and displacement distributions are represented graphically.     

A BEM for transient thermoelastic analysis of a functionally graded layer on a homogeneous substrate under thermal shock

Transient thermoelastic analysis of isotropic and linear thermoelastic bimaterials, which are constituted by a functionally graded (FG) layer attached to a homogeneous substrate, subjected to thermal shock is presented in this paper. For this purpose, a boundary element method for transient linear coupled thermoelasticity is developed. The material properties of the FG layer are assumed to be continuous functions of the spatial coordinates. The boundary-domain integral equations are derived by using the fundamental solutions of linear coupled thermoelasticity for the corresponding isotropic, homogeneous and linear thermoelastic solids in the Laplace-transformed domain. For the numerical solution, a collocation method with piecewise quadratic approximation is implemented. Numerical results for the dynamic stress intensity factors are presented and discussed. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effects of the material gradation on the SIFs of a crack in a 2-D FGM plate under thermal shock

Crack analysis of linear coupled thermoelasticity in two-dimensional, isotropic, non-homogeneous and linear elastic functionally graded materials subjected to thermal shock is performed by using a boundary-domain element method. The material parameters are assumed to be continuous functions of the spatial coordinates. Fundamental solutions of linear coupled thermoelasticity for the corresponding isotropic, homogeneous and linear elastic solids in Laplace-transformed domain are applied in the boundary-domain integral formulation. A collocation method is implemented for the numerical solution. Numerical examples for an exponential gradation of the material parameters are presented and discussed. The influences of the material gradation on the stress intensity factors are investigated. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Families of relations modelling preferences under incomplete information

Let us consider a preferential information of type preference–indifference–incomparability (P, I, J), with additional information about differences in attractiveness between pairs of alternatives. The present paper offers a theoretical framework for the study of the “level of constraint” of this kind of partial preferential information. It suggests a number of structures as potential models being less demanding than the classical one in which differences in utilities can be used to represent the comparison of differences in attractiveness. The models are characterized in the more general context of families of non-complete preference structures, according to two different perspectives (called “semantico-numerical” and “matrix”). Both perspectives open the door to further practical applications connected with elicitation of the preferences of a decision maker.