Computational Mesomechanics of Materials

Mishnaevsky, Leon

doi:10.1007/978-1-4020-2316-3_20

Cited by 3 publications

(2 citation statements)

References 5 publications

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“…3b as the meso level event rather than micro-or macroscopic ones, commonly associated with a single fiber and entire composite part, respectively. Due to these reasons, we will call our model as a ''meso cell"; for more discussion on the subject, see Mishnaevsky (2007).…”

Section: Model Geometrymentioning

confidence: 99%

Meso cell model of fiber reinforced composite: Interface stress statistics and debonding paths

Кущ

Shmegera

Mishnaevsky

2008

International Journal of Solids and Structures

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The primary goal of this work is to develop an efficient analytical tool for the computer simulation of progressive damage in the fiber reinforced composite (FRC) materials and thus to provide the micro mechanics-based theoretical framework for a deeper insight into fatigue phenomena in them. An accurate solution has been obtained for the micro stress field in a meso cell model of fibrous composite. The developed method combines the superposition principle, Kolosov-Muskhelishvili's technique of complex potentials and Fourier series expansion. By using the properly chosen periodic potentials, the primary boundary-value problem stated on the multiple-connected domain has been reduced to an ordinary, wellposed set of linear algebraic equations. The meso cell can include up to several hundred inclusions which is sufficient to account for the micro structure statistics of composite. The presented numerical examples demonstrate an accuracy and high numerical efficiency of the method which makes it to be a promising tool for studying progressive damage in FRCs. By averaging over a number of random structure realizations, the statistically meaningful results have been obtained for both the local stress and effective elastic moduli of disordered fibrous composite. A special attention has been paid to the interface stress statistics and the fiber debonding paths development, which appear to correlate well with the experimental observations.

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Section: Model Geometrymentioning

confidence: 99%

Meso cell model of fiber reinforced composite: Interface stress statistics and debonding paths

Кущ

Shmegera

Mishnaevsky

2008

International Journal of Solids and Structures

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“…Соответствующее направление получило название вычислительной кристаллической пластичности (Computational Crystal Plasticity). Разработано много вариантов этого метода, опубликованы многочисленные обзоры [1][2][3][4][5]. Метод вычислительной кристаллической пластичности позволяет проследить эволюцию деформирования индивидуальных зерен, что особенно важно в проблемах высокоцикловой и гиперцикловой усталости, где зарождение усталостных повреждений происходит в результате накопления малых пластических деформаций в отдельных зернах.…”

Section: Introductionunclassified

Elastoplastic interaction of grains in polycrystalline materials

Tashkinov

Shavshukov

2019

PNRPU Mechanics Bulletin

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A new method is developed for solving boundary value problems of elastoplastic deformation of polycrystalline materials based on the field-theoretical approach. The boundary value problem for inhomogeneous global strain fields in differential form is transformed into a system of integral equations for mesostrain tensors in grains. In this approach, strain at any point of any grain represented as a superposition of homogeneous macrostrain and contributions of interactions with strain in given grain and all another grains of polycrystalline body . It is shown that the effects of the interaction of strains in polycrystal grains can be described using tensors of the fourth rank. This tensor has 36 independent components. The interactions are additive in nature, that drastically simplifies the solution of some problems, for example, search for extreme microstructures of a polycrystal in which critical localized phenomena arise, such as nucleation of the first plastic slips occur. Constitutive equations of deformation type are used for whole body and separate grains. A model of elastoplastic deformation of single crystals of grains is constructed. The physical mechanisms of plastic deformation are shifts in slip systems of crystals. General expressions are obtained for calculating the secant modules of single crystals for any multiaxial deformation. To solve systems of integral equations for mesostrains in grains the perturbation theory upon intergrains interaction used. Nonlinear systems of equations for plastic strains are solved by the iteration method. The features of the elastoplastic interaction of grains are theoretically investigated. The intensity of the elastoplastic interaction depends on the deformed state of the grains. For two identical grains, the elastoplastic interaction of the pair is several times more intense than the elastic one. In this case, the effect of plastically deformed grain on elastically deformed grain is much higher than the inverse effect. An increase in the intensity of interaction with the development of plastic deformations leads to the effect of homogenization of mesodeformations. Computational experiments were performed using polycrystalline titanium as an example.

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