Meshfree Methods – Institute of Continuum Mechanics

Simulation driven engineering is nowadays an essential part in the development process. Especially in the field of subtractive or additive manufacturing their is an increasing interest on high fidelity modeling. Due to their flexibility meshfree solution schemes are very attractive for the simulation of such processes which involve intrinsic and varying discontinuities.

Many meshfree methods were developed over the years. However all of these schemes to model continua need either special stabilization algorithm, regularization techniques or correction schemes to reproduce the behavior of academic test examples. However, even an approximate prediction of real dynamic systems can not be guaranteed with these methods. Additionally, unphysical parameters have to be determined, if such stabilization, regularization or correction schemes are used.

Nevertheless, in order to be able to make reliable statements in the high fidelity modeling of engineering applications the need on more flexible solution schemes which ensures robustness, efficiency and accuracy is still present.

The shortcomings of truly meshfree methods result mostly from a violation of mathematical requirements on computational solution schemes, like the consistency conditions or the integration constraint. Additionally, phenomena like under-integration can likely occur.

A meshfree solution scheme which exhibits the same accuracy as the meshbased Finite Element Method, which can be applied for all engineering application cases and which is robust and efficient is still not found.

Improving Accuracy and Performance of Meshfree Methods

Numerical simulation of pile installation in a hypoplastic framework using an SPH based Method

In this project, a 3D computational tool using smoothed particle hydrodynamics (SPH) is developed which based on a hypoplastic constitutive approach for the mechanical behavior of the soil. The numerical code is firstly validated against a benchmark problem. Then several test cases are simulated including monotonic and vibratory penetration of piles into the soil. A good agreement with the experimental observation is found. Additionally, the impact of pile running in the presence of sheetpiles (retainers) are investigated to see how pile running can alter the applied forces on the sheet piles. The simulation of such complex geotechnical problems which involve large deformation, material nonlinearity and moving boundary conditions demonstrates the applicability and versatility of the proposed numerical tool in this field.

Led by: Peter Wriggers

Team: Meisam Soleimani, Christian Weißenfels

Year: 2020
Peridynamic Galerkin Methods

Simulation-driven product development is nowadays an essential part in the industrial digitalization. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Thanks to their flexibility, meshfree solution methods are particularly suitable for simulating the stated processes, often accompanied by large deformations, variable discontinuities, or phase changes. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. Over the years, several meshfree schemes have been developed. Nevertheless, along with their flexibility in discretization, meshfree methods often endure a decrease in accuracy, efficiency and stability or suffer from a significantly increased computation time. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. The combination of the so-called peridynamic correspondence formulation with a particle discretization yields a flexible meshfree simulation method, though does not lead to reliable results without further treatment. In order to develop a reliable, robust and still flexible meshfree simulation method, the classical correspondence formulation is generalized into the Peridynamic Galerkin (PG) methods in this project. On this basis, conditions on the meshfree shape functions of virtual and actual displacement are presented, which allow an accurate imposition of force and displacement boundary conditions and lead to stability and optimal convergence rates. Based on Taylor expansions moving with the evaluation point, special shape functions are introduced that satisfy all the previously mentioned requirements employing correction schemes. In addition to displacement-based formulations, a variety of stabilized, mixed and enriched variants are developed, which are tailored in their application to the nearly incompressible and elasto-plastic finite deformation of solids, highlighting the broad design scope within the PG methods. Compared to related Finite Element formulations, the PG methods exhibit similar convergence properties. Furthermore, an increased computation time due to non-locality is counterbalanced by a considerably improved robustness against poorly meshed discretizations.

Led by: Christian Weißenfels, Peter Wriggers

Team: M.Sc. Tobias Bode

Year: 2019
Using Machine Learning to Improve the Modelling of Machining and Cutting Processes

Metal cutting is a fundamental process in industrial production. The fast and accurate on-line prediction of metal cutting processes is crucial for the Intelligent Manufacturing (IM). With the advent of high-speed computing, robust numerical algorithms and machine learning technology, computational modelling serves as a tool for not only accurate but also fast predicting the complex machining processes and understanding the complex physics. In this work, the machine learning based numerical model is developed for simulation of metal cutting processes.

Led by: C. Weißenfels, P. Wriggers

Team: M.Sc. Dengpeng Huang

Year: 2018

Funding: China Scholarship Council (CSC)
ISPH-based Simulation of the Selective Laser Melting Process

Development of a thermo-mechanical model for the simulation of the SLM process.

Led by: Christian Weißenfels, Peter Wriggers

Team: M.Sc. Jan-Philipp Fürstenau

Year: 2017
Process Simulation for Selective Laser Melting

A phase change model for solution with the meshfree Galerkin OTM method is developed.

Led by: Christian Weißenfels, Peter Wriggers

Team: M.Sc. Henning Wessels

Year: 2016
3D-Printing of Curing Polymers

3D-Printing simulations of curing polymers within the concept of Peridynamics are developed.

Led by: Christian Weißenfels, Peter Wriggers

Team: M.Sc. Philipp Hartmann

Year: 2016

Funding: DFG (Graduiertenkolleg 1627)