The Experts below are selected from a list of 1623 Experts worldwide ranked by ideXlab platform
M B Rubin - One of the best experts on this subject based on the ideXlab platform.
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equivalence of a constrained Cosserat Theory and antman s special Cosserat Theory of a rod
2020Co-Authors: M B RubinAbstract:The general nonlinear Cosserat Theory of a rod allows for tangential shear deformation, axial extension and a deformable cross-section. Simplified equations are obtained by introducing kinematic constraints and associated constraint responses which force the cross-section to remain rigid. The equations of motion of this constrained Cosserat rod are shown to be equivalent to those of Antman’s nonlinear special Cosserat Theory of a rod. Strain measures motivated by the general Cosserat rod Theory are used to develop explicit hyperelastic constitutive equations for the force and moment applied to the rod’s ends.
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three dimensional free vibrations of a circular arch using the Theory of a Cosserat point
2005Co-Authors: M B Rubin, Ekrem TufekciAbstract:Small deformation three-dimensional free vibrations of a circular arch with uniform rectangular cross-section have been investigated by using different theoretical approaches and by experimental verification. Special emphasis has been focused on a numerical formulation which models each element of the arch using the Theory of a Cosserat point. Comparison has been made with accurate three-dimensional numerical modeling of the arch using the computer program ANSYS. Also, three-dimensional beam elements in the computer programs ANSYS and I-DEAS have been considered along with an exact solution of approximate model equations of the arch. The results indicate that appropriate modeling of rotary inertia is necessary to predict accurate frequencies associated with torsional out-of-plane modes. Moreover, in its general form the Theory of a Cosserat point is a fully nonlinear Theory that has already been tested for buckling of beams and arches. Therefore, the success of the Cosserat Theory for the dynamic problem considered in this paper suggests that the Theory of a Cosserat point can be used for more complicated nonlinear dynamic problems of thin rod-like structures.
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numerical solution procedures for nonlinear elastic curved rods using the Theory of a Cosserat point
2005Co-Authors: M B RubinAbstract:The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the Theory of a Cosserat point. Although the general Theory is valid for curved rods, the constitutive coefficients have been determined by comparison with exact linear solutions only for straight beams. The objective of this paper is to explore the accuracy of the predictions of the Cosserat Theory for curved rods by comparison with exact solutions. Specifically, these problems include: linearized axisymmetric deformation of a circular ring loaded with internal and external pressures; nonlinear axisymmetric inversion of a circular ring; and linearized pure bending of a section of a circular ring. In all cases, the Cosserat Theory performs well with no modifications of the constitutive constants, even in the limit of reasonably thick rods. Also, it is shown that the Cosserat Theory does not exhibit shear locking in the limit of thin rods.
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buckling of elastic shallow arches using the Theory of a Cosserat point
2004Co-Authors: M B RubinAbstract:The numerical solution of problems of curved rods can be formulated using rod elements developed within the context of the Theory of a Cosserat point. It is well known that the buckling of shallow arches presents a formidable challenge to theoretical models because it necessarily requires accurate modeling of the nonlinear coupling of membrane and bending effects as well as the accurate prediction of prebuckled deformations. This paper shows that the Cosserat Theory predicts buckling loads and deformed shapes of elastic clamped circular arches which are in excellent agreement with the experiments over the full range of arch geometries that were tested. This success suggests that the Cosserat Theory can be used to obtain reliable results for nonlinear deformations of curved elastic rods. Moreover, the analysis of these experiments indicates that variations in the thicknesses of shallow arch structures due to standard tolerances have a strong influence on buckling loads and should be measured and controlled in accurate buckling experiments.
