Review article: Buryachenko V. (2022) Critical analysis of generalized Maxwell homogenization schemes and related prospective problems. Mechanics of Materials. 165, 104181(123 refs). https://www.sciencedirect.com/science/article/pii /S0167663621003926

Abstract:

A linear composite medium consisting of a homogeneous matrix containing either the periodic or random set of heterogeneities is considered. Both the original and generalized Maxwell schemes are analyzed by reducing the problem to calculation of elastic fields in a finite volume of the composite embedded in the infinite homogeneous matrix medium and subjected to a constant external stress or strain field at infinity. We investigate (qualitatively and quantitatively) a correspondence between the Maxwell schemes (the original and generalized versions) and other different basic assumptions, conceptions, and methods of analytical micromechanics such as effective field method (EFM) and Mori-Tanaka method (MTM). Some deficiencies and inconsistencies of generalized Maxwell schemes in particular examples are detected and explained how the mentioned difficulties can be easily overcome by the classical micromechanical methods EFM and MTM. For the modeling of both periodic and random structure composites, the generalized Maxwell schemes taking into account the inclusion interactions inside the cluster are analyzed. The incorrectness of using of some generalized Maxwell schemes for the modeling of random structure composite materials (CMs) is shown and the directions for its improvements in the framework of the new (second) background of analytical micromechanics are proposed

Paper: Buryachenko V. (2022) Critical analysis of generalized Maxwell homogenization schemes and related prospective problems. Mechanics of Materials. 165, 104181(123 refs). https://www.sciencedirect.com/science/article/pii /S0167663621003926

ABSTRACT: A linear composite medium consisting of a homogeneous matrix containing either the periodic or random set of heterogeneities is considered. Both the original and generalized Maxwell schemes are analyzed by reducing the problem to calculation of elastic fields in a finite volume of the composite embedded in the infinite homogeneous matrix medium and subjected to a constant external stress or strain field at infinity. We investigate (qualitatively and quantitatively) a correspondence between the Maxwell schemes (the original and generalized versions) and other different basic assumptions, conceptions, and methods of analytical micromechanics such as effective field method (EFM) and Mori-Tanaka method (MTM). Some deficiencies and inconsistencies of generalized Maxwell schemes in particular examples are detected and explained how the mentioned difficulties can be easily overcome by the classical micromechanical methods EFM and MTM. For the modeling of both periodic and random structure composites, the generalized Maxwell schemes taking into account the inclusion interactions inside the cluster are analyzed. The incorrectness of using of some generalized Maxwell schemes for the modeling of random structure composite materials (CMs) is shown and the directions for its improvements in the framework of the new (second) background of analytical micromechanics are proposed

A new book is published: Buryachenko V. A. (2022) Local and Nonlocal Micromechanics of Heterogeneous Materials. Springer, NY (1,011 pages and 1,711 references, see https://link.springer.com/book/10.1007/978-3-030-81784-8). Table of contents is attached. Enjoy reading this book

An extended abstract dedicated to nonlocal (in the sense of either Eringen or Silling) micromechanics is attached. It can’t be considered as a review in any sense. It is just a personal vision on a new area of micromechanics, in particularly based on the author’s publications (references on hundreds related papers can be found in the referred publications). The style of the abstract is plausible rather than rigorous that willfully used by the author just for initiation of discussions in the new prospective area of micromechanics.

Dear Colleagues,

One proposes a new background of micromechanics (NBM) of composites. NBM offers opportunities for a fundamental jump in multi-scale and multi-physics modeling of random heterogeneous media with drastically improved accuracy of local field estimations. In so doing, a difference of linear effective properties estimated by the use of either the new background or the classical one (proposed in 1830-1880) is not significant. See the abstract attached describing a list of 40 papers and conference presentations dedicated to the NBM.

Valeriy Buryachenko

Dear Colleagues,

One proposes a new background of micromechanics defining a new field of micromechanics called computational analytical micromechanics (CAM, see the abstract attached). It offers opportunities for a fundamental jump in multi-scale and multi-physics modeling of random heterogeneous media with drastically improved accuracy of local field estimations. I would be happy if you pay your attention to CAM.

Valeriy Buryachenko

Dear Colleagues,

I am please to let you know about the birth of a new background of micromechanics defining a new field of micromechanics called computational analytical micromechanics (CAM). It offers opportunities for a fundamental jump in multiscale research (see the abstract attached, where avalable electronic publications are indicated and encouraged for reading). However, these opportunities can be realized only in the case of joint efforts of both computational micromechanic's society and the analyticalone. I would be happy if CAM piques your attention.

Season's greatings and a Happy New Year.

Valeriy Buryachenko