Energetic modelling for carbon fibre reinforced carbon

In this contribution an energetic model for multi-phase materials is developed describing the influence of microstructure on different length scales as well as the evolution of phase changes. Restrictions on the energy functional are discussed. In such a non-convex framework, interfacial contributions serve for relaxing the total energy. Such models can be applied to describe the macroscopic material properties of carbon fibre reinforced carbon where phase transitions between regions of different texture of the carbon matrix are observed on nanoscale as well as columnar microstructures on microscale [2]. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A mathematical model for induction hardening including mechanical effects

We investigate a mathematical model for induction hardening of steel. It accounts for electromagnetic effects that lead to the heating of the workpiece as well as thermomechanical effects that cause the hardening of the workpiece. The new contribution of this paper is that we put a special emphasis on the thermomechanical effects caused by the phase transitions. We take care of effects like transformation strain and transformation plasticity induced by the phase transitions and allow for physical parameters depending on the respective phase volume fractions.The coupling between the electromagnetic and the thermomechanical part of the model is given through the temperature-dependent electric conductivity on the one hand and through the Joule heating term on the other hand, which appears in the energy balance and leads to the rise in temperature. Owing to the quadratic Joule heat term and a quadratic mechanical dissipation term in the energy balance, we obtain a parabolic equation with L¹ data. We prove existence of a weak solution to the complete system using a truncation argument.     

Mass Transfer in Porous Media

In this contribution, a constitutive model based on the macromechanical Theory of Porous Media (TPM) for a saturated thermo elastic porous body has been developed. The body under investigation consists of an organic and inorganic moisturized phases and a gas phase. Based on a consistent thermomechanical treatment, the governing equations and constitutive equations will be given. Thus, we obtain a mathematical concept describing the motion of the solid phase, the pressure of the gas phase, the temperature of the mixture and the biodegradation of organic material into a gas mixture of methane and carbon dioxide produced by bacterial decomposition during stable methane fermentation (biogas). (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

AN INDIVIDUAL‐BASED MODEL TO ESTIMATE THE DAILY ENERGETIC COST OF GREATER RHEAS AND ITS CONTRIBUTION ON POPULATION RECRUITMENT

Abstract An individual‐based model for estimating the energetic costs in Rhea americana was developed considering their sexual and seasonal differences in the behavioral activities. The model includes as variables the individual's characteristics, as well as corporal weight, the time spent on different activities, and the cost associated with each activity. We estimated the daily energetic demand of an adult rhea based on the activities individuals normally develop during postreproductive, nonreproductive, and reproductive seasons, differentiating between sexes. The time spent in each activity for one given animal was calculated from field observations of individuals and the estimations of energetic costs for each activity were obtained from specialized literature. The model built varied between sexes because males and females have different reproductive costs. Both models have the same general formulation but they differ in the cost associated with reproduction. In Greater Rheas, while males assume all of the incubation, the females only lay eggs communally in a single nest. Also the possibility that the individual reproduces or not was considered. The model does not allow to determine whether the energetic costs associated with the breeding are the reason why few individuals try to reproduce but it indicates that there is a clear difference in the daily energetic costs of individuals which reproduce and those which do not reproduce. Other activities associated with parental care posthatching, not taken into account here, would increase these differences, and would explain the low number of breeding attempts observed at wild.     

Towards the simulation of Internal Traverse Grinding – from mesoscale modelling to process simulations

The present work aims at the modelling and simulation of Internal Traverse Grinding of hardened 100Cr6/AISI 52100 using electro plated cBN grinding wheels. We focus on the thermomechanical behaviour resulting from the interaction of tool and workpiece in the process zone on a mesoscale. Based on topology analyses of the grinding wheel surface, two-dimensional single- and multigrain representative numerical experiments are performed to investigate the resulting load-displacement-behaviour as well as the specific heat generation due to friction and plastic dissipation. A thermoelastic-viscoplastic constitutive model is used to capture thermal softening of the material taken into account. Based on previous work, an adaptive remeshing scheme which uses a combination of error estimation and indicator methods, is applied to overcome mesh dependence. In consequence, the formulation allows to resolve the complex deformation patterns and to predict a realistic thermomechanical state of the resulting workpiece surface. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Analysis of a thermomechanical phase transition model

Subject of this work is a macroscopic thermomechanical model of phase transitions in steel. Effects like transformation strain and transformation plasticity induced by the phase transitions are considered and used to formulate a consistent thermomechanical model. The resulting system of state equations consists of a quasistatic momentum balance coupled with a nonlinear stress-strain relation, a nonlinear energy balance equation and a system of ODEs for the phase volume fractions. We prove the existence of a unique weak solution using fixed-point arguments. A key issue is a regularity analysis for the mechanical subsystem to obtain continuity of the stress tensor. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermomechanical modeling and simulation of aluminum alloys during extrusion process