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analysis of blank thickening in deep drawing processes using the Theory of a Cosserat generalized membrane
2004Co-Authors: A Peled, M B Rubin, J TiroshAbstract:Abstract This paper analyzes a transient, nonlinear deep drawing process where a circular blank of a rigid-plastic material is forced by a rigid circular punch to deform into a cylindrical cup. Attention is focused on the plastic flow beneath the blank-holder. Using the Cosserat Theory of a generalized membrane it is possible to obtain analytical solutions which examine the following two major effects: (a) the importance of added “rim pressure” acting on the outer edge of the blank; and (b) the importance of a controlled moveable blank-holder to allow blank thickening during the drawing process. Guided by these analytical results, a new deep drawing machine was built to exploit these effects and increase the limit drawing ratio (LDR) of the drawing process. Specifically, the LDR (in one stroke) reached the value of 3.16 compared with the value of about 2.0 in the conventional process. Moreover, the analytical prediction of the punch force versus the punch stroke is in good agreement with the experimental data and with simulations using the computer code DYTRAN.
Patrizio Neff - One of the best experts on this subject based on the ideXlab platform.
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the relaxed polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3d ebsd experiments
2017Co-Authors: Andreas Fischle, Patrizio Neff, Dierk RaabeAbstract:The rotation \({{\mathrm{polar}}}(F) \in {{\mathrm{SO}}}(3)\) arises as the unique orthogonal factor of the right polar decomposition \(F = {{\mathrm{polar}}}(F)\,U\) of a given invertible matrix \(F \in {{\mathrm{GL}}}^+(3)\). In the context of nonlinear elasticity Grioli (Boll Un Math Ital 2:252–255, 1940) discovered a geometric variational characterization of \({{\mathrm{polar}}}(F)\) as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli’s variational approach with weights (material parameters) \(\mu > 0\) and \(\mu _c \ge 0\) (Grioli: \(\mu = \mu _c\)). The energy subject to minimization coincides with the Cosserat shear–stretch contribution arising in any geometrically nonlinear, isotropic and quadratic Cosserat continuum model formulated in the deformation gradient field \(F :=\nabla \varphi : \Omega \rightarrow {{\mathrm{GL}}}^+(3)\) and the microrotation field \(R: \Omega \rightarrow {{\mathrm{SO}}}(3)\). The corresponding set of non-classical energy-minimizing rotations $$\begin{aligned} \mathrm{rpolar}^\pm _{\mu ,\mu _c}(F) :=\mathop {\hbox {arg min}}\limits _{R\,\in \,{{\mathrm{SO}}}(3)}{\Big \{{{\mathrm{W_{\mu ,\mu _c}}}}(R\,;F) :=\mu \left||\hbox {sym}(R^TF - {{\mathbbm {1}}}) \right||^2 + \mu _c\left||\hbox {skew}(R^TF - {{\mathbbm {1}}}) \right||^2\Big \}} \end{aligned}$$ represents a new relaxed-polar mechanism. Our goal is to motivate this mechanism by presenting it in a relevant setting. To this end, we explicitly construct a deformation mapping \(\varphi _\mathrm{nano}\) which models an idealized nanoindentation and compare the corresponding optimal rotation patterns \({{\mathrm{rpolar}}}^\pm _{1,0}(F_\mathrm{nano})\) with experimentally obtained 3D-EBSD measurements of the disorientation angle of lattice rotations due to a nanoindentation in solid copper. We observe that the non-classical relaxed-polar mechanism can produce interesting counter-rotations. A possible link between Cosserat Theory and finite multiplicative plasticity Theory on small scales is also explored.
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On the dislocation density tensor in the Cosserat Theory of elastic shells
2016Co-Authors: Mircea Bîrsan, Patrizio NeffAbstract:We consider the Cosserat continuum in its finite strain setting and discuss the dislocation density tensor as a possible alternative curvature strain measure in three-dimensional Cosserat models and in Cosserat shell models. We establish a close relationship (one-to-one correspondence) between the new shell dislocation density tensor and the bending-curvature tensor of 6-parameter shells.
