Fully-coupled micro–macro finite element simulations of the Nakajima test using parallel computational homogenization

The Nakajima test is a well-known material test from the steel and metal industry to determine the forming limit of sheet metal. It is demonstrated how FE2TI, our highly parallel scalable implementation of the computational homogenization method FE$$^2$$ 2 , can be used for the simulation of the Nakajima test. In this test, a sample sheet geometry is clamped between a blank holder and a die. Then, a hemispherical punch is driven into the specimen until material failure occurs. For the simulation of the Nakajima test, our software package FE2TI has been enhanced with a frictionless contact formulation on the macroscopic level using the penalty method. The appropriate choice of suitable boundary conditions as well as the influence of symmetry assumptions regarding the symmetric test setup are discussed. In order to be able to solve larger macroscopic problems more efficiently, the balancing domain decomposition by constraints (BDDC) approach has been implemented on the macroscopic level as an alternative to a sparse direct solver. To improve the computational efficiency of FE2TI even further, additionally, an adaptive load step approach has been implemented and different extrapolation strategies are compared. Both strategies yield a significant reduction of the overall computing time. Furthermore, a strategy to dynamically increase the penalty parameter is presented which allows to resolve the contact conditions more accurately without increasing the overall computing time too much. Numerically computed forming limit diagrams based on virtual Nakajima tests are presented.

Development of Line-to-Line Contact Formulation for Continuum Beams

A line-to-line beam contact formulation in the framework of the absolute nodal coordinate formulation (ANCF) is introduced in this paper. Higher- and lower-order ANCF beam elements employ the introduced beam contact formulation. The higher- and lower-order ANCF beam elements are compared in terms of their accuracy and performance in a large deformation contact problem. Efficiency of numerical integration of contact energy variation contribution to the system’s equations of motion is studied. The contacting elements’ surfaces of the ANCF beam elements are parameterized by segmentation of integration over the contact patch. Numerical results investigate the accuracy, robustness and efficiency of the developed line-to-line contact formulation by comparing against a solid element type using commercial finite element code. According to the numerical results, the higher-order ANCF beam element’s solution is closer than the lower-order ANCF beam element’s in accordance with the reference solution provided by a solid element type using commercial finite element code ABAQUS. Furthermore, the higher-order beam element is found to be more efficient than the lower-order beam with respect to the numerical integration of the contact energy variation. Expectedly, the higher-order ANCF beam element is able to capture the cross-section deformation in a large deformation contact problem, while the lower-order element fails to exhibit such cross-sectional deformation.

Multilevel augmented Lagrangian solvers for overconstrained contact formulations

Multigrid methods for two-body contact problems are mostly based on special mortar discretizations, nonlinear Gauss-Seidel solvers, and solution-adapted coarse grid spaces. Their high computational efficiency comes at the cost of a complex implementation and a nonsymmetric master-slave discretization of the nonpenetration condition. Here we investigate an alternative symmetric and overconstrained segment-to-segment contact formulation that allows for a simple implementation based on standard multigrid and a symmetric treatment of contact boundaries, but leads to nonunique multipliers. For the solution of the arising quadratic programs, we propose augmented Lagrangian multigrid with overlapping block Gauss-Seidel smoothers. Approximation and convergence properties are studied numerically at standard test problems.

Biomechanical Model of Human Index Finger During Examination

We have developed a mathematical model based on the Hunt-Crossley’s viscoelastic contact formulation for predicting the contact forces in the upper-body. The simulations were carried out in OpenSim software package and the simulations results were compared to experimentally recorded contact forces measured using a pressure algometer for assessing pressure pain sensitivity in the pelvic region 1. We observed a very good agreement between the model prediction and algometer data. Our simulation revealed that by pressing down on the tissue both normal and frictional contact forces increase up to a point- ceiling effect. Moreover, viscoelastic properties of the examinee’s tissue were associated with force; specifically, as the stiffness of the tissue declined both normal and frictional contact forces similarly declined albeit in a different way. Once the contact force reaches a peak point (irrespective of the baseline stiffness of the tissue) additional pressure application by the examiner was associated with incremental decrease in both normal and frictional (wasted) contact force.

Frictional Flexible Pipe Model Using Macroelements

Flexible pipes are structures composed by many layers varying in composition and shapes, in which the structural behavior is defined by the role it must play. Flexible pipes construction is such that layers are unbounded, allowing relative movement between them and modifying its behavior. Many approaches are used to model such cables, both analytical and numerical, such as the macroelements model. This sort of model consists in finite elements where geometrical characteristics are taken into account by the formulation and is under development by the authors. Previous works have shown in detail the modeled cylindrical and helical elements, as well node-to-node connection elements (bounded, frictionless and frictional), which have allowed simplified flexible pipe with bonded elements simulations. This article will focus on modeling a simplified cable consisting in an external sheath, two armor layers and a polymeric core, since recent advances in the contact formulation opens the possibility to incorporate friction between the layers. Taking into consideration accuracy, computational time and memory usage, results from macroelements are compared to commercial finite element software.