hyperelastic shell element算法
如题，找了一下，没找到好的算法或者paper.有知道的朋友麻烦推荐一下，或者谈谈感想，具体实现。
纯solid单元的超弹单元没什么搞头了，教科书上都有。
由于壳单元采用了多自由度，除displacement 以外又增加了director。
那么如何建立其 strain invarient 呢？
难道是将两个分别基于displacement和director的deformation gradient叠加起来求
最终壳单元的deformation gradient?从而推导出green strain,并得出I1, I2, I3吗？
有懂得进来聊聊，或者发paper上来，有加分。 本帖最后由 北鹰南飞 于 2011-7-14 11:11 编辑
1# caoer
不明白楼主的意思，hyperelastic不就是本构模型吗？这个与壳单元算法为什么一定要扯到一起？壳单元相对实体单元就多了3个节点转动自由度，基于的壳理论无非薄壳理论，厚壳理论。就拿普通钢材，不也一样既用到实体单元也用到壳单元。
难道是我没理解LZ的意思？？ 不明白楼主的意思，hyperelastic不就是本构模型吗？
-- 是的，但是一种特殊的本构，非线性本构
这个与壳单元算法为什么一定要扯到一起？
-- 壳和solid是不一样的，壳如何计算deformaiton gradient呢？
壳单元相对实体单元就多了3个节点转动自由度，基于的壳理论无非薄壳理论，厚壳理论。就拿普通钢材，不也一样既用到实体单元也用到壳单元。
-- 同意，壳多了几个自由度，不一定是3个，也可能是2个。普通钢材不是超弹物质，泊松比一般低于0.4。弹性属性也是属于线性变化（塑性阶段除外）。 When using degenerated shell element (see, e.g. Zienkiewicz & Taylor; FEM for solid and structural mechanics, chapter 15: shells as a special case of three-dimensional analysis ), you can get displacement gradient just as that of solid elements. In this case, there is coupling between gradient from displacement and director change, not only 两个分别基于displacement和director的deformation gradient叠加起来求最终壳单元的deformation gradient.
The only difference between solid and shell elements is that for shell elements, stress(33), normal stress along shell normal is zero. You should modify your constutive relation (not just hyperelastic relation) to satisfy this condition. And, keep stress(33)=0 when doing stress update calculation. 本帖最后由 caoer 于 2011-7-19 19:34 编辑
interesting statement.
so you meant the deformation graident F = epi_{3x3} + 1_{3x3}, where the epi{3x3} is converted from the (15.11)? The director variables are not involved to the hyperelastic model? I may agree with you about this if deformation is small. I am not sure what you mean! But
1. The director variables enter Eq.(15.11) as it is obtained from Eq.(15.4), where director exists.
2. There is no strain(33) in Eq.(15.11), because stress(33)=0.0, the energy term of stress(33)*strain(33) doesn't exist.
You cannot obtain strain(33) directly but from supposition stress(33)=0.0
3. Such supposition (stress(33)=0.0) is characteristic of shell elements, it is irrelevent with all other things. 1. this equation makes sense, which also answer my questions, thanks.
2&3. I agree, the transverse normal stress/strain is zero if thickness is constant.
This set of equation looks good and doable. Thanks! Thickness is not constant and strain(33) is not zero. In some casees, such as stamping processes, considering the variation of shell thickness is quite important. 如题，找了一下，没找到好的算法或者paper.
有知道的朋友麻烦推荐一下，或者谈谈感想，具体实现。
纯solid单元的超弹单元没什么搞头了，教科书上都有。
由于壳单元采用了多自由度，除displacement 以外又增加了 ...
caoer 发表于 2011-7-14 10:48 http://forum.simwe.com/images/common/back.gif
I thought this problem is already well addressed in Bathe's papers, such as
http://web.mit.edu/kjb/www/Principal_Publications/3D-Shell_Elements_and_Their_Underlying_Mathematical_Model.pdf
Bathe mainly focused on degenerated 3D shell elements. 本帖最后由 mxlzhenzhu 于 2013-8-31 18:51 编辑
楼主，我最近编程，实体单元，四面体没有问题；六面体线性单元采用减缩积分，就发生沙漏了，不知道楼主是如何解决的？这是我的一个帖子，请查看。
http://forum.chinavib.com/thread-128077-1-1.html
可惜的是，帖子里面的论文没有看懂，附带的程序也不懂，所以现在我只能做四面体。
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