TY - JOUR

T1 - Finite strain expansion/contraction of a hollow sphere made of strain- and rate- hardening material

AU - Alexandrov, Sergei

AU - Jeng, Yeau Ren

N1 - Funding Information:
This work was financially supported by the Ministry of Science and Technology of Taiwan (MOST 106-2923-E-194-002-MY3, 108- 2221-E-006-228-MY3 and 108-2119-M-006-010) and Air Force Office of Science Research (AFOSR) under contract no. FA4869- 06-1-0056 AOARD 064053. Professor Yeau-Ren Jeng would like to acknowledge Medical Device Innovation Center (MDIC) and Intelligent Manufacturing Research Center (iMRC) from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan and AC2T research GmbH (AC2T) in Austria (COMET InTribology, FFG-No.872176).
Funding Information:
This work was financially supported by the Ministry of Science and Technology of Taiwan (MOST 106-2923-E-194-002-MY3, 108- 2221-E-006-228-MY3 and 108-2119-M-006-010) and Air Force Office of Science Research (AFOSR) under contract no. FA4869- 06-1-0056 AOARD 064053. Professor Yeau-Ren Jeng would like to acknowledge Medical Device Innovation Center (MDIC) and Intelligent Manufacturing Research Center (iMRC) from The Featured Areas Research Center Program within the framework of the Higher Education Sprout Project by the Ministry of Education (MOE) in Taiwan and AC2T research GmbH (AC2T) in Austria (COMET InTribology, FFG-No.872176).
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2022

Y1 - 2022

N2 - This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow sphere at large strains. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution reduces to a single ordinary differential equation for determining the radial stress. The independent variable in this equation is the equivalent strain. Moreover, the equivalent strain rate is expressed in terms of elementary functions of the equivalent strain, which allows for representing the yield stress as a function of the equivalent strain and a time-like independent variable. In the course of deriving the equations above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. The motivation of this research is that solutions for the expansion/contraction of a hollow sphere are widely used at the micro-level to calculate some material properties at the macro-level. To this end, it is necessary to specify constitutive equations for micromechanical modeling. The accuracy of these equations is questionable. An advantage of the solution found is that it is practically analytic for quite a general material model that accounts for both strain- and rate-hardening. Therefore, it is straightforward to generate a large amount of theoretical data for comparing with measurable quantities at the macro-level.

AB - This paper presents a semi-analytic rigid/plastic solution for the expansion/contraction of a hollow sphere at large strains. The yield stress depends on the equivalent strain rate and the equivalent strain. No restriction is imposed on this dependence. The solution reduces to a single ordinary differential equation for determining the radial stress. The independent variable in this equation is the equivalent strain. Moreover, the equivalent strain rate is expressed in terms of elementary functions of the equivalent strain, which allows for representing the yield stress as a function of the equivalent strain and a time-like independent variable. In the course of deriving the equations above, the transformation between Eulerian and Lagrangian coordinates is used. A numerical example illustrates the solution for a material model available in the literature. The motivation of this research is that solutions for the expansion/contraction of a hollow sphere are widely used at the micro-level to calculate some material properties at the macro-level. To this end, it is necessary to specify constitutive equations for micromechanical modeling. The accuracy of these equations is questionable. An advantage of the solution found is that it is practically analytic for quite a general material model that accounts for both strain- and rate-hardening. Therefore, it is straightforward to generate a large amount of theoretical data for comparing with measurable quantities at the macro-level.

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U2 - 10.1007/s00161-022-01103-w

DO - 10.1007/s00161-022-01103-w

M3 - Article

AN - SCOPUS:85129370360

SN - 0935-1175

JO - Continuum Mechanics and Thermodynamics

JF - Continuum Mechanics and Thermodynamics

ER -