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1.	Fredriksson, Per, et al. (author) Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites 2009 In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 46:22-23, s. 3977-3987 Journal article (peer-reviewed)abstract A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories.

Fredriksson, Per, et al. (author)
Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites
2009
In: International Journal of Solids and Structures. - : Elsevier BV. - 0020-7683 .- 1879-2146. ; 46:22-23, s. 3977-3987
Journal article (peer-reviewed)abstract
- A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories.

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