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Higher-order theories have a broad range of successful applications but also suffer from localization instability and mesh-size dependency when modeling quasi-brittle materials such as concrete with strain-softening behavior. To overcome the above difficulties, this paper proposes a fracture energy regularization method with a unified, consistent crack bandwidth specifically tailored for higher-order beam theories. The Carrera unified formulation (CUF) is applied to develop scalable structural theories and related finite elements. To evaluate the accuracy of the new crack bandwidth, three typical experimental quasi-static benchmarks of pure concrete structures are utilized. A modified Mazars damage model with tensile and compressive softening laws is implemented in these benchmarks. The comparison between numerical and experimental results demonstrates that the proposed method can accurately determine the correct crack bandwidth and preserve the dissipated energy per unit area of a fracture surface. Moreover, this robust estimation of crack bandwidth reduces the mesh dependency in general, ensuring the high efficiency of the CUF model. [ABSTRACT FROM AUTHOR]

This article has been retracted. A retraction notice can be found at https://doi.org/10.3233/JIFS-219433. [ABSTRACT FROM AUTHOR]

Site quality evaluation is an important foundation for decision-making and planning in forest management and provides scientific decision support and guidance for the sustainable development of forests and commercial plantations. Site index and site form models were constructed and subsequently compared utilizing fir (Cunninghamia lanceolata) plantations in Nanping City, Fujian Province, China. This papers aim was to construct a site quality classification model, conduct further analysis on the effects of different site factors on the quality of the site, and achieve an assessment of site quality for Chinese fir plantations. An algebraic difference approach was used to establish a site index model and a site form model for Chinese fir in Fujian Province. The suitability of the two models was compared using model accuracy analysis and partial correlation, and the optimal model was chosen for classifying the site quality of the stands. On this basis, a site quality classification model was established using the random forest algorithm, and the importance of each site factor was determined through importance ranking in terms of their impact on site quality. Within the study area, the R2 of the site index model results was 0.581, and the R2 values of the five site form models based on different reference breast diameters, ranked from high to low, were 0.894, 0.886, 0.884, 0.880, and 0.865. The bias correlation coefficient between site form and stand volume was 0.71, and the bias correlation coefficient between site index and stand volume was 0.52. The results confirmed that the site form model is better suited for evaluating the site quality of Chinese fir plantations. The random forest-based site form classification model had a high classification accuracy with a generalization accuracy of 0.87. The factors that had the greatest impact on site form were altitude, canopy closure, and slope gradient, whereas landform had the smallest impact on site form. These results can provide a reference for the evaluation of the site quality of plantations and natural forests in southern China to ensure the long-term sustainable use of forest resources. [ABSTRACT FROM AUTHOR]