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the relaxed polar mechanism of locally optimal Cosserat rotations for an idealized nanoindentation and comparison with 3d ebsd experiments
2016Co-Authors: Andreas Fischle, Patrizio Neff, Dierk RaabeAbstract:The rotation ${\rm polar}(F) \in {\rm SO}(3)$ arises as the unique orthogonal factor of the right polar decomposition $F = {\rm polar}(F) \cdot U$ of a given invertible matrix $F \in {\rm GL}^+(3)$. In the context of nonlinear elasticity Grioli (1940) discovered a geometric variational characterization of ${\rm polar}(F)$ as a unique energy-minimizing rotation. In preceding works, we have analyzed a generalization of Grioli's variational approach with weights (material parameters) $\mu > 0$ and $\mu_c \geq 0$ (Grioli: $\mu = \mu_c$). The energy subject to minimization coincides with the Cosserat shear-stretch contribution arising in any geometrically nonlinear, isotropic and quadratic Cosserat continuum model formulated in the deformation gradient field $F := \nabla\varphi: \Omega \to {\rm GL}^+(3)$ and the microrotation field $R: \Omega \to {\rm SO}(3)$. The corresponding set of non-classical energy-minimizing rotations $$ {\rm rpolar}^\pm_{\mu,\mu_c}(F) := \substack{{\rm argmin}\\ R\,\in\,{\rm SO(3)}} \Big\{ W_{\mu, \mu_c}(R\,;F) := \mu\, || {\rm sym}(R^TF - 1)||^2 + \mu_c\, ||{\rm skew}(R^TF - 1)||^2 \Big\} $$ represents a new relaxed-polar mechanism. Our goal is to motivate this mechanism by presenting it in a relevant setting. To this end, we explicitly construct a deformation mapping $\varphi_{\rm nano}$ which models an idealized nanoindentation and compare the corresponding optimal rotation patterns ${\rm rpolar}^\pm_{1,0}(F_{\rm nano})$ with experimentally obtained 3D-EBSD measurements of the disorientation angle of lattice rotations due to a nanoindentation in solid copper. We observe that the non-classical relaxed-polar mechanism can produce interesting counter-rotations. A possible link between Cosserat Theory and finite multiplicative plasticity Theory on small scales is also explored.
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A GEOMETRICALLY EXACT PLANAR Cosserat SHELL-MODEL WITH MICROSTRUCTURE: EXISTENCE OF MINIMIZERS FOR ZERO Cosserat COUPLE MODULUS
2007Co-Authors: Patrizio NeffAbstract:The existence of minimizers to a geometrically exact Cosserat planar shell model with microstructure is proven. The membrane energy is a quadratic, uniformly Legendre–Hadamard elliptic energy in contrast to traditional membrane energies. The bending contribution is augmented by a curvature term representing the interaction of the rotational microstructure in the Cosserat Theory. The model includes non-classical size effects, transverse shear resistance, drilling degrees of freedom and accounts implicitly for thickness extension and asymmetric shift of the midsurface. Upon linearization with zero Cosserat couple modulus μc = 0, one recovers the infinitesimal-displacement Reissner–Mindlin model. It is shown that the Cosserat shell formulation admits minimizers even for μc = 0, in which case the drill-energy is absent. The midsurface deformation m is found in H1(ω, ℝ3). Since the existence of energy minimizers rather than equilibrium solutions is established, the proposed analysis includes the large deformation/large rotation buckling behaviour of thin shells.
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the Cosserat couple modulus for continuous solids is zero viz the linearized cauchy stress tensor is symmetric
2006Co-Authors: Patrizio NeffAbstract:We investigate weaker than usual constitutive assumptions in linear Cosserat Theory still providing for existence and uniqueness and show a continuous dependence result for Cosserat couple modulus µc → 0. This result is needed when using Cosserat elasticity not as a physical model but as a numerical regularization device. Thereafter it is shown that the usually adopted material restrictions of uniform positivity for a linear Cosserat model cannot be consistent with experimental findings for continuous solids: the analytical solutions for both the torsion and the bending problem in general predict an unbounded stiffness for ever thinner samples. This unphysical behaviour can only be avoided for specific choices of parameters in the curvature energy expression. However, these choices do not satisfy the usual constitutive restrictions. We show that the possibly remaining linear elastic Cosserat problem is nevertheless well-posed but that it is impossible to determine the appearing curvature modulus independent of boundary conditions. This puts a doubt on the use of the linear elastic Cosserat model (or the geometrically exact model with µc > 0) for the physically consistent description of continuous solids like polycrystals in the framework of elasto-plasticity. The problem is avoided in geometrically exact Cosserat models if the Cosserat couple modulus µc is set to zero.
