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The paper presents an assumed strain formulation over polygonal meshes to accurately evaluate the strain fields in nonlocal damage models. An assume strained technique based on the Hu-Washizu variational principle is employed to generate a new strain approximation instead of direct derivation from the basis functions and the displacement fields. The underlying idea embedded in arbitrary finite polygons is named as Polytopal composite finite elements (PCFEM). The PCFEM is accordingly applied within the framework of the nonlocal model of continuum damage mechanics to enhance the description of damage behaviours in which highly localized deformations must be captured accurately. This application is helpful to reduce the mesh-sensitivity and elaborate the process-zone of damage models. Several numerical examples are designed for various cases of fracture to discuss and validate the computational capability of the present method through comparison with published numerical results and experimental data from the literature.

Facial wound segmentation plays a crucial role in preoperative planning and optimizing patient outcomes in various medical applications. In this paper, we propose an efficient approach for automating 3D facial wound segmentation using a two-stream graph convolutional network. Our method leverages the Cir3D-FaIR dataset and addresses the challenge of data imbalance through extensive experimentation with different loss functions. To achieve accurate segmentation, we conducted thorough experiments and selected a high-performing model from the trained models. The selected model demonstrates exceptional segmentation performance for complex 3D facial wounds. Furthermore, based on the segmentation model, we propose an improved approach for extracting 3D facial wound fillers and compare it to the results of the previous study. Our method achieved a remarkable accuracy of 0.9999986\% on the test suite, surpassing the performance of the previous method. From this result, we use 3D printing technology to illustrate the shape of the wound filling. The outcomes of this study have significant implications for physicians involved in preoperative planning and intervention design. By automating facial wound segmentation and improving the accuracy of wound-filling extraction, our approach can assist in carefully assessing and optimizing interventions, leading to enhanced patient outcomes. Additionally, it contributes to advancing facial reconstruction techniques by utilizing machine learning and 3D bioprinting for printing skin tissue implants. Our source code is available at \url{https://github.com/SIMOGroup/WoundFilling3D}.

In this study, we emphasize the integration of a pre-trained MICA model with an imperfect face dataset, employing a self-supervised learning approach. We present an innovative method for regenerating flawed facial structures, yielding 3D printable outputs that effectively support physicians in their patient treatment process. Our results highlight the model's capacity for concealing scars and achieving comprehensive facial reconstructions without discernible scarring. By capitalizing on pre-trained models and necessitating only a few hours of supplementary training, our methodology adeptly devises an optimal model for reconstructing damaged and imperfect facial features. Harnessing contemporary 3D printing technology, we institute a standardized protocol for fabricating realistic, camouflaging mask models for patients in a laboratory environment.

This study explores the potential of a fully convolutional mesh autoencoder model for regenerating 3D nature faces with the presence of imperfect areas. We utilize deep learning approaches in graph processing and analysis to investigate the capabilities model in recreating a filling part for facial scars. Our approach in dataset creation is able to generate a facial scar rationally in a virtual space that corresponds to the unique circumstances. Especially, we propose a new method which is named 3D Facial Imperfection Regeneration(3D-FaIR) for reproducing a complete face reconstruction based on the remaining features of the patient face. To further enhance the applicable capacity of the present research, we develop an improved outlier technique to separate the wounds of patients and provide appropriate wound cover models. Also, a Cir3D-FaIR dataset of imperfect faces and open codes was released at https://github.com/SIMOGroup/3DFaIR. Our findings demonstrate the potential of the proposed approach to help patients recover more quickly and safely through convenient techniques. We hope that this research can contribute to the development of new products and innovative solutions for facial scar regeneration.

Functionally graded porous plates have been validated as remarkable lightweight structures with excellent mechanical characteristics and numerous applications. With inspiration from the high strength-to-volume ratio of triply periodic minimal surface (TPMS) structures, a new model of porous plates, which is called a functionally graded TPMS (FG-TPMS) plate, is investigated in this paper. Three TPMS architectures including Primitive (P), Gyroid (G), and wrapped package-graph (IWP) with different graded functions are presented. To predict the mechanical responses, a new fitting technique based on a two-phase piece-wise function is employed to evaluate the effective moduli of TPMS structures, including elastic modulus, shear modulus, and bulk modulus. In addition, this function corresponds to the cellular structure formulation in the context of relative density. The separated phases of the function are divided by the different deformation behaviors. Furthermore, another crucial mechanical property of porous structure, i.e, Poisson's ratio, is also achieved by a similar fitting technique. To verify the mechanical characteristics of the FG-TPMS plate, the generalized displacement field is modeled by a seventh-order shear deformation theory (SeSDT) and isogeometric analysis (IGA). Numerical examples regarding static, buckling, and free vibration analyses of FG-TPMS plates are illustrated to confirm the reliability and accuracy of the proposed approach. Consequently, these FG-TPMS structures can provide much higher stiffness than the same-weight isotropic plate. The greater stiffness-to-weight ratio of these porous plates compared to the full-weight isotropic ones should be considered the most remarkable feature. Thus, these complex porous structures have numerous practical applications because of these high ratios and their fabrication ability through additive manufacturing (AM) technology., Comment: 27 pages (including references), 15 figures, 12 tables

