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Policonvexity Failure

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  • Policonvexity Failure

    Hi All,

    Courtesy of valent mathematicians, we know that, in order for a solution to exist in general to a quasistatic problem the constitutive model must be quasiconvex. The latter property is rather hard to prove, and it was later proven that the property of policonvexity implies quasiconvexity. As policonvexity can be easier to prove, it is often used.

    Sorry for the tedious preamble, just to place a setting. Now my question.

    Can anybody produce a simple example of a deformation for which failure to converge can be attributed to lack of quasiconvexity/policonvexity?

    For example, take the Ogden model. Commercial software can provide fitting parameters which do not satisfy policonvexity (e.g negative parameters). The Baker-Eriksen conditions for stability are weaker, and i think Abaqus always satisfies them.

    Has anybody experienced a problem in converging caused by lack of policonvexity for such a material?
    Or ran into problems such as localisation when using a non-policonvex material?

    Thanks a lot

  • #2
    Hello Muzialis - Good to hear from you again!

    I used to care about polyconvexity back in my PhD student days. Since then I have developed a more practical approach when it comes to FE modeling. My experience is that mMost reasonably formulated material models have little issues with stability. There are certainly cases when instabilities can occur, these are often effectively address using numerical damping or contact stability. In other words, I have not seen real problems based on lack of polyconvexity.

    Jorgen Bergstrom, Ph.D. PolymerFEM Administrator