scholarly journals Effective balance equations for poroelastic composites

2020 ◽  
Vol 32 (6) ◽  
pp. 1533-1557
Author(s):  
Laura Miller ◽  
Raimondo Penta
Keyword(s):  
Spatial Scales ◽  
Fluid Phase ◽  
Positive Definiteness ◽  
Elasticity Tensor ◽  
Linear Elastic ◽  
Biot’S Coefficient ◽  
The Matrix ◽  
The Given ◽  
Fluid Interaction ◽  
Interaction Problem

Abstract We derive the quasi-static governing equations for the macroscale behaviour of a linear elastic porous composite comprising a matrix interacting with inclusions and/or fibres, and an incompressible Newtonian fluid flowing in the pores. We assume that the size of the pores (the microscale) is comparable with the distance between adjacent subphases and is much smaller than the size of the whole domain (the macroscale). We then decouple spatial scales embracing the asymptotic (periodic) homogenization technique to derive the new macroscale model by upscaling the fluid–structure interaction problem between the elastic constituents and the fluid phase. The resulting system of partial differential equations is of poroelastic type and encodes the properties of the microstructure in the coefficients of the model, which are to be computed by solving appropriate cell problems which reflect the complexity of the given microstructure. The model reduces to the limit case of simple composites when there are no pores, and standard Biot’s poroelasticity whenever only the matrix–fluid interaction is considered. We further prove rigorous properties of the coefficients, namely (a) major and minor symmetries of the effective elasticity tensor, (b) positive definiteness of the resulting Biot’s modulus, and (c) analytical identities which allow us to define an effective Biot’s coefficient. This model is applicable when the interactions between multiple solid phases occur at the porescale, as in the case of various systems such as biological aggregates, constructs, bone, tendons, as well as rocks and soil.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

scholarly journals Integrated Recycling Process of Matrices of Organic Moulding Sands

2013 ◽  
Vol 58 (3) ◽  
pp. 809-812 ◽  
Author(s):  
R. Dańko
Keyword(s):  
Recycling Process ◽  
Conceptual Approach ◽  
Assessment Index ◽  
Experimental Stand ◽  
Synthetic Resins ◽  
The Matrix ◽  
Ignition Loss ◽  
On Line ◽  
The Given ◽  
Reclamation Process

Abstract The idea and experimental verification of assumptions of the integrated recycling process of matrices of uniform self-hardening moulding sands with synthetic resins, leading to obtaining moulding sands matrix of expected quality - is presented in the hereby paper. The basis of the presented process constitutes a combination of the method of forecasting averaged ignition losses of moulding sands after casting and defining the range of necessary matrix reclamation treatments in order to obtain its full recycling. Simultaneously, the empirically determined dependence of dusts amounts emitted during the reclamation process of the matrix from the given spent sand on the ignition loss values (which is the most proper assessment index of the obtained reclaimed material quality) was taken into account. The special experimental stand for investigations of the matrix recycling process was one of the elements of the conceptual approach and verification of its assumptions. The stand was equipped with the system of current on-line control of the purification degree of matrix grains from organic binder remains. The results of own investigations, allowing to combine ignition loss values of spent moulding sands after casting knocking out with amounts of dusts generated during the mechanical reclamation treatment of such sands, were utilized in the system.

scholarly journals State estimation for bilinear impulsive control systems under uncertainties

2018 ◽  
pp. 35-41 ◽  
Author(s):  
Oxana G. Matviychuk
Keyword(s):  
Differential Equations ◽  
State Estimation ◽  
Control Systems ◽  
Uncertain Systems ◽  
Impulsive Control ◽  
Compact Set ◽  
The Matrix ◽  
Initial States ◽  
Impulsive Control Systems ◽  
The Given

The state estimation problem for uncertain impulsive control systems with a special structure is considered. The initial states are taken to be unknown but bounded with given bounds. We assume here that the coefficients of the matrix included in the differential equations are not exactly known, but belong to the given compact set in the corresponding space. We present here algorithms that allow to find the external ellipsoidal estimates of reachable sets for such bilinear impulsive uncertain systems.

scholarly journals Transformation of land use pattern in the East Borsod coal basin from the beginning of minig industry to the political changes

2016 ◽  
Vol 10 (3-4) ◽  
pp. 223-231
Author(s):  
László Sütő ◽  
Erika Homoki ◽  
Zoltán Dobány ◽  
Péter Rózsa
Keyword(s):  
Land Cover ◽  
Human Disturbance ◽  
The Political ◽  
Early 20Th Century ◽  
Late Period ◽  
Topographic Map ◽  
Coal Basin ◽  
Land Use Pattern ◽  
The Matrix ◽  
The Given