The purpose of this work is to simulate the microstructure development of aluminum alloys during hot metal forming processes such as extrusion with the help of the Finite Element Method (FEM). To model the thermomechanical coupled behavior of the material during the extrusion process an appropriate material model is required. In the current work a Johnson–Cook like thermoelastic viscoplastic material model is used. To overcome the numerical difficulties during simulation of extrusion such as contact problem and element distortion an adaptive meshing system is developed and applied. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Monotone strain-stress models for shape memory alloys hysteresis loop and pseudoelastic behaviorx

To describe the behavior of Shape Memory Alloy we use a thermomechanical model, founded on a free energy which is a convex function with respect to the strain and to the martensitic volume fraction, and a concave one with respect to the temperature. The material parameters of the model are experimentally determined.Received: November 26, 2001; revised: March 20, 2002     

Alternative positional FEM applied to thermomechanical impact of truss structures

This paper presents a formulation to deal with dynamic thermomechanical problems by the finite element method. The proposed methodology is based on the minimum potential energy theorem written regarding nodal positions, not displacements, to solve the mechanical problem. The thermal problem is solved by a regular finite element method. Such formulation has the advantage of being simple and accurate. As a solution strategy, it has been used as a natural split of the thermomechanical problem, usually called isothermal split or isothermal staggered algorithm. Usual internal variables and the additive decomposition of the strain tensor have been adopted to model the plastic behavior. Four examples are presented to show the applicability of the technique. The results are compared with other authors’ numerical solutions and experimental results.     

Mathematical modeling and interpretation of reactive plasma chemistry

A problem of much recent technological interest is the analysis and interpretation of the chemistry of audiofrequency plasma enhanced chemical vapor deposition of thin films. In this process, low pressure methane gas is input into a reactor chamber and a low-current, high-voltage audiofrequency electric discharge applied. The energetic electrons thus produced bombard the methane molecules, fragmenting them, and causing radical and ion formation. These new species go on to form a range of products under various operating conditions from soot-like amorphous carbon, to diamond-like carbon. Despite the increasing experimental understanding of reactive organic plasma dynamics, the chemical kinetics of the reactions in the gas phase is still not completely understood: quite different species densities are found in different regions of the discharge system implying spatially inhomogeneous physiochemical processes. The experimental problem is first outlined, and a simple physiochemically-motivated reaction-advection-diffusion model of the reactive plasma chemistry described. Results of the kinetics models are presented and discussed in terms of the input model parameters and related to surface deposition.     

Thermomechanical Simulation of the Electron Beam Melting Process for TiAl6V4

In the present contribution a nonlinear thermomechanical finite element model with temperature dependent material parameters is used to simulate the electron beam melting process for TiAl6V4. The beam is modeled as a moving heat source and the isentropic split solution scheme is applied. The temperature and stress distribution during the process were simulated and showed sound results from a qualitative point of view. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Global solution to the full one-dimensional Frémond model for shape memory alloys

In this paper, we prove the existence and uniqueness of the solution to the one-dimensional initial-boundary value problem resulting from the Frémond thermomechanical model of structural phase transitions in shape memory materials. In this model, the free energy is assumed to depend on temperature, macroscopic deformation and phase fractions. The resulting equilibrium equations are the balance laws of (linear) momentum and energy, coupled with an evolution variational inequality for the phase fractions. Fourth-order regularizing terms in the quasi-stationary momentum balance equation are not necessary, and, as far as we know for the first time, all the non-linear terms of the energy balance equation are taken into account.     

The Cyclic Thermomechanical Coupled Problem of Thermal Gradients in Friction Railway Disc Brakes

The emergency braking distance of a TGV train at a speed of 320 km/h is almost 3000 m. Dry running brakes are reliable due to their predictable response to external stress and are thus used in such applications. The kinetic energy is dissipated proportionately into the brake disc and brake pad. This induced dissipation of energy and the high frequency of brake application cause high temperatures. These immense temperature changes could cause macroscopic cracks leading to failure of discs and accidents [1]. Generally, hot spotting describes the development of thermal localizations and can lead to early damage, early wear, pad performance loss, and squeal noise [2]. The aim of the present study is to improve a disc-pad transient numerical model by use of a coupled thermomechanical method. It is based on full 3-d thermomechanical calculations taking disc rotation into account. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Deformation and strength of hybrid composites reinforced with unidirectional fibers. 1. Numerical models

