Extreme mechanics modeling

Stably(!) modeling extreme mechanics without a mesh

Meshfree modeling provides significant advantages over traditional mesh/grid-based methods for solid mechanics problems, particularly in handling problems involving complex geometries, large deformations, and evolving interfaces. By eliminating the constraints of a fixed mesh, these methods offer greater flexibility and robustness when simulating extreme mechanical behavior, especially in scenarios where traditional methods fail due to mesh distortion or remeshing requirements.

In this context, we are dedicated to advancing the field of computational mechanics, with a particular focus on modeling extreme mechanical behaviors. To this end, we have developed an improved meshfree modeling framework, which builds on the local maximum-entropy strategy of striking a balance between shape function locality and approximation entropy in an information-theoretic sense. This new scheme is specifically tailored for problems involving severe deformations, offering a significant improvement in both stability and accuracy over traditional methods. Key aspects include the following.

• Updated Lagrangian formulation that ensures stability during large deformations.

• Anisotropic shape function support, which adapts to directional variations in nodal spacing as deformation progresses, eliminating the classical tensile instability seen in many meshfree methods.

• Spatially evolving shape functions that dynamically adjust their support domain, improving computational efficiency.

• Interface truncation to accurately handle multi-component systems, such as composites or polycrystals, without the need for remeshing.

We applied this framework to create a multiscale model for thermomechanical processing of metallic systems. Moreover, through collaborators (lead: De Lorenzis group at ETHZ), we adapted similar ideas of meshfree modeling to isogeometric analyses (paper-1, paper-2), opening new avenues for modeling of extreme mechanics phenomena during additive manufacturing.

Coming soon!

Building on this foundation, our current research is expanding into several exciting areas. We are developing frameworks to model multiphysics-based smart materials that can perform in extreme environments. Moreover, we are actively working on unraveling the shock physics, fracture mechanics, and energy absorption in metamaterials under high-velocity impacts, with applications ranging from aerospace and defense to medical implants. Stay tuned! :-)

Publications

• S. Kumar, K. Danas, D. M. Kochmann, Enhanced local maximum-entropy approximation for stable meshfree simulations, Computer Methods in Applied Mechanics and Engineering, 344 (2019), 858-886.

• S. Kumar, A. Vidyasagar, D. M. Kochmann, An assessment of numerical techniques to find energy‐minimizing microstructures associated with nonconvex potentials, International Journal for Numerical Methods in Engineering, 121 (2020), 1595-1628 (cover article).

• S. Kumar*, A. D. Tutcuoglu*, Y. Hollenweger, D. M. Kochmann, A meshless multiscale approach to modeling severe plastic deformation of metals: Application to ECAE of pure copper, Computational Material Science,  173 (2020), 109329.

• S.K. Kota, S. Kumar, B. Giovanardi, A discontinuous Galerkin / cohesive zone model approach for the computational modeling of fracture in geometrically exact slender beams, Computational Mechanics (2024).

• H. C. Hille, S. Kumar, L. De Lorenzis, Enhanced Floating Isogeometric Analysis, Computer Methods in Applied Mechanics and Engineering, 417 (2023), 116346. 

• H. C. Hille, S. Kumar, L. De Lorenzis, Floating Isogeometric Analysis, Computer Methods in Applied Mechanics and Engineering, 392 (2022), 114684.