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Within polycrystalline porous ceramics used in automotive applications as diesel particulate filters, it is evidenced that during cooling from firing temperature micro cracks are gradually formed. The cracks are formed as a consequence of strong thermal anisotropy of grains. Typically these micro cracks are granting better thermal shock resistance, with respect to dense materials, but reduce stiffness. The reduction can be quantified by measuring the drop in elastic properties of bulk material which, depending on the level of porosity, can decrease even by 50% with respect to its value at high temperature. It is further observed that upon subsequent heating these cracks are closing and partially or totally healing at very high temperatures. Such peculiar behavior results in partial or complete recovery of the elastic properties of bulk material upon completing one thermal cycle. Despite its evident practical application, still there is no constitutive description of this phenomenon, capable of predicting the evolution of Young's modulus as a function of temperature history. For reliable numerical simulation of this phenomenon, it is required to model fracture. To model inter-crystalline fracture, an effective strategy is to use cohesive elements, since crack patterns are a priori known. Major limitation of this approach is that the cohesive elements already implemented within commercial codes cannot take into account crack healing upon subsequent heating. In this study new cohesive element is developed and numerically implemented within ABAQUS commercial finite element code, capable to model crack opening, closing and healing. Further on, a computer code is generated to build numerical model of porous ceramic specimens that takes into account experimentally measured crystallographic orientation and porosity, and models the microstructure by using Voronoi polygons. The developed numerical tools serve as a framework for more realistic simulations, required to study the hysteresis in elastic properties within porous ceramics provoked by thermal cyclic. In a subsequent phase, an inverse analysis procedure is developed, in which macroscopic properties are used to calibrate parameters entering into micro crack model. The approach is centered on a minimization of a discrepancy function designed to quantify the difference between experimentally measured quantities and their computed counterpart. The model is calibrated on the basis of experimental data regarding the drop of bulk Young's modulus with decrease of temperature. Developed procedure is tested with porous cordierite sample, and obtained results are quit promising despite the current limitation of using only two-dimensional model.
Compressive strength of concrete is highly temperature dependent. Using experimentally obtained relations as input for numerical simulations is problematic. A more accurate and reliable material model results from taking the coupling between thermal and mechanical behaviour into account. In this contribution, a coupled finite element solution on mesoscale geomtries is shown to exhibit a loss in compressive strength at higher temperatures. This is purely a result of the incompatible expansion of mortar matrix and aggregates, with no explicit temperature dependency of the employed constitutive models.
A three-phase transport model for high-temperature concrete simulations validated with X-ray CT data
(2021)
Concrete exposure to high temperatures induces thermo-hygral phenomena, causing water phase changes, buildup of pore pressure and vulnerability to spalling. In order to predict these phenomena under various conditions, a three-phase transport model is proposed. The model is validated on X-ray CT data up to 320 ◦C, showing good agreement of the temperature profiles and moisture changes. A dehydration description, traditionally derived from thermogravimetric analysis, was replaced by a formulation based on data from neutron radiography. In addition, treating porosity and dehydration evolution as independent processes, previous approaches do not fulfil the solid mass balance. As a consequence, a new formulation is proposed that introduces the porosity as an independent variable, ensuring the latter condition.
The Perfectly Matched Layer (PML) method is an efficient approach to imposing radiation conditions at the bounded region of interest in case of wave propagation in unbounded domains. This paper presents and validates 3D FE/PML numerical schemes based on two different PML formulations for homogeneous and inhomogeneous geological media exhibiting discrete or continuous inhomogeneity. In the equation of motion for the PML domain the applied stretching behavior is expressed either as complex material properties or as complex coordinates. Both PML formulations are implemented in the FEM and verified against analytical solutions. Three different types of material inhomogeneity are considered: layered half-space, continuously inhomogeneous half-space with linear velocity profile and continuously inhomogeneous half-space with nonlinear velocity profile. Sensitivity analyses are conducted, and the performance of the developed numerical schemes is investigated taking into account a broad variation of the PML parameters. Recommendations are given for the optimal values of the PML parameters for the case of homogeneous and inhomogeneous geological media.
In this paper, a new methodology based on the Hill–Mandel lemma in an FE² sense is proposed that is able to deal with localized deformations. This is achieved by decomposing the displacement field of the fine scale model into a homogeneous part, fluctuations, and a
cracking part based on additional degrees of freedom (X¹)—the crack opening in normal and tangential directions. Based on this decomposition, the Hill–Mandel lemma is extended to relate coarse and fine scale energies using the assumption of separation of scales such
that the fine scale model is not required to have the same size as the corresponding
macroscopic integration point. In addition, a procedure is introduced to mimic periodic
boundary conditions in the linear elastic range by adding additional shape functions for the boundary nodes that represent the difference between periodic boundary conditions and pure displacement boundary conditions due to the same macroscopic strain. In order to decrease the computational effort, an adaptive strategy is proposed allowing different
macroscopic integration points to be resolved in different levels on the fine scale.