Thermomechanical models, development

Over the last decade considerable effort of the tectonics community has been directed towards the development of thermomechanical models that describe the collisional history and the internal dynamics of orogenic belts and continental plateaus (e.g., Beaumont et al. 2001, 2004 Koons et al. 2002). These models are commonly tested against thermobarometric, thermochronologic, and geochronologic data. However, by definition, these data sets only provide constraints on rates of rock uplift or exhumation the surface response to tectonic... 

Thermomechanical models for FRP materials were first developed in the 1980s. One of the first thermomechanical models for FRP materials was introduced by Springer in 1984 [1], where the degradation of mechanical properties was empirically related to the mass loss. In 1985, Chen et al. [2] added a mechanical model to the thermochemical model presented by Griffis et al. in 1981 [3] mechanical properties at several specified temperature points were assembled into a finite element formulation. Griffis et al. [4] introduced an updated version of Chen s model in 1986, whereby an extrapolation process was used to obtain the data in a higher temperature range. 

In 2004, Gibson et al. [10] then presented an upgraded version by adding a new mechanical model. A function that assumes the relaxation intensity is normally distributed over the transition temperature was used to fit the temperature-dependent Young s modulus. Furthermore, in order to consider the resin decomposition, each mechanical property was modified by a power law factor. Predictions of mechanical responses based on the thermomechanical models were also performed by Bausano et al. [11] and Halverson et al. [12]. Mechanical properties were correlated to temperatures through dynamic mechanical analysis (DMA) but no special temperature-dependent mechanical property models were developed. 

The above-mentioned thermomechanical models only consider the elastic behavior of materials. Boyd et al. [13] reported on compression creep rapture tests performed on unidirectional laminates of E-glass/vinylester composites subjected to a combined compressive load and one-sided heating. Models were developed to describe the thermoviscoelasticity of the material as a function of time and temperature. In their work, the temperature-dependent mechanical properties were determined by fitting the Ramberg-Osgood equations and the temperature profiles were estimated by a transient 2D thermal analysis in ANSYS 9.0. 

The material constitutive model plays an important role in the development of thermomechanical models for microelectronic packaging assembly. Under thermomechanical loading, solder alloy undergoes elastic and inelastic de-... 

The development of thermomechanical models typically involves (a) the development of constitutive models for the solder alloy and other materials in the packaging assembly, (b) the development of geometry models to represent the solder interconnects and the packaging assembly, and (c) the development of failure predictive models for the various material systems in the assembly. The thermomechanical models, when subjected to thermal excursions seen dixring accelerated qualifications or during field-use, will identify the location of failure, mode of failixre, and time to failure in various parts of the packaging assembly. Prior to usage, the models should be validated with experimental test data. 

Up-front thermomechanical modeling and physics-based reliability prediction of lead-free solder joints could save significant amount of cost and time in microsystem product develop-... 

The analysis of structure development is based on the combination of a thermomechanical model and of an experimental study of structures and morphologies inside the films. 

A study of the effect of the mesophase layer on the thermomechanical behaviour and the transfer mechanism of loads between phases of composites will be presented in this study. Suitable theoretical models shall be presented, where the mesophase is taken into consideration as an additional intermediate phase. To a first approximation the mesophase material is considered as a homogeneous isotropic one, while, in further approximations, more sophisticated models have been developed, in which the mesophase material is considered as an inhomogeneous material with progressively varying properties between inclusions and matrix. Thus, improvements of the basic Hashin-Rosen models have been incorporated, making the new models more flexible and suitable to describe the real behaviour of composites. 

The above model has been successfully used to describe the thermomechanical behaviour of iron-particle reinforced resins. More precisely, the importance of this model is that it provides a quantitative means for assessing the adhesion efficiency between the phases and its effect on the thermomechanical properties of the composite. Moreover, by using this model the thermomechanical behaviour, as well as the extent of the mesophase developed in particulates could be described. The... 

Computational design and life prediction codes should be developed explicitly for CMCs. Computational models and predictions should be validated by subelement and component tests that include representative thermomechanical loadings. Rigorous analyses of failure modes should then be performed. 

Thereby, for chosen experimental objects were determined unknown parameters of developed mathematical model hyperelastic state constant, weighting coefficient and relaxation spectmm properties. Prediction results of thermomechanical curves trend successfully demonstrated prediction abihty of introduced mathematical description of thick cross-linked polymers viscoelastic pliability in all their physical states (Figure). 

As an example, showing that on the base of the developed model and put in it calculated theoretically values of constants, it is possible to cany out good conformed to cjqteri-mental results numerical experiments of the evaluation of cross-linked polymers defor-mative behavior, which progresses without destraction of their chemical stracture, were predicted resrrlts of thermomechanical experiment of experimental objects (Figure 3). 

The above understanding forms the basis for the development of thermophysical and thermomechanical property sub-models for composite materials at elevated and high temperatures, and also for the description of the post-fire status of the material. By incorporating these thermophysical property sub-models into heat transfer theory, thermal responses can be calculated using finite difference method. By integrating the thermomechanical property sub-models within structural theory, the mechanical responses can be described using finite element method and the time-to-failure can also be predicted if a failure criterion is defined. 

Like other polymeric materials, rheological modeling was first attempted to predict the constitutive behavior of SMPs. Although earher efforts [5-8] using rheological models were able to describe the characteristic thermomechanical behavior of SMPs, loss of the strain storage and release mechanisms usually led to limited prediction accuracy. Also, the models were 1-D and could only predict the behavior under a uniaxial stress condition, such as 1-D tension. Furthermore, these models can oidy work for a small strain. They cannot predict the thermomechanical behavior of SMPs with finite strain, which is the case for most SMPs. Later, meso-scale models [9,10] were developed to predict the constitutive behavior of SMPs. However, one limitation is that a meso-scale model cannot understand the shape memory mechanisms in detail because the mechanisms controlling the shape memory are in a molecular... 

It is noted that while the majority of constitutive modeling focuses on thermally induced dual-shape memory behavior, triple-shape and multishape SMPs have been developed recently and they call for constimtive modeling [1]. In addition, the effect of programming temperature and strain rate on the constimtive behavior also needs modeling [2]. Furthermore, some recent smdies have found that while the shape recovery ratio can be 100%, other mechanical properties such as recovery stress or modulus become smaller and smaller as the thermomechanical cycles increase, which has been explained by the shape memory effect in the microscopic scale [24]. Obviously, these new findings also call for constitutive modeling. 

In this study, the same parameters calibrated in modeling the constitutive behavior of the SMP programmed by 30% pre-strain level were also used to predict the thermomechanical behavior of the same SMP programmed by a 10% pre-strain level (see Figure 4.13(b)). It is clear that, with the same set of parameters, the model predicted the constitutive behavior well for the SMP programmed by the 10% pre-strain. This further validated the developed model. 

A structure evolving, damage-allowable thermoviscoplastic model has been developed and reasonably captured the most essential shape memory response of the SMP based syntactic foam during this process. A finite deformation, continuum constimtive model has been developed to study the thermomechanical behavior of the SMP based self-healing syntactic... 

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