A phase-field approach becomes a more popular candidate in modeling crack propagation. It uses a scalar auxiliary variable, namely a phase-field variable, to model a discontinuity zone in a continuity domain. Furthermore, the fourth-order phase-field approach produces a better convergence rate and more accurate solutions than the second-order one. However, it is available for modeling crack propagation in brittle material. This study addresses the fourth-order phase-field model combining the non-standard phase-field form with a cohesive zone model (CZM) to predict crack propagation in quasi-brittle material. A Cornelisson's softening law is used to capture the high precision of crack propagation prediction. The concrete material is considered as a quasi-brittle one. For computation efficiency using NURBS-based finite elements, Virtual Uncommon-Knot-Inserted Master-Slave (VUKIMS) technique is employed to derive a local refinement mesh. Numerical results are verified by the published ones from literature. It was found that the peak load and crack path are independent of the element size and insensitive to the length-scale number using the fourth-order phase-field CZM. Our proposed model shows the most significant advantage compared to the standard phase-field approach in terms of computational cost and solution accuracy., Comment: 11 pages, 11 figures

This paper proposes an effective computational tool for brittle crack propagation problems based on a combination of a higher-order phase-field model and a non-conforming mesh using a NURBS-based isogeometric approach. This combination, as demonstrated in this paper, is of great benefit in reducing the computational cost of using a local refinement mesh and a higher-order phase-field, which needs higher derivatives of basis functions. Compared with other approaches using a local refinement mesh, the Virtual Uncommon-Knot-Inserted Master-Slave (VUKIMS) method presented here is not only simple to implement but can also reduce the variable numbers. VUKIMS is an outstanding choice in order to establish a local refinement mesh, i.e. a non-conforming mesh, in a multi-patch problem. A phase-field model is an efficient approach for various complicated crack patterns, including those with or without an initial crack path, curved cracks, crack coalescence, and crack propagation through holes. The paper demonstrates that cubic NURBS elements are ideal for balancing the computational cost and the accuracy because they can produce accurate solutions by utilising a lower degree of freedom number than an extremely fine mesh of first-order B-spline elements., Comment: 40 pages, 35 figures

The modeling of large deformation fracture mechanics has been a challenging problem regarding the accuracy of numerical methods and their ability to deal with considerable changes in deformations of meshes where having the presence of cracks. This paper further investigates the extended finite element method (XFEM) for the simulation of large strain fracture for hyper-elastic materials, in particular rubber ones. A crucial idea is to use a polygonal mesh to represent space of the present numerical technique in advance, and then a local refinement of structured meshes at the vicinity of the discontinuities is additionally established. Due to differences in the size and type of elements at the boundaries of those two regions, hanging nodes produced in the modified mesh are considered as normal nodes in an arbitrarily polygonal element. Conforming these special elements becomes straightforward by the flexible use of basis functions over polygonal elements. Results of this study are shown through several numerical examples to prove its efficiency and accuracy through comparison with former achievements.

We propose a simple and efficient scheme based on adaptive finite elements over conforming quadtree meshes for collapse plastic analysis of structures. Our main interest in kinematic limit analysis is concerned with both purely cohesive-frictional and cohesive materials. It is shown that the most computational efficiency for collapse plastic problems is to employ an adaptive mesh strategy on quadtree meshes. However, a major difficulty in finite element formulations is the appearance of hanging nodes during adaptive process. This can be resolved by a definition of conforming quadtree meshes in the context of polygonal elements. Piecewise-linear shape functions enhanced with generalized bubble functions in barycentric coordinates are used to approximate the velocity field. Numerical results prove the reliability and benefit of the present approach., Comment: arXiv admin note: text overlap with arXiv:1603.01866

In this paper, we propose an effective computational approach to analyze and active control of geometrically nonlinear responses of functionally graded (FG) porous plates with graphene nanoplatelets (GPLs) reinforcement integrated with piezoelectric layers. The key concept behind this work is to utilize isogeometric analysis (IGA) based on B\'ezier extraction technique and $C^0$-type higher-order shear deformation theory ($C^0$-HSDT). By applying B\'ezier extraction, the original Non-Uniform Rational B-Spline (NURBS) control meshes can be transformed into B\'ezier elements which allow us to inherit the standard numerical procedure like the standard finite element method (FEM). In this scenario, the approximation of mechanical displacement field is calculated via $C^0$-HSDT whilst the electric potential field is considered as a linear function across the thickness of each piezoelectric sublayer. The FG plate includes internal pores and GPLs dispersed into metal matrix either uniformly or non-uniformly along plate's thickness. To control responses of structures, the top and bottom surfaces of FG plate are firmly bonded with piezoelectric layers which are considered as sensor and actuator layers. The geometrically nonlinear equations are solved by Newton-Raphson iterative procedure and Newmark's integration. The influence of porosity coefficient, weight fraction of GPLs as well as external electrical voltage on geometrically nonlinear behaviors of plate structures with various distributions of porosity and GPLs are thoroughly investigated. A constant displacement and velocity feedback control approaches are then adopted to actively control geometrically nonlinear static and dynamic responses, where structural damping effect is taken into account, based on a closed-loop control with sensor and actuator layers., Comment: 36 pages, 21 figures