有限应变下纤维增强粘弹性结构的模拟：乘法方法
Simulation of fiber-reinforced viscoelastic structures subjected to finite strains: multiplicative approach
摘要：
本研究致力于纤维增强复合材料结构的几何非线性模拟。本文对乘性方法在复合材料粘弹性模拟中的适用性进行了评价，并提出了一些改进意见。为了在局部压缩纤维屈曲的应用中获得更高的精度，引入了一个新的超弹性势族。这个家庭使我们能够占可变的临界压应力，这取决于纤维-基体相互作用。对于粘弹性的模拟，实施了变形梯度的公认的Sidoroff分解。为了解释基质材料的粘度，使用Simo和Miehe（1992）的模型;实现了高效的无迭代算法。纤维的粘度同样描述的乘法分解的变形梯度，导致一个标量微分方程，提出了一个有效的无迭代算法的隐式时间步进。新的迭代方法的精度和收敛性进行了测试和比较，标准计划实施牛顿迭代。为了证明该方法的适用性，加压多层复合管建模，所谓的拉伸反转现象再现和解释。应力分布是由一个半解析的程序，它可以作为一个基准有限元计算。最后讨论了参数辨识问题。
英文摘要：
The study is devoted to the geometrically nonlinear simulation of fiber-reinforced composite structures. The applicability of the multiplicative approach to the simulation of viscoelastic properties of a composite material is assessed, certain improvements are suggested. For a greater accuracy in applications involving local compressive fiber buckling, a new family of hyperelastic potentials is introduced. This family allows us to account for the variable critical compressive stress, which depends on the fiber-matrix interaction. For the simulation of viscoelasticity, the well-established Sidoroff decomposition of the deformation gradient is implemented. To account for the viscosity of the matrix material, the model of Simo and Miehe (1992) is used; highly efficient iteration-free algorithms are implemented. The viscosity of the fiber is likewise described by the multiplicative decomposition of the deformation gradient, leading to a scalar differential equation; an efficient iteration-free algorithm is proposed for the implicit time stepping. The accuracy and convergence of the new iteration-free method is tested and compared to that of the standard scheme implementing the Newton iteration. To demonstrate the applicability of the approach, a pressurized multi-layer composite pipe is modelled; the so-called stretch inversion phenomenon is reproduced and explained. The stress distribution is obtained by a semi-analytical procedure; it may serve as a benchmark for FEM computations. Finally, the issue of the parameter identification is addressed.
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