Historical geographic studies on land cover may support the understanding of the recent state. Focusing on coal mining, this process was followed and analyzed in the case of the East Borsod Coal Basin from the early 20th century to the political change. The contemporaneous maps and manuscripts concerning the mining were evaluated using geoinformatic techniques. Moreover, digitalized topographic map coming from the early and late period of mining (1924 and 1989, respectively) were analyzed. To determine the degree of human disturbance hemerobic relations and changes of the given land cover patches were quantified on the basis of the maps of the three military surveys, too. It can be stated that montanogenic subtype of an industrialagricultural landscape has been formed in the Bükkhát area. Beside the concentrated artificial surfaces, however, relative dominance of forest forming the matrix of the landscape remained.

scholarly journals COMPUTATIONAL MICROSTRUCTURE-BASED ANALYSIS OF RESIDUAL STRESS EVOLUTION IN METAL-MATRIX COMPOSITE MATERIALS DURING THERMOMECHANICAL LOADING

2021 ◽  
Vol 19 (2) ◽  
pp. 241
Author(s):  
Ruslan Balokhonov ◽  
Varvara Romanova ◽  
Eugen Schwab ◽  
Aleksandr Zemlianov ◽  
Eugene Evtushenko
Keyword(s):  
Residual Stress ◽  
Metal Matrix ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Matrix Composites ◽  
Two Phase ◽  
Irregular Shapes ◽  
The Matrix ◽  
Stress Formation ◽  
Mechanical Fragmentation

A technique for computer simulation of three-dimensional structures of materials with reinforcing particles of complex irregular shapes observed in the experiments is proposed, which assumes scale invariance of the natural mechanical fragmentation. Two-phase structures of metal-matrix composites and coatings of different spatial scales are created, with the particles randomly distributed over the matrix and coating computational domains. Using the titanium carbide reinforcing particle embedded into the aluminum as an example, plastic strain localization and residual stress formation along the matrix-particle interface are numerically investigated during cooling followed by compression or tension of the composite. A detailed analysis is performed to evaluate the residual stress concentration in local regions of bulk tension formed under all-round and uniaxial compression of the composite due to the concave and convex interfacial asperities.

scholarly journals ВДОСКОНАЛЕНА ПОЛІНОМІАЛЬНО-СКЛАДНА АТАКА ВІДНОВЛЕННЯ ВІДКРИТОГО ТЕКСТУ НА РАНЦЕВИЙ ШИФР НА ОСНОВІ МАТРИЦЬ

2020 ◽  
pp. 67-74
Author(s):  
Олексій Сергійович Вамболь
Keyword(s):  
Discrete Logarithm ◽  
Public Information ◽  
Galois Field ◽  
Secret Key ◽  
The Matrix ◽  
Encryption Schemes ◽  
Shared Secret ◽  
Symmetric Key ◽  
Asymmetric Encryption ◽  
The Given

Asymmetric ciphers are widely used to ensure the confidentiality of data transmission via insecure channels. These cryptosystems allow the interacting parties to create a shared secret key for a symmetric cipher in such a way that an eavesdropper gets no information useful for cryptanalysis. Network security protocols that use asymmetric ciphers include TLS, S/MIME, OpenPGP, Tor, and many others. Some of the asymmetric encryption schemes are homomorphic, that is, that they allow calculations on encrypted data to be performed without preliminary decryption. The aforesaid property makes possible using these cryptosystems not only for symmetric key establishment but also in several areas of application, in particular in secret voting protocols and cloud computing. The matrix-based knapsack cipher is a new additively homomorphic asymmetric encryption scheme, which is based on the properties of isomorphic transformations of the inner direct product of diagonal subgroups of a general linear group over a Galois field. Unlike classic knapsack encryption schemes, the cryptographic strength of this cipher depends on the computational complexity of the multidimensional discrete logarithm problem. Despite some useful properties, further research into the cryptographic strength of the matrix-based knapsack cipher has found serious drawbacks inherent in this cryptographic scheme. In the given paper an improved polynomial-time plaintext-recovery attack on the matrix-based knapsack cipher is proposed. Applying this cryptanalytic method requires only public information and has time complexity O(t1.34), where t denotes the decryption time of the attacked cryptosystem. The aforementioned attack is more productive and easier to implement in software in comparison with the original one. The advantages of the proposed method are due to using in its algorithm the simple and relatively fast matrix trace operation instead of more complex and slower transformations.

