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Contemporary Meshfree Methods in Computational Mechanics

Masoud Behzadinasab, Brown University

Yuri Bazilevs, Brown University

John Foster, University of Texas at Austin

Meshfree methods have evolved as a new class of promising computational tools which can handle various demanding limitations experienced by conventional mesh-based techniques. There are several methods that can be categorized under the meshfree realm, e.g. meshfree peridynamics (PD), the reproducing kernel particle method (RKPM), smoothed particle hydrodynamics (SPH), and the material point method (MPM), among others. The main feature of meshfree methods is their flexibility in representing geometries by relaxing the mesh connectivity. The accuracy of meshfree solutions are not strongly tied to their discretizations. These methods have been developed and applied to solving challenging computational mechanics problems involving complex geometries, large deformation, material discontinuities (e.g. cracks), and flow surrounding deformable structures. The meshfree techniques provide new paradigms for numerically solving PDEs as an alternative to FEM-type methods. Topics of interest for this symposium include, but are not limited to the following:

• Recent theoretical developments of meshfree methods

• Modeling of failure, fracture and fragmentation in brittle and ductile materials

• Simulation of problems involving multiple physical domains (e.g. solid, fluid) and/or multiple physical fields (e.g. mechanical, thermal, chemical) at multiple length scales

• Response of structures subjected to extreme loading conditions such as blast events and impact and penetration problems

• Numerical implementation of meshfree techniques

• Coupling of meshfree and mesh-based methods

• Coupling of meshfree methods and data-driven approaches

• Simulation of microstructural response and microstrutcture evolution

• Multiscale modeling and integrating the microstructural effects into the higher scales

• Modeling of additive manufacturing processes

• Application of meshfree methods for solving inverse problems

• Nonlocal theories in mechanics