论文标题
基于乘法表面变形的边界和外壳粘弹性的等几何有限元公式
An isogeometric finite element formulation for boundary and shell viscoelasticity based on a multiplicative surface deformation split
论文作者
论文摘要
这项工作为对膜和薄壳的各向同性粘弹性材料行为进行了建模。表面和壳理论是在曲线性坐标系中制定的，该系统允许表示一般表面和变形。运动学源自基尔乔夫 - 爱理论，离散化可以利用同几幅形状函数。采用了表面变形梯度的乘法分裂，从而引入了中间表面构型。该中间构型的表面度量和曲率来自非线性进化定律的解 - 普通微分方程（ODES） - 源于广义粘弹性固体模型。进化定律与隐式Euler方案进行数值整合，并在非线性有限元元素的Newton-Raphson方案中线性化。在分析溶液的帮助下验证了膜和弯曲粘度的实施，并显示了理想的收敛行为。所选的数值示例捕获了较大的变形和典型的粘弹性行为，例如蠕变，放松和应变率依赖性。还表明，所提出的配方可以直接应用于3D主体的模型边界粘弹性。
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.