The hybrid composite consists of n(n > 2) jointly working phases. We define the thermomechanical characteristics and strength of composites by filling and reinforcing materials thermomechanical characteristics and strength basing on the suggestion that thin and strong fibre reinforced composite is quasiuniform, and there is a continuous contact between the filling medium and reinforcing fibers. The development of a mathematical model of the design under consideration has been based on following assumptions: 1) for irreversible processes, the classical thermodynamic postulates are valid, and they are introduced as functions of state of internal energy and entropy; 2) for a solitary volume of materials, internal energy is assumed to be proportional to the volume fraction of the j-th phase v_j; 3) for the material pressure limit conditions just before the essential damage, it is suggested that: a) the whole composite as well as the components are steady, i.e. Drukker's postulate is valid; b) the deformation law associated with the corresponding strength surface is valid, and c) small values of increases in plastic deformation play the leading role. The strength of unidirectionally reinforced hybrid monolayers is predicted by using a linear programming code.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 186–192, March–April, 1995.The studies were carried out with financial support of the International Scientific Fund founded by G. Soros.     

Hydrogen Storage: Modeling and Analytical Results

We present a thermomechanical model describing hydrogen storage by use of metal hydrides. The problem is considered as a phase transition phenomenon. The model is recovered by continuum mechanics laws, using a generalization of the principle of virtual power accounting for microscopic movements related to the phase transition. The resulting nonlinear PDE system is investigated from the point of view of existence, uniqueness, and regularity of solutions.     

Method of thermomechanical characteristics as a means of studying crosslinking and degradation processes in multicomponent polymer systems

A method of obtaining and interpreting thermomechanical curves has been developed to facilitate the study of crosslinking and degradation processes in multicomponent polymer systems. The method is highly sensitive and makes it possible to study on small specimens a variety of structural changes governed by the nature of the polymer, by the macrostructure of the test pieces, by the mixture composition, and by the action of various external factors. It is also shown that the thermomechanical characteristics can conveniently be used as a criterion for evaluating working properties (e.g., heat resistance, etc.).Mekhanika Polimerov. Vol. 3, No. 3, pp. 387–391, 1967     

移动热源作用下基于分数阶应变的三维弹性体热-机响应

基于分数阶应变理论,研究了移动热源作用下三维弹性体的热-机动态响应.将分数阶应变理论下的控制方程应用于三维半空间模型,通过Laplace积分变换、双重Fourier变换及其数值反变换对控制方程进行求解,得到了不同热源速度和不同分数阶参数下,无量纲温度、应力、应变和位移的分布规律.结果表明,分数阶应变参数对机械波影响显著...     

A thermo-mechanical energetic cohesive zone model accounting for Kapitza interfaces

The objective of this contribution is to study computational aspects of modeling thermo-mechanical solids containing mechanically energetic, geometrically non-coherent Kapitza interfaces under cyclic loading. The interface is termed energetic in the sense that it possesses its own energy, entropy, constitutive relations and dissipation. To date, classical thermo-mechanical cohesive zone models do not account for elastic interfaces. Therefore we propose a novel interface model that couples the classical cohesive zone formulation to the interface elasticity theory under the Kapitza assumption within a thermo-mechanical framework. In other words, such an interface model allows for discontinuities in geometry, temperature and normal stress fields, while not permitting a jump in the normal heat flux across the interface. The equations governing a fully non-linear transient problem are given. In particular, a comparison is made between the results of the classical thermo-mechanical cohesive zone model and our novel (cohesive + energetic Kapitza) interface formulation. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Sul criterio dell'energia per la stabilitá di un sistema termomeccanico

Summary The energy criterion for mechanical stability asserts that the stable configurations are those that minimize the potential energy. Recent studies have shown that the energy criterion can be extended to stability of thermomechanical systems under suitable environment conditions, provided that the «stored energy» is interpreted as the equilibrium free-energy at the environmental temperature ^e. The aim of this paper is to provide a contribution to a general theory of thermomechanical stability. Essentially we have restated the theory for general materials introduced by Gurtin with a new framework in the light of recent theories of Noll and Coleman-Owen on simple materials and on thermodynamical potentials. We define a «thermomechanical system» which posseses two main features: i) state space has a «natural topology» depending on the thermodynamical behaviour of system; ii) internal energy E and entropy S are not supposed to exist but are expressely obtained with their smoothness properties.

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Lavoro eseguito nell'ambito del G.N.F.M. del C.N.R,     

Modeling and computation of metal powder compaction processes

In this short communication the numerical treatment of a thermomechanical consistent finite strain viscoplasticity model for metal powder compaction is discussed. The convex single surface yield function evolves according to two evolution equations and remains convex under all loading conditions. The very challenging numerical treatment on local level for integrating the constitutive model requires particular globally convergent Newton-like method with inequality constraints so that a stable solution scheme results. This is embedded into a time-adaptive finite element program which makes use of diagonally-implicit Runge-Kutta methods combined with a Multilevel-Newton algorithm. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)