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首页> 外文期刊>ZAMP: Zeitschrift fur Angewandte Mathematik und Physik: = Journal of Applied Mathematics and Physics: = Journal de Mathematiques et de Physique Appliquees >A geometrically exact viscoplastic membrane-shell with viscoelastic transverse shear resistance avoiding degeneracy in the thin-shell limit. Part I: The viscoelastic membrane-plate
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A geometrically exact viscoplastic membrane-shell with viscoelastic transverse shear resistance avoiding degeneracy in the thin-shell limit. Part I: The viscoelastic membrane-plate

机译：几何精确的粘塑性膜壳，具有粘弹性横向剪切力，避免了薄壳极限的退化。第一部分：粘弹性膜板

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We reduce a viscoelastic finite-strain continuum model to a two-dimensional membrane-plate. The reduction is based on assumed kinematics, analytical integration through the thickness and physically motivated simplifications. The resulting formulation is observer-invariant and accounts for thickness stretch and finite rotations. The membrane energy is a quadratic, uniformly Legendre-Hadamard elliptic, first order energy in contrast to classical membrane models and the corresponding system of balance equations remains of second order. An evolution equation for some independent rotation is appended (already in the bulk-model) introducing viscoelastic transverse shear resistance. It can be shown that this reduced membrane formulation is locally well-posed. Use is made of a dimensionally reduced version of an extended Korn's first inequality. In the equilibrium relaxation limit an intrinsic membrane-plate formulation is obtained similar to the proposal of Fox/Simo, which is, however, non-elliptic. Nevertheless, the linearization of this last equilibrium model coincides with the classical linear membrane-plate model. In this sense, the new viscoelastic membrane-plate model regularizes the occurring loss of ellipticity in classical finite-strain membrane models.
机译：我们将粘弹性有限应变连续体模型简化为二维膜板。减少的依据是假设的运动学，通过厚度进行的分析集成和基于物理的简化。所得公式是观察者不变的，并说明了厚度拉伸和有限的旋转。与经典的膜模型相比，膜能量是二次均匀的Legendre-Hadamard椭圆形一阶能量，而相应的平衡方程组仍为二阶。附加了一些独立旋转的演化方程（已经在体模型中），引入了粘弹性横向剪切阻力。可以证明，这种减少的膜配方是局部良好的。使用了扩展的Korn的第一个不等式的缩小版本。在平衡弛豫极限下，类似于Fox / Simo的建议获得了固有的膜板配方，但是该配方是非椭圆形的。然而，最后一个平衡模型的线性化与经典线性膜板模型相吻合。从这个意义上讲，新的粘弹性膜板模型规范了经典有限应变膜模型中椭圆度的发生损失。

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