Composite materials demonstrate different failure modes including volumetric damage to the various phases and interfacial damage along the matrix/reinforcement interfaces. From a numerical point of view, accounting for these different failure modes not only pose significant challenges in the modeling strategy (e.g., representation of continuum and interfacial damage), but also requires an efficient multiscale solution approach that bridges the response at the microstructure scale to that of the structural scale.

In this talk, we present a multiscale reduced-order modeling framework for heterogeneous materials that accounts for both cohesive interface failure and continuum damage. The model builds on the eigendeformation-based reduced-order homogenization model (EHM), and works in a two-scale homogenization setting with a focus on reducing the computational cost associated with the microscale problem. EHM first pre-computes a set of coefficient tensors associated with subdomains (volumetric and interfacial) of the microstructure known as parts through finite element analysis of the fully resolved microstructure considering linear elasticity. These coefficient tensors are integral function of the numerical Green's function, representing the interactions between subdomains, and between one subdomain and the entire microstructure. Using these coefficient tensors, and assumed spatial variation (i.e., piece-wise constant) of the response over the microstructure parts, a set of linear algebraic equations with part-wise response as unknowns is derived from the microscale equilibrium, which is a reduced-order representation of the full field microscale problem. EHM provides a hierarchy of reduced-order models, ranging from low-fidelity-high-efficiency to high-fidelity-low-efficiency. The finest reduced-order model is partitioning each element of the microstructure as one part, which recovers the solution of full field finite element simulation. To balance the accuracy and efficiency, a k-means clustering algorithm is used to optimally construct these parts and a new formulation for the partitioning of interfaces using this method is proposed. The extraction of the volumetric and interfacial influence functions in the preprocessing stage is performed using the Interface-enriched Generalized Finite Element Method (IGFEM), which relies on a finite element discretization that does not conform to the material phase boundaries. A Lagrange multiplier method is also used in this preprocessing phase, allowing for the reuse of the matrix factorization for different influence function problems and hence leading to efficiency improvement. A newly proposed traction calculation for the interface partition is also used to alleviate the instability caused by traction calculations along interfaces. The accuracy and efficiency of the IGFEM-EHM method is assessed through comparison with reference IGFEM simulations. The method is then used to extract the nonlinear multiscale response of particulate, unidirectional fiber-reinforced, and woven composites. The IGFEM-EHM demonstrates its capability of modeling complex microstructure with the presents of both volumetric and interfacial damage.


Integrating GFEM and Eigendeformation-Based Reduced-Order Homogenization Model for Simulating Heterogeneous Materials Under Volumetric and Interfacial Damage

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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