Jun Li

University of Massachusetts Dartmouth | UMD · Department of Mechanical Engineering

Nodaway, additive manufacturing (AM) technologies are becoming a transubstantiate for the conventional manufacturing methodologies that can deliberate a flexible and efficient production system. AM uses the computer-aided-design (CAD) software to deliver the desired output by depositing material, layer upon layer, through thermo-mechanical cycles. This process implies a multi-physics system; on the other hand, due to AM process capabilities, the process can build a full-scale functional part with a complex geometrical shape within short cycle-time. Thus, AM machine suppliers do not guarantee the best optimal settings for the AM process parameters. Accordingly, a multi-objective optimization problem (MOOP) is formulated constrained with space mapping problem. The computational complexity of the emerged MOOP prevents a broader adoption of additively manufactured functional parts. This work proposes a realistic and efficient data-driven approach for predicting, optimizing and simulating the additive manufacturing process parameters using surrogate modeling. The proposed themes consist of three popular methods: (1) Group Method for Data Handling (GMDH) variants as the engine of prediction modeling technique, the modified polynomial neural network can characterize the spatial collinearity for the input arguments along with dependency relationship among the multiple outputs. (2) Evolutionary algorithms (EA) to find the optimal operational settings and extract the Pareto-frontier space from the approximated design space. (3) Reduce-order modeling techniques to provide a numerical simulation for the AM process, which could expand the exploration of the design space. The numerical results from different data-driven techniques correlate well with the Abaqus FE simulation and the lab experimental results. This approach provides a feasible and realistic approach for the AM process modeling and optimization.

The developed anisotropic damage models for 3D printed polymer materials based on layer orientation has potential applications on the study of orthotropic fracture behavior of bone as well as 3D printed bone substitutes.

Unlike the fractional derivative, the Hausdorff derivative, one kind of fractal derivatives (also called the non-local fractional derivative), introduced by Chen (2006), is a local derivative instead of a global operation. Thus, the computing costs of the Hausdorff fractal derivative are far less than the global fractional derivative, while performing almost equally well in modeling a variety of complex problems. In particular, the Hausdorff fractal derivative diffusion equation characterizes the stretched Gaussian process in space and fractal exponental decay, also known as the stretched relaxation, in time. In contrast, the fractional derivative diffusion equation underlies the Levy statistics in space and the ML function power law decay in time. By extending the concept of fundamental solution of integer-order differential operators to fractal by Chen et al (2016), the fractal differential operators are defined and employed to describe various mechanical behaviors of fractal materials. Fractal calculus operator significantly extends the application scope of the classical calculus modeling approach under the framework of continuum mechanics to fractal materials. It is noted that there exist quite a few different definitions of fractal derivative, among which, to the best understanding and knowledge, the Hausdorff derivative is mathematically the most simple and numerically the easiest to implement with clear physical significance and the most real-world applications.