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Fracture Prediction in Beam Lattices with Mixed-Order Quasicontinuum Approach

Core Concepts
Efficiently predicting fracture toughness in beam lattices using a mixed-order quasicontinuum approach.
The study introduces a novel mixed-order quasicontinuum approach for predicting fracture toughness in beam lattices. The method combines first-order elements for full resolution around the crack flank and second-order elements for efficient coarse-graining away from the crack. Adaptive refinement is applied to improve accuracy, with results showing significant error reduction with increasing refinement steps. The approach accurately captures strain energy in stretching-dominated lattices, while overcoming issues of overprediction observed in bending-dominated topologies.
A relative density of ¯ρ = 1% was used for lattice simulations. Young's modulus E = 430 MPa and Poisson's ratio ν = 0.3 were employed. Critical failure stress σf of the base material was set at 11 MPa. Shear correction factor of 1.2 was applied to mimic TMPTA samples.
"The second-order interpolation considerably outperforms the first-order one." "Errors dropped by about 96% when transitioning from first- to second-order interpolation." "The mixed-order QC formulation showed excellent accuracy and overcame stretch locking issues."

Deeper Inquiries

How does the adaptive refinement strategy impact computational efficiency

The adaptive refinement strategy impacts computational efficiency by allowing for a more targeted allocation of computational resources. By refining the mesh only in regions where it is necessary to capture detailed information, such as around the crack tip or areas with high strain gradients, the overall number of degrees of freedom and hence computational cost can be reduced. This targeted refinement ensures that the simulation captures important features accurately while minimizing unnecessary computations in less critical areas.

What are the implications of applying different sampling rules on accuracy and computational cost

Applying different sampling rules can have significant implications on both accuracy and computational cost. The choice of sampling rule directly affects how well the QC approximation represents the true behavior of the system. A more accurate sampling rule will lead to better results but may come at a higher computational cost due to increased calculations required for energy approximations at each sampling site. On the other hand, a less accurate sampling rule may reduce computation time but could result in errors or inaccuracies in the simulation output.

How can this mixed-order approach be extended to three-dimensional beam lattices

This mixed-order approach can be extended to three-dimensional beam lattices by adapting the formulation and implementation to account for an additional dimension. In 3D simulations, similar principles would apply regarding using first-order elements for fully-resolved regions (such as around cracks) and second-order elements for coarse-grained domains away from critical areas. Adaptive refinement strategies would need to consider three-dimensional aspects like volume instead of area when determining where to refine the mesh further based on specific criteria related to stress distributions or deformation patterns within 3D structures.