Thence the moment of momentum

Müller, Wolfgang; Rickert, Wilhelm; Иванова, Е. В.

doi:10.1002/zamm.202000117

Cited by 17 publications

(17 citation statements)

References 39 publications

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“…where q is the heat flux vector and r the specific radiation supply. It is the consequence of the principle that the total energy of the material body, i.e., the sum of kinetic energy in the form (4.8) and the internal energy, is conserved (see [26]). In order to obtain the formula (6.13) several algebraic manipulations are required after scalar multiplication of the balance of linear momentum (6.9) with v and the balance for the spin inertia tensor (6.10) by ν.…”

Section: Balances Of 3m Theoriesmentioning

confidence: 99%

Extended micropolar approach within the framework of 3M theories and variations thereof

Vilchevskaya

Müller

Eremeyev

2022

Continuum Mech. Thermodyn.

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As part of his groundbreaking work on generalized continuum mechanics, Eringen proposed what he called 3M theories, namely the concept of micromorphic, microstretch, and micropolar materials modeling. The micromorphic approach provides the most general framework for a continuum with translational and (internal) rotational degrees of freedom (DOF), whilst the rotational DOFs of micromorphic and micropolar continua are subjected to more and more constraints. More recently, an “extended” micropolar theory has been presented by one of the authors: Eringen’s 3M theories were children of solid mechanics based on the concept of the indestructible material particle. Extended micropolar theory was formulated both ways for material systems as well as in spatial description, which is useful when describing fluid matter. The latter opens the possibility to model situations and materials with a continuum point that on the microscale consists no longer of the same elementary units during a physical process. The difference culminates in an equation for the microinertia tensor, which is no longer a kinematic identity. Rather it contains a new continuum field, namely an independent production term and, consequently, establishes a new constitutive quantity. This makes it possible to describe processes of structural change, which are difficult if not impossible to be captured within the material particle model. This paper compares the various theories and points out their communalities as well as their differences.

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Section: Balances Of 3m Theoriesmentioning

confidence: 99%

Extended micropolar approach within the framework of 3M theories and variations thereof

Vilchevskaya

Müller

Eremeyev

2022

Continuum Mech. Thermodyn.

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“…In particular, it is shown that the distinction between macroscopic angular momentum and moment of momentum, argued masterfully in [27], albeit with only a general allusion to directed media, is a natural implication of the homogenization theory. In fact, it is rigorously confirmed that couple forces, defined in terms of the microscopic state, enter in a non-trivial statement of macroscopic angular momentum balance [28,29]. The proposed theory differs from the micromorphic theory [30–33] both methodologically and philosophically.…”

Section: Introductionmentioning

confidence: 98%

On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization

Mandadapu

Abali²,

Papadopoulos

2021

Mathematics and Mechanics of Solids

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This paper makes a rigorous case for considering the continuum derived by the homogenization of extensive quantities as a polar medium in which the balances of angular momentum and energy contain contributions due to body couples and couple stresses defined in terms of the underlying microscopic state. The paper also addresses the question of invariance of macroscopic stress and heat flux and form-invariance of the macroscopic balance laws.

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“…For metamaterials and their description, the scientific scrutiny is still ongoing [7,41,67]. The use of homogenization techniques for metamaterials is under development as well [56,66].…”

Section: Introductionmentioning

confidence: 99%

Mechanical analysis of heterogeneous materials with higher-order parameters

Važić

Abali

Yang

et al. 2021

Engineering with Computers

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Even though heterogeneous porous materials are widely used in a variety of engineering and scientific fields, such as aerospace, energy-storage technology, and bio-engineering, the relationship between effective material properties of porous materials and their underlying morphology is still not fully understood. To contribute to this knowledge gap, this paper adopts a higher-order asymptotic homogenization method to numerically investigate the effect of complex micropore morphology on the effective mechanical properties of a porous system. Specifically, we use the second-order scheme that is an extension of the first-order computational homogenization framework, where a generalized continuum enables us to introduce length scale into the material constitutive law and capture both pore size and pore distribution. Through several numerical case studies with different combinations of porosity, pore shapes, and distributions, we systematically studied the relationship between the underlying morphology and effective mechanical properties. The results highlight the necessity of higher-order homogenization in understanding the mechanical properties and reveal that higher-order parameters are required to capture the role of realistic pore morphologies on effective mechanical properties. Furthermore, for specific pore shapes, higher-order parameters exhibit dominant influence over the first-order continuum.

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Thence the moment of momentum

Cited by 17 publications

References 39 publications

Extended micropolar approach within the framework of 3M theories and variations thereof

Extended micropolar approach within the framework of 3M theories and variations thereof

On the polar nature and invariance properties of a thermomechanical theory for continuum-on-continuum homogenization

Mechanical analysis of heterogeneous materials with higher-order parameters

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