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. Peridynamics is an alternative theory to local continuum mechanics for describing partial differential equations in a non-local integro-differential form. 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. Over the years, several meshfree schemes have been developed. Furthermore, in the industrial domain, the meshing of complex geometries represents a significant workload, which is usually minor for meshfree methods. 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. Notably, there is an increasing interest in realistic high-fidelity simulation methods in the fast-growing field of additive and ablative manufacturing processes. Simulation-driven product development is nowadays an essential part in the industrial digitalization. Additionally, phenomena like under-integration can likely occur.Ī 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. 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. 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. Additionally, unphysical parameters have to be determined, if such stabilization, regularization or correction schemes are used. However, even an approximate prediction of real dynamic systems can not be guaranteed with these methods. 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. Many meshfree methods were developed over the years. Due to their flexibility meshfree solution schemes are very attractive for the simulation of such processes which involve intrinsic and varying discontinuities.
Especially in the field of subtractive or additive manufacturing their is an increasing interest on high fidelity modeling. Simulation driven engineering is nowadays an essential part in the development process.
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