Jena Jeong - One of the best experts on this subject based on the ideXlab platform.
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a new multi scale modeling approach based on hygro Cosserat Theory for self induced stress in hydrating cementitious mortars
2011Co-Authors: Jena Jeong, Hamidreza Ramezani, Pierre Mounanga, Marwen BouaskerAbstract:Abstract The present paper focuses on the modeling of internal stresses induced by the restrained autogenous shrinkage of hydrating cementitious matrix in cement-based mortars. At very early age (0–48 h), these self-induced stresses may be relatively high and even critical, especially for cementitious systems with low water-to-cement ratio, since the physico-chemical phenomena involved (hydration and self-desiccation) are particularly intense. To pursue the mentioned objective, an original multi-scale approach based on the application of hygro-Cosserat Theory has been developed to model the self-induced stress variation in the cement paste surrounding the aggregates. In fact, the characteristic length scale parameter Lc in the Cosserat Theory helps us to reduce the specimen size from macro-scale to micro-scale and even sub-micro-scale due to its explicit size effect features, which is not feasible in the classical Theory, i.e. Cauchy–Bolzmann’s Theory. The self-shrinkage phenomenon at early age has been observed and modeled via the experiments and a freshly defined Cosserat Size effect number (CS) based upon the Representative Volume Element (RVE) concept. The proposed method is capable of treating the internal stress and could be followed by cracks appearance investigation in the cementitious matrix surrounding the sand inclusions, which should occur inside of the RVE of mortar subjected to self-desiccation shrinkage during the hydration process at early age. The occurrence of these micro-cracking networks are confirmed by Scanning Electronic Microscopy (SEM) observations at the interface cement paste/aggregate performed on different mortars at early age. By taking advantage of the time-dependent Finite Element Analysis (FEA), the numerical outcomes are well agreed with the experimental observations coming from SEM. It concludes that the inclusion creates high hygro-stress concentration around the grains: when the number of inclusions increases, this hygro-stress could lead to a micro-crack network through the matrix.
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enhanced numerical study of infinitesimal non linear Cosserat Theory based on the grain size length scale assumption
2010Co-Authors: Jena Jeong, Hamidreza RamezaniAbstract:Abstract A non-linear Cosserat Theory involving the Arbitrary Lagrangian–Eulerian (ALE) method has been introduced into the brittle isotropic materials (amorphous glass and cement mortar) using the Modified Brazilian Disk (MBD) under an uni-axial compressive loading. These numerical experiments shed light on the nature of the Cosserat-based media and material moduli determination which are difficult to acquire using the most well-known experimental viewpoints. By using the identical micro-rotation constants α = β = γ = μ L G 2 and Ψ = 2 / 3 , the Cosserat moduli reduce to only four constants for the 3D cases. According to the results obtained in this paper, the present methodology substantiates that the Cosserat Theory would be readily applied to the wide range of materials from the full amorphous materials to the heterogeneous materials by changing the length scale parameter. Some fresh routes and new outlooks are discussed afterwards.
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new approach of multi scale modeling based on the hygro Cosserat Theory for self desiccation deformation of cement mortars at early age
2010Co-Authors: Jena Jeong, Hamidreza Ramezani, Pierre Mounanga, Marwen Bouasker, David BassirAbstract:In the present paper, we concentrate on the heterogeneous cement mortars and we treat them as Cosserat-based media. The autogenous shrinkage phenomenon at early age (from 1 up to 3 days after mixing) has been analyzed by means of Cosserat Theory. The characteristic length scale parameter Lc in this Theory helps us to change the size specimen from macro-scale to micro-scale using the theoretical size effect aspects. This methodology is also capable of treating cracks initiation and their appearance in the cementitious matrix surrounding the sand-inclusions, which should occurred inside of the Representative Volume Elementary (RVE) of mortar subjected to self-desiccation shrinkage during hydration at early age. By taking advantage of the Nonlinear Finite Element Analysis (NFEA), the numerical experiments have been performed. The numerical outcomes are well agreed with the experimental observations coming from Scanning Electronic Microscopy (SEM) images. It concludes that the inclusions create not only a hygro stress concentration around the grains but also the number of inclusions should influence the network in cementitous matrix.
