Numerical treatment of cosserat based rate independent strain gradient plasticity theories
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| Format: | Artículo científico |
| Langue: | en |
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Universidad EAFIT
2008
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| _version_ | 1876441590041411584 |
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| author | Juan David Gómez C. |
| author_facet | Juan David Gómez C. |
| contents | Numerical treatment of cosserat based rate independent strain gradient plasticity theories Juan David Gómez C. Ingeniería Non couple stress theory constitutive modeling integration algorithms finite element analysis The current trend towards miniaturization in the microelectronics industry has pushed for the development of theories intended to explain the behavior of materials at small scales. In the particular case of metals, a class of available non-classical continuum mechanics theories has been recently employed in order to explain the wide range of observed behavior at the micron scale. The practical use of the proposed theories remains limited due to issues in its numerical implementation. First, in displacement-based finite element formulations the need appears for higher orders of continuity in the interpolation shape functions in order to maintain the convergence rate upon mesh refinement. This limitation places strong restrictions in the geometries of the available elements. Second, the available inelastic constitutive models for small scale applications have been cast into deformation theory formulations limiting the set of problems to those exhibiting proportional loading only. In this article two contributions are made for the particular case of a Cosserat couple stress continuum. First it describes a numerical scheme based on a penalty function/reduced integration approach that allows for the proper treatment of the higher order terms present in Cosserat like theories. This scheme results in a new finite element that can be directly implemented into commercial finite element codes. Second, a flow theory of plasticity incorporating size effects is proposed for the case of rate independent materials overcoming the limitations in the deformation theory formulations. The constitutive model and its corresponding time-integration algorithm are coupled to the new proposed finite element and implemented in the form of a user element subroutine into the commercial code ABAQUS. The validity of the approach is shown via numerical simulations of the microbending experiment on thin Nickel foils reported in the literature. 2008 artículo científico 1794-9165 https://www.redalyc.org/articulo.oa?id=83540806 en http://www.redalyc.org/revista.oa?id=835 Ingeniería y Ciencia application/pdf Universidad EAFIT Ingeniería y Ciencia (Colombia) Num.8 Vol.4 |
| format | Artículo científico |
| id | redalyc_83540806 |
| institution | Redalyc |
| language | en |
| publishDate | 2008 |
| publisher | Universidad EAFIT |
| spellingShingle | Numerical treatment of cosserat based rate independent strain gradient plasticity theories Juan David Gómez C. Ingeniería Non couple stress theory constitutive modeling integration algorithms finite element analysis Numerical treatment of cosserat based rate independent strain gradient plasticity theories Juan David Gómez C. Ingeniería Non couple stress theory constitutive modeling integration algorithms finite element analysis The current trend towards miniaturization in the microelectronics industry has pushed for the development of theories intended to explain the behavior of materials at small scales. In the particular case of metals, a class of available non-classical continuum mechanics theories has been recently employed in order to explain the wide range of observed behavior at the micron scale. The practical use of the proposed theories remains limited due to issues in its numerical implementation. First, in displacement-based finite element formulations the need appears for higher orders of continuity in the interpolation shape functions in order to maintain the convergence rate upon mesh refinement. This limitation places strong restrictions in the geometries of the available elements. Second, the available inelastic constitutive models for small scale applications have been cast into deformation theory formulations limiting the set of problems to those exhibiting proportional loading only. In this article two contributions are made for the particular case of a Cosserat couple stress continuum. First it describes a numerical scheme based on a penalty function/reduced integration approach that allows for the proper treatment of the higher order terms present in Cosserat like theories. This scheme results in a new finite element that can be directly implemented into commercial finite element codes. Second, a flow theory of plasticity incorporating size effects is proposed for the case of rate independent materials overcoming the limitations in the deformation theory formulations. The constitutive model and its corresponding time-integration algorithm are coupled to the new proposed finite element and implemented in the form of a user element subroutine into the commercial code ABAQUS. The validity of the approach is shown via numerical simulations of the microbending experiment on thin Nickel foils reported in the literature. 2008 artículo científico 1794-9165 https://www.redalyc.org/articulo.oa?id=83540806 en http://www.redalyc.org/revista.oa?id=835 Ingeniería y Ciencia application/pdf Universidad EAFIT Ingeniería y Ciencia (Colombia) Num.8 Vol.4 |
| title | Numerical treatment of cosserat based rate independent strain gradient plasticity theories |
| topic | Ingeniería Non couple stress theory constitutive modeling integration algorithms finite element analysis |
| url | https://www.redalyc.org/articulo.oa?id=83540806 |