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A data-driven multiscale theory for modeling damage and fracture of composite materials. (English) Zbl 1428.74229
Griebel, Michael (ed.) et al., Meshfree methods for partial differential equations IX. Selected papers of the ninth international workshop, Bonn, Germany, September 18–20, 2017. Cham: Springer. Lect. Notes Comput. Sci. Eng. 129, 135-148 (2019).
Summary: The advent of advanced processing and manufacturing techniques has led to new material classes with complex microstructures across scales from nanometers to meters. In this paper, a data-driven computational framework for the analysis of these complex material systems is presented. A mechanistic concurrent multiscale method called Self-consistent Clustering Analysis (SCA) is developed for general inelastic heterogeneous material systems. The efficiency of SCA is achieved via data compression algorithms which group local microstructures into clusters during the training stage, thereby reducing required computational expense. Its accuracy is guaranteed by introducing a self-consistent method for solving the Lippmann-Schwinger integral equation in the prediction stage. The proposed framework is illustrated for a composite cutting process where fracture can be analyzed simultaneously at the microstructure and part scales.
For the entire collection see [Zbl 1422.65012].

74S99 Numerical and other methods in solid mechanics
65T50 Numerical methods for discrete and fast Fourier transforms
74E30 Composite and mixture properties
74R05 Brittle damage
74A60 Micromechanical theories
74N15 Analysis of microstructure in solids
74M25 Micromechanics of solids
74S05 Finite element methods applied to problems in solid mechanics
74B05 Classical linear elasticity
65R20 Numerical methods for integral equations
65H10 Numerical computation of solutions to systems of equations
65N50 Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs
35Q74 PDEs in connection with mechanics of deformable solids
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