Hamidreza Ramezani - One of the best experts on this subject based on the ideXlab platform.
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a new multi scale modeling approach based on hygro Cosserat Theory for self induced stress in hydrating cementitious mortars
2011Co-Authors: Jena Jeong, Hamidreza Ramezani, Pierre Mounanga, Marwen BouaskerAbstract:Abstract The present paper focuses on the modeling of internal stresses induced by the restrained autogenous shrinkage of hydrating cementitious matrix in cement-based mortars. At very early age (0–48 h), these self-induced stresses may be relatively high and even critical, especially for cementitious systems with low water-to-cement ratio, since the physico-chemical phenomena involved (hydration and self-desiccation) are particularly intense. To pursue the mentioned objective, an original multi-scale approach based on the application of hygro-Cosserat Theory has been developed to model the self-induced stress variation in the cement paste surrounding the aggregates. In fact, the characteristic length scale parameter Lc in the Cosserat Theory helps us to reduce the specimen size from macro-scale to micro-scale and even sub-micro-scale due to its explicit size effect features, which is not feasible in the classical Theory, i.e. Cauchy–Bolzmann’s Theory. The self-shrinkage phenomenon at early age has been observed and modeled via the experiments and a freshly defined Cosserat Size effect number (CS) based upon the Representative Volume Element (RVE) concept. The proposed method is capable of treating the internal stress and could be followed by cracks appearance investigation in the cementitious matrix surrounding the sand inclusions, which should occur inside of the RVE of mortar subjected to self-desiccation shrinkage during the hydration process at early age. The occurrence of these micro-cracking networks are confirmed by Scanning Electronic Microscopy (SEM) observations at the interface cement paste/aggregate performed on different mortars at early age. By taking advantage of the time-dependent Finite Element Analysis (FEA), the numerical outcomes are well agreed with the experimental observations coming from SEM. It concludes that the inclusion creates high hygro-stress concentration around the grains: when the number of inclusions increases, this hygro-stress could lead to a micro-crack network through the matrix.
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enhanced numerical study of infinitesimal non linear Cosserat Theory based on the grain size length scale assumption
2010Co-Authors: Jena Jeong, Hamidreza RamezaniAbstract:Abstract A non-linear Cosserat Theory involving the Arbitrary Lagrangian–Eulerian (ALE) method has been introduced into the brittle isotropic materials (amorphous glass and cement mortar) using the Modified Brazilian Disk (MBD) under an uni-axial compressive loading. These numerical experiments shed light on the nature of the Cosserat-based media and material moduli determination which are difficult to acquire using the most well-known experimental viewpoints. By using the identical micro-rotation constants α = β = γ = μ L G 2 and Ψ = 2 / 3 , the Cosserat moduli reduce to only four constants for the 3D cases. According to the results obtained in this paper, the present methodology substantiates that the Cosserat Theory would be readily applied to the wide range of materials from the full amorphous materials to the heterogeneous materials by changing the length scale parameter. Some fresh routes and new outlooks are discussed afterwards.
