This work presents a numerical formulation to model isotropic viscoelastic material behavior for membranes and thin shells. The surface and the shell theory are formulated within a curvilinear coordinate system, which allows the representation of general surfaces and deformations. The kinematics follow from Kirchhoff-Love theory and the discretization makes use of isogeometric shape functions. A multiplicative split of the surface deformation gradient is employed, such that an intermediate surface configuration is introduced. The surface metric and curvature of this intermediate configuration follow from the solution of nonlinear evolution laws - ordinary differential equations (ODEs) - that stem from a generalized viscoelastic solid model. The evolution laws are integrated numerically with the implicit Euler scheme and linearized within the Newton-Raphson scheme of the nonlinear finite element framework. The implementation of membrane and bending viscosity is verified with the help of analytical solutions and shows ideal convergence behavior. The chosen numerical examples capture large deformations and typical viscoelasticity behavior, such as creep, relaxation, and strain rate dependence. It is also shown that the proposed formulation can be straightforwardly applied to model boundary viscoelasticity of 3D bodies.
翻译:这项工作为膜膜和薄壳提供了一种用于模拟等离子色相对弹性物质行为的数字配方。 表面和贝壳理论是在曲线坐标系统内形成的, 从而可以代表一般表面和变形。 运动学学学学来自Kirchhoff- Love 理论, 离散化则使用异形形状功能。 采用了表层变形梯度的多倍分解, 从而引入了中间表面配置。 这种中间结构的表面计量和曲度来自非线性演变法的解决方案―― 普通差异方程式( ODEs) —— 由普遍粘结性固态模型形成。 进化法在数字上与隐含的 Euler 方案相结合, 并在非线性定质元素框架的 Newton- Raphson 方案内线性地化。 利用分析解决方案的帮助, 和显示理想的趋同行为。 所选的数字示例是, 大规模变异形和典型的对比性行为, 如模型、 放松度和压力度 3 的立度等。 也显示, 拟应用到直态 。