Multiscale Modeling and Simulation of Complex Systems

The field of multiscale modeling and simulation is rapidly advancing, with a focus on developing innovative methods to capture the behavior of complex systems. Recent developments have highlighted the importance of accounting for nonlinearities, geometric adaptability, and conservation fidelity in modeling multiphysics interactions. The use of hybrid numerical strategies, such as the Element-based Finite Volume Method, has shown promise in reconciling geometric flexibility with strict conservation enforcement. Additionally, variational multiscale enrichment methods have been extended to model the dynamic response of hyperelastic materials undergoing large deformations. Noteworthy papers in this area include: A paper proposing a multicontinuum homogenization approach for nonlinear problems involving dynamically evolving multiscale media, which allows for the formulation of macroscopic variables and derivation of new macroscopic models. A paper introducing a novel three-dimensional adaptation of the Element-based Finite Volume Method, which enables accurate modeling in geometrically and physically challenging interfacial systems. A paper extending the variational multiscale enrichment method to model the dynamic response of hyperelastic materials, which provides a foundation for studying the dynamic response of architected materials.

Sources

Dynamic nonlinear multicontinuum homogenization of systems with intrinsically evolving microstructure

Modelling Heterogeneous Interfaces using Element-based Finite Volumes

Variational multiscale enrichment method for dynamic response of hyperelastic materials at finite deformation

A Phase-Field Model for Vesicle Membranes Incorporating Area-Difference Elasticity

A Hybrid-High Order method for fracture modelling

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