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In this paper, a contact problem between two bodies, discretized by finite elements, is solved by adding an auxiliary NURBS layer between the bodies. The advantages of a smooth contact formulation in a NURBS approach are combined with simple mesh generation procedures for the bodies discretized with finite elements. Mesh tying conditions are used to couple the NURBS layer with the finite element discretization. The NURBS layer is the master side for contact and mesh tying. Mesh tying is enforced either using pointwise or mortar type approaches. Frictionless 2D and 3D contact problems are considered using small deformations. The contact problem is discretized with the mortar method and a penalty approach is used to enforce the contact constraints. A robust element-based quadrature is applied for mortar tying and contact discretizations, thus avoiding computationally expensive Segmentation.
A regularized model for impact in explicit dynamics applied to the split Hopkinson pressure bar
(2016)
In the numerical simulation of Impact phenomena, artificial oscillations can occur due to an instantaneous change of velocity in the contact area. In this paper, a nonlinear penalty regularization is used to avoid these oscillations. Aparticular focus is the investigation of higher order methods in space and time to increase the computational efficiency. The spatial discretization is realized by higher order spectral element methods that are characterized by a diagonal mass matrix. The time integration scheme is based on half-explicit Runge–Kutta scheme of fourth order. For the conditionally stable scheme, the critical time step is influenced by the penalty regularization. A framework is presented to adjust the penalty stiffness and the time step for a specific mesh to avoid oscillations. The methods presented in this paper are applied to 1D-simulations of a split Hopkinson pressure bar, which is commonly used for the investigation of materials under dynamic loading.
In this paper, the impact problem and the subsequent wave propagation are considered. For the contact discretization an intermediate NURBS layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element‐based integration. The impact event is ill‐posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization and the coupled FE‐NURBS approach the bulk part of the mass matrix is diagonal.
In this paper, the impact problem and the subsequent wave Propagation are considered. For the contact discretization an intermediate non-uniform rational B-spline (NURBS) layer is added between the contacting finite element bodies, which allows a smooth contact formulation and efficient element-based integration.
The impact event is ill-posed and requires a regularization to avoid propagating stress oscillations. A nonlinear mesh-dependent penalty regularization is used, where the stiffness of the penalty regularization increases upon mesh refinement. Explicit time integration methods are well suited for wave propagation problems, but are efficient only for diagonal mass matrices. Using a spectral element discretization in combination with a NURBS contact layer the bulk part of the mass matrix is diagonal.