However, many studies rely on simplified approaches, such as equivalent diameters 9, 51, 53 or defect-based corrections 39, 43, while computationally efficient, lack the integration of detailed defect data into multiscale frameworks. Other approaches, like homogenization techniques and machine learning 55, 56, have reduced computational effort but often overlook the critical influence of defects on mechanical performance. Additionally, experimental validation is frequently limited or absent, restricting the applicability of these methods for real-world applications. The proposed HMM framework takes a fundamentally different approach with the following advantages. First, the HMM approach does not require pre-defining model partition boundaries or reducing the model prior to simulation. Instead, it decomposes the simulation process https://wizardsdev.com/en/vacancy/senior-product-manager-ai-product/ in time by automatically alternating between a micro-process for detailed EMT simulation and a macro-process focusing on slower dynamics, both conducted on the same EMT model of the original system.
Materials and experiments
Like the 2 × 2 × 2 model, the defect-inclusive approach better predicts the first peak force compared to the defect-free model though with a slightly higher discrepancy. The experimental first peak force is in the range of 25–26.5 kN (38.4—40.8 MPa), while the defect-free model predicts 30 kN Multi-scale analysis (46 MPa) and the defect-inclusive model estimates approximately 28.5 kN (43.8 MPa). This discrepancy likely arises from using the defect population of the 2 × 2 × 2 specimen as defect distributions vary between specimens and with material volume 57. This section compares the experimental and numerical results for the 2 × 2 × 2 specimen to validate the proposed multiscale approach. Additionally, it includes a comparison with experimental results for a 3 × 3 × 3 lattice specimen from 51.
- Other approaches, like homogenization techniques and machine learning 55, 56, have reduced computational effort but often overlook the critical influence of defects on mechanical performance.
- However, a performance study of DMC can be found in another contribution in this Theme Issue 10.
- Common cubic RVEs assume 3D material periodicity, while CY-RVEs limit periodicity to the truss’s axial dimension, modeling its response for a given diameter and arbitrary length.
- These defects can initiate damage, promote fatigue cracks, or reduce local stiffness and strength 43,44,45.
- Standard dog-bone specimens, produced using the same process parameters as the lattice structures, were subjected to quasi-static tests to determine the material properties for the Finite Element Model.
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Despite this, the defect-inclusive model better captures the post-peak failure behavior and absorbed energy compared to the defect-free model. These findings confirm that the multiscale methodology effectively captures the degrading influence of defects on the compressive response of lattice structures. By incorporating randomized defect populations and locations, the methodology accounts for response scatter and supports the identification of a lower-bound design curve through statistical analysis. While a detailed power system model is presented here, the proposed approach also applies to models of other forms or time scales. A distinguishing feature of the HMM framework is that it requires only a single ODE model of the power system, namely the full EMT model.
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- Additive manufacturing (AM) has become a key production technology, recognized as a pillar of the Industry 4.0 revolution 1, 2.
- Multiple-scale analysis is particularly useful for constructing uniformly valid approximations to solutions of perturbation problems.
- However, as IBRs become more prevalent in power grids, the analysis and control of power grid dynamics become more complex due to their increased timescales, as well as the high dimensionality and nonlinearity of power grid models.
- It can be concluded that for all contingencies, increasing H𝐻Hitalic_H can accelerate the simulation, and the speedup ratio is proportional to H/η𝐻𝜂H/\etaitalic_H / italic_η, matching exactly the definition in (14).
- These findings confirm that the multiscale methodology effectively captures the degrading influence of defects on the compressive response of lattice structures.
When these interacting processes are modelled by different scientific disciplines, they are multi-science (or multi-physics) as well as multi-scale. Biomedical applications, where biology is coupled to fluid mechanics, are an illustration of a multi-scale, multi-science problem. For instance, in the how to hire a software developer problem of in-stent restenosis 1–4, blood flow, modelled as a purely physical process, is coupled to the growth of smooth muscle cells (SMCs). Haemodynamics is a fast varying process, acting over spatial scales ranging from micrometres to centimetres. A total of 21 CY-RVEs were generated, each representing a defect class defined by the histogram in Fig. The defect diameter was set to the average of each class, while the beam diameter and the length were fixed at 1.4 mm and 2 mm.
- Starting with defect population characterization via micro-CT scans, Finite Element Analyses (FEAs) were performed on Representative Volume Elements (RVEs) with variable defects to determine the effective stress–strain response.
- These scans, or 2D tomograms, are digitally combined to form the 3D structure.
- A 0.2 mm displacement was applied to the beam’s boundary face, and simulations were performed in Abaqus CAE using a nonlinear implicit solver on 16 CPUs.
- With concepts such as the scale separation map, the generic submodel execution loop (SEL) and the coupling templates, one can define a multi-scale modelling language which is a bridge between the application design and the computer implementation.
- The viscosity and diffusion coefficients can be computed from a fully resolved simulation, at a smaller scale, for each shear rate condition 17.
- This discrepancy likely arises from using the defect population of the 2 × 2 × 2 specimen as defect distributions vary between specimens and with material volume 57.
