On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media

By V. Smyshlyaev, Kirill D. Cherednichenko. 2000

256 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/470f3642aa60e6c4c5d05417da39837934b4a212

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Mgd Marc Geers
2. V. Kouznetsova
3. H. Askes
4. W. Brekelmans
5. T. Tran
6. V. monchiet
7. Guy Bonnet
8. Julius Kaplunov

In Materials Chemistry

1. V. Kouznetsova
2. V. monchiet
3. Mgd Marc Geers
4. W. Brekelmans
5. H. Askes
6. T. Tran
7. Guy Bonnet
8. Graeme W. Milton

In Mechanics of Materials

1. V. Kouznetsova
2. Mgd Marc Geers
3. V. monchiet
4. H. Askes
5. W. Brekelmans
6. T. Tran
7. Guy Bonnet
8. Julius Kaplunov

Citations in the corpus

• Size effects in the constrained deformation of metallic foams (2002, unknown): “Micromechanical methods show promise in making this connection, and recently notable progress has been made by a number of researchers including Drugan and Willis (1996) and Smyshlyaev and Cherednichenko (2000).”
• Higher order asymptotic homogenization and wave propagation in periodic composite materials (2008, background): “Mathematical aspects of the higher order homogenization have been intensively developed (Smyshlyaev & Cherednichenko 2000; Cherednichenko & Smyshlyaev 2004).”
• High-frequency homogenization for periodic media (2010, background): “…the frequency range of such models can be extended by considering higher-order correction terms (Santosa & Symes, 1991; Bakhvalov & Eglit, 2000; Smyshlyaev & Cherednichenko, 2000), the resulting models cannot fully reproduce high frequency dynamic behaviours characteristic of microstructured…”
• Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories (2008, methodology): “This problem has been previously considered for periodically inhomogeneous elastic medium, see [2], where newly-designed variational/asymptotic homogenisation procedure was used to derive strain gradient theories that are both asymptotically consistent and stable.”
• A micromechanics-based approach for the derivation of constitutive elastic coefficients of strain-gradient media (2012, methodology): “By taking the variation of their elastic functional, Smyshlyaev and Cherednichenko (2000) observe that the balance equation does not reduce to the standard, Cauchy-type, one but introduces new additional terms.”
• The Theory of Composites (2002, background): “Smyshlyaev and Cherednichenko (2000) show how the higher order homogenized solutions also can be justified variationally, by using an energy that depends on higher order gradients.”
• Computational homogenization for the multi-scale analysis of multi-phase materials (2002, methodology): “Smyshlyaev and Cherednichenko (2000) have combined the asymptotic method with a variational technique, which allowed them to minimize the difference between the real and homogenized behaviour and to ensure that the higher-order homogenized equations remain elliptic.”
• Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme (2002, methodology): “Smyshlyaev and Cherednichenko [28] have combined the asymptotic method with a variational technique, which allowed them to minimize the di erence between the real and homogenized behaviour and to ensure that the higher-order homogenized equations remain elliptic.”