Establishment of deformation simulation procedure by finite element method based on second-order homogenization using characteristic displacement function for macroscopic strain gradient

Makoto Uchida, Naoya Tada

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

To evaluate effect of a relative scale of microstructure to macrostructure, a simulation procedure using second-order homogenization based finite element method was proposed. In this method, a microscopic characteristic displacement function for macroscopic strain gradient was added to the conventional first order homogenization method. Then, a procedure to solve a macroscopic boundary problem was established based on the principle of virtual work in macroscopic scale represented by the microscopic characteristic displacement function. To validate the proposed second-order homogenization method, computational simulations of deformation behavior of cavitated rubber (void) blended amorphous polymer were performed using the proposed second-order homogenization. From the result of bending deformation where tension or compression was given to upper side or lower side of the macroscopic model, the material containing larger void required a larger energy for the bending of the model. With decrease in the void size, the energy converged to that predicted by first-order homogenization method. Basically, the deformation behavior predicted by proposed homogenization model was qualitatively and quantitatively similar to that predicted by full scale model. The proposed model is expected to be applied for computational prediction of the scale-dependent deformation in various cases because the model does not limit the form of constitutive equation, shape of the unit cell and deformation mechanisms and structure of the material.

Original languageEnglish
Pages (from-to)1486-1503
Number of pages18
JournalNippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A
Volume79
Issue number806
DOIs
Publication statusPublished - 2013
Externally publishedYes

Fingerprint

Homogenization method
Finite element method
Rubber
Constitutive equations
Polymers
Microstructure

Keywords

  • Finite Element Method
  • Length Scale
  • Second-Order Homogenization
  • Strain Gradient

ASJC Scopus subject areas

  • Mechanical Engineering
  • Mechanics of Materials
  • Materials Science(all)

Cite this

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abstract = "To evaluate effect of a relative scale of microstructure to macrostructure, a simulation procedure using second-order homogenization based finite element method was proposed. In this method, a microscopic characteristic displacement function for macroscopic strain gradient was added to the conventional first order homogenization method. Then, a procedure to solve a macroscopic boundary problem was established based on the principle of virtual work in macroscopic scale represented by the microscopic characteristic displacement function. To validate the proposed second-order homogenization method, computational simulations of deformation behavior of cavitated rubber (void) blended amorphous polymer were performed using the proposed second-order homogenization. From the result of bending deformation where tension or compression was given to upper side or lower side of the macroscopic model, the material containing larger void required a larger energy for the bending of the model. With decrease in the void size, the energy converged to that predicted by first-order homogenization method. Basically, the deformation behavior predicted by proposed homogenization model was qualitatively and quantitatively similar to that predicted by full scale model. The proposed model is expected to be applied for computational prediction of the scale-dependent deformation in various cases because the model does not limit the form of constitutive equation, shape of the unit cell and deformation mechanisms and structure of the material.",
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AU - Tada, Naoya

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AB - To evaluate effect of a relative scale of microstructure to macrostructure, a simulation procedure using second-order homogenization based finite element method was proposed. In this method, a microscopic characteristic displacement function for macroscopic strain gradient was added to the conventional first order homogenization method. Then, a procedure to solve a macroscopic boundary problem was established based on the principle of virtual work in macroscopic scale represented by the microscopic characteristic displacement function. To validate the proposed second-order homogenization method, computational simulations of deformation behavior of cavitated rubber (void) blended amorphous polymer were performed using the proposed second-order homogenization. From the result of bending deformation where tension or compression was given to upper side or lower side of the macroscopic model, the material containing larger void required a larger energy for the bending of the model. With decrease in the void size, the energy converged to that predicted by first-order homogenization method. Basically, the deformation behavior predicted by proposed homogenization model was qualitatively and quantitatively similar to that predicted by full scale model. The proposed model is expected to be applied for computational prediction of the scale-dependent deformation in various cases because the model does not limit the form of constitutive equation, shape of the unit cell and deformation mechanisms and structure of the material.

KW - Finite Element Method

KW - Length Scale

KW - Second-Order Homogenization

KW - Strain Gradient

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