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new approach of multi scale modeling based on the hygro Cosserat Theory for self desiccation deformation of cement mortars at early age
2010Co-Authors: Jena Jeong, Hamidreza Ramezani, Pierre Mounanga, Marwen Bouasker, David BassirAbstract:In the present paper, we concentrate on the heterogeneous cement mortars and we treat them as Cosserat-based media. The autogenous shrinkage phenomenon at early age (from 1 up to 3 days after mixing) has been analyzed by means of Cosserat Theory. The characteristic length scale parameter Lc in this Theory helps us to change the size specimen from macro-scale to micro-scale using the theoretical size effect aspects. This methodology is also capable of treating cracks initiation and their appearance in the cementitious matrix surrounding the sand-inclusions, which should occurred inside of the Representative Volume Elementary (RVE) of mortar subjected to self-desiccation shrinkage during hydration at early age. By taking advantage of the Nonlinear Finite Element Analysis (NFEA), the numerical experiments have been performed. The numerical outcomes are well agreed with the experimental observations coming from Scanning Electronic Microscopy (SEM) images. It concludes that the inclusions create not only a hygro stress concentration around the grains but also the number of inclusions should influence the network in cementitous matrix.
Marwen Bouasker - One of the best experts on this subject based on the ideXlab platform.
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a new multi scale modeling approach based on hygro Cosserat Theory for self induced stress in hydrating cementitious mortars
2011Co-Authors: Jena Jeong, Hamidreza Ramezani, Pierre Mounanga, Marwen BouaskerAbstract:Abstract The present paper focuses on the modeling of internal stresses induced by the restrained autogenous shrinkage of hydrating cementitious matrix in cement-based mortars. At very early age (0–48 h), these self-induced stresses may be relatively high and even critical, especially for cementitious systems with low water-to-cement ratio, since the physico-chemical phenomena involved (hydration and self-desiccation) are particularly intense. To pursue the mentioned objective, an original multi-scale approach based on the application of hygro-Cosserat Theory has been developed to model the self-induced stress variation in the cement paste surrounding the aggregates. In fact, the characteristic length scale parameter Lc in the Cosserat Theory helps us to reduce the specimen size from macro-scale to micro-scale and even sub-micro-scale due to its explicit size effect features, which is not feasible in the classical Theory, i.e. Cauchy–Bolzmann’s Theory. The self-shrinkage phenomenon at early age has been observed and modeled via the experiments and a freshly defined Cosserat Size effect number (CS) based upon the Representative Volume Element (RVE) concept. The proposed method is capable of treating the internal stress and could be followed by cracks appearance investigation in the cementitious matrix surrounding the sand inclusions, which should occur inside of the RVE of mortar subjected to self-desiccation shrinkage during the hydration process at early age. The occurrence of these micro-cracking networks are confirmed by Scanning Electronic Microscopy (SEM) observations at the interface cement paste/aggregate performed on different mortars at early age. By taking advantage of the time-dependent Finite Element Analysis (FEA), the numerical outcomes are well agreed with the experimental observations coming from SEM. It concludes that the inclusion creates high hygro-stress concentration around the grains: when the number of inclusions increases, this hygro-stress could lead to a micro-crack network through the matrix.
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new approach of multi scale modeling based on the hygro Cosserat Theory for self desiccation deformation of cement mortars at early age
2010Co-Authors: Jena Jeong, Hamidreza Ramezani, Pierre Mounanga, Marwen Bouasker, David BassirAbstract:In the present paper, we concentrate on the heterogeneous cement mortars and we treat them as Cosserat-based media. The autogenous shrinkage phenomenon at early age (from 1 up to 3 days after mixing) has been analyzed by means of Cosserat Theory. The characteristic length scale parameter Lc in this Theory helps us to change the size specimen from macro-scale to micro-scale using the theoretical size effect aspects. This methodology is also capable of treating cracks initiation and their appearance in the cementitious matrix surrounding the sand-inclusions, which should occurred inside of the Representative Volume Elementary (RVE) of mortar subjected to self-desiccation shrinkage during hydration at early age. By taking advantage of the Nonlinear Finite Element Analysis (NFEA), the numerical experiments have been performed. The numerical outcomes are well agreed with the experimental observations coming from Scanning Electronic Microscopy (SEM) images. It concludes that the inclusions create not only a hygro stress concentration around the grains but also the number of inclusions should influence the network in cementitous matrix.