Micromechanics Approach for the Overall Elastic Properties of Ceramic Matrix Composites Incorporating Defect Structures

2020 ◽  
Author(s):  
Rajesh S. Kumar
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Ceramic Matrix Composites ◽  
Ceramic Matrix ◽  
Volume Shrinkage ◽  
Matrix Composites ◽  
Defect Structures ◽  
Linear Elastic ◽  
Elastic Tensor ◽  
The Matrix

Abstract Initial mechanical behavior of Ceramic Matrix Composites (CMCs) is linear until the proportional limit. This initial behavior is characterized by linear elastic properties, which are anisotropic due to the orientation and arrangement of fibers in the matrix. The linear elastic properties are needed during various phases of analysis and design of CMC components. CMCs are typically made with ceramic unidirectional or woven fiber preforms embedded in a ceramic matrix formed via various processing routes. The matrix processing of interest in this work is that formed via Polymer Impregnation and Pyrolysis (PIP). As this process involves pyrolysis process to convert a pre-ceramic polymer into ceramic, considerable volume shrinkage occurs in the material. This volume shrinkage leads to significant defects in the final material in the forms of porosity of various size, shape, and volume fraction. These defect structures can have a significant impact on the elastic and damage response of the material. In this paper, we develop a new micromechanics modeling framework to study the effects of processing-induced defects on linear elastic response of a PIP-derived CMC. A combination of analytical and computational micromechanics approaches is used to derive the overall elastic tensor of the CMC as a function of the underlying constituents and/or defect structures. It is shown that the volume fraction and aspect ratio of porosity at various length-scales plays an important role in accurate prediction of the elastic tensor. Specifically, it is shown that the through-thickness elastic tensor components cannot be predicted accurately using the micromechanics models unless the effects of defects are considered.

Micromechanics Approach for the Overall Elastic Properties of Ceramic Matrix Composites Incorporating Defect Structures

2021 ◽  
Author(s):  
Rajesh Kumar
Keyword(s):  
Elastic Properties ◽  
Volume Fraction ◽  
Ceramic Matrix Composites ◽  
Ceramic Matrix ◽  
Matrix Composites ◽  
Defect Structures ◽  
Modeling Framework ◽  
Linear Elastic ◽  
Elastic Tensor ◽  
The Matrix

Abstract Initial mechanical behavior of Ceramic Matrix Composites (CMCs) is linear until the proportional limit. This initial behavior is characterized by linear elastic properties, which are anisotropic due to the orientation and arrangement of fibers in the matrix. The linear elastic properties are needed during analysis and design of CMC components. CMCs are made with ceramic unidirectional or woven fiber preforms embedded in a ceramic matrix formed via various processing routes. The matrix processing of interest in this work is the Polymer Impregnation and Pyrolysis (PIP) process. As this process involves pyrolysis to convert a pre-ceramic polymer into ceramic, considerable volume shrinkage occurs in the material. This leads to significant defects in the form of porosity of various size, shape, and volume fraction. These defect structures can have a significant impact on the elastic and damage response of the material. In this paper, we develop a new micromechanics modeling framework to study the effects of processing-induced defects on linear elastic response of a PIP-derived CMC. A combination of analytical and computational micromechanics approaches is used to derive the overall elastic tensor of the CMC as a function of the underlying constituents and/or defect structures. It is shown that the volume fraction and aspect ratio of porosity at various length-scales plays an important role in accurate prediction of the elastic tensor. Specifically, it is shown that the through-thickness elastic tensor components cannot be predicted accurately using the micromechanics models unless the effects of defects are considered.

Post-recrystallisation mobilisation phenomena in metamorphosed stratabound sulphide ores

1993 ◽  
Vol 57 (386) ◽  
pp. 19-28 ◽  
Author(s):  
F. M. Vokes ◽  
J. R. Craig
Keyword(s):  
Solid Phase ◽  
Dominant Role ◽  
Fluid Phase ◽  
Shear Zones ◽  
External Source ◽  
Triple Junctions ◽  
Sulphide Ores ◽  
Extreme Degree ◽  
The Matrix ◽  
Retrograde Shear

AbstractMetamorphosed stratabound iron- and base-metal sulphide deposits often exhibit microtextures in which fractures in cataclastically-deformed pyrite porphyroblasts are filled with matrix sulphides; chalcopyrite, sphalerite, pyrrhotite or galena. Discussions of such textures have mostly centred on whether solid-phase or fluid-phase mechanisms were responsible for the movement of the matrix sulphides.The small Zn-Cu sulphide body at Gressli, in the central Norwegian Caledonides, shows these textural features to an extreme degree. Both chalcopyrite and sphalerite show heavy replacive relations to the cataclastically deformed metablastic pyrite, along fracture walls and grain boundaries. They also occur injected along the opened-up triple junctions of foam-textured pyrite. In addition, parts of the ore show patchy quartz with clear replacive relationship to all three sulphides, a feature not often reported from such ores. Such textures can be interpreted to support a mobilisation sequence chalcopyrite-sphalerite-quartz within the Gressli ore. Their extent and degree of development indicate that fluid-phase mobilisation of the three minerals must have played a dominant role. Chalcopyrite and sphalerite are most likely derived from within the ore-mass itself; an external source for the SiO2 seems most probable, in the form of metahydrothermal solutions moving along retrograde shear zones at or near ore-walls.

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