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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

This paper investigates nonlinear bending and buckling behaviours of composite plates characterized by a thickness variation. Layer interfaces are described as functions of inplane coordinates. Top and bottom surfaces of the plate are symmetric about the midplane and the plate could be considered as a flat surface in analysis along with thickness parameters which vary over the plate. The variable thickness at a certain position in the midplane is modeled by a set of control points (or thickness-parameters) through NURBS (Non-Uniform Rational B-Spline) basic functions. The knot parameter space which is referred in modelling geometry and approximating displacement variables is employed for approximating thickness, simultaneously. The use of quadratic NURBS functions results in C^1 continuity of modeling variable thickness and analyzing solutions. Thin to moderately thick laminates in bound of first-order shear deformation theory (FSDT) are taken into account. Strain-displacement relations in sense of von-Karman theory are employed for large deformation. Riks method is used for geometrically nonlinear analysis. The weak form is approximated numerically by the isogeometric analysis (IGA), which has been found to be a robust, stable and realistic numerical tool. Numerical results confirm the reliability and capacity of the propose method.

Analysis of static bending, free vibration and buckling behaviours of functionally graded microplates is investigated in this study. The main idea is to use the isogeometric analysis in associated with novel four-variable refined plate theory and quasi-3D theory. More importantly, the modified couple stress theory with only one material length scale parameter is employed to effectively capture the size-dependent effects within the microplates. Meanwhile, the quasi-3D theory which is constructed from a novel seventh-order shear deformation refined plate theory with four unknowns is able to consider both shear deformations and thickness stretching effect without requiring shear correction factors. The NURBS-based isogeometric analysis is integrated to exactly describe the geometry and approximately calculate the unknown fields with higher-order derivative and continuity requirements. The convergence and verification show the validity and efficiency of this proposed computational approach in comparison with those existing in the literature. It is further applied to study the static bending, free vibration and buckling responses of rectangular and circular functionally graded microplates with various types of boundary conditions. A number of investigations are also conducted to illustrate the effects of the material length scale, material index, and length-to-thickness ratios on the responses of the microplates., Comment: 57 pages, 14 figures, 18 tables

We propose an adaptive polygonal finite element formulation for collapse plastic analysis of solids. The article contributes into four crucial points: 1) Wachspress shape functions at vertex and bubble nodes handled at a primal-mesh level; 2) plastic strain rates and dissipation performed over a dual-mesh level; 3) a new adaptive primal-mesh strategy driven by the L^2 -norm-based indicator of strain rates; and 4) a spatial decomposition structure obtained from a so-called polytree mesh scheme. We investigate both purely cohesive and cohesive-frictional materials. We prove numerically that the present method performs well for volumetric locking problem. In addition, the optimization formulation of limit analysis is written by the form of second-order cone programming (SOCP) in order to exploit the high efficiency of interior-point solvers. The present method retains a low number of optimization variables. This convenient approach allows us to design and solve the large-scale optimization problems effectively. Numerical validations show the excellent performance of the proposed method., Comment: This manuscript needs to be improved furthermore

In this paper, equilibrium and stability equations of functionally graded material (FGM) plate under thermal environment are formulated based on isogeometric analysis (IGA) in combination with higher-order shear deformation theory (HSDT). The FGM plate is made by a mixture of two distinct components, for which material properties not only vary continuously through thickness according to a power-law distribution but also are assumed to be a function of temperature. Temperature field is assumed to be constant in any plane and uniform, linear and nonlinear through plate thickness, respectively. The governing equation is in nonlinear form based on von Karman assumption and thermal effect. A NURBS-based isogeometric finite element formulation is utilized to naturally fulfil the rigorous C1-continuity required by the present plate model. Influences of gradient indices, boundary conditions, temperature distributions, material properties, length-to-thickness ratios on the behaviour of FGM plate are discussed in details. Numerical results demonstrate excellent performance of the present approach.

In this paper, we present an effectively numerical approach based on isogeometric analysis (IGA) and higher-order shear deformation theory (HSDT) for geometrically nonlinear analysis of laminated composite plates. The HSDT allows us to approximate displacement field that ensures by itself the realistic shear strain energy part without shear correction factors. IGA utilizing basis functions namely B-splines or non-uniform rational B-splines (NURBS) enables to satisfy easily the stringent continuity requirement of the HSDT model without any additional variables. The nonlinearity of the plates is formed in the total Lagrange approach based on the von-Karman strain assumptions. Numerous numerical validations for the isotropic, orthotropic, cross-ply and angle-ply laminated plates are provided to demonstrate the effectiveness of the proposed method.

We apply the finite element cell-centered (FECC) scheme [2] to the solution of the nearly incompressible elasticity problem. By applying a technique of dual mesh, such a low-order finite element scheme can be constructed from any given mesh and it is proved to satisfy the "macroelement condition" [5], meaning that the stability condition is fulfilled. Numerical results show that the method, which is simple to implement, is effective in terms of accuracy and computational cost compared with other methods.

In this paper, a novel and effective formulation based on isogeometric approach (IGA) and Refined Plate Theory (RPT) is proposed to study the behavior of laminated composite plates. Using many kinds of higher-order distributed functions, RPT model naturally satisfies the traction-free boundary conditions at plate surfaces and describes the non-linear distribution of shear stresses without requiring shear correction factor (SCF). IGA utilizes the basis functions, namely B-splines or non-uniform rational B-splines (NURBS), which achieve easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The static, dynamic and buckling analysis of rectangular plates is investigated for different boundary conditions. Numerical results show high effectiveness of the present formulation., Comment: arXiv admin note: substantial text overlap with arXiv:1310.1847

A novel and effective formulation that combines the eXtended IsoGeometric Approach (XIGA) and Higher-order Shear Deformation Theory (HSDT) is proposed to study the free vibration of cracked Functionally Graded Material (FGM) plates. Herein, the general HSDT model with five unknown variables per node is applied for calculating the stiffness matrix without needing Shear Correction Factor (SCF). In order to model the discontinuous and singular phenomena in the cracked plates, IsoGeometric Analysis (IGA) utilizing the Non-Uniform Rational B-Spline (NURBS) functions is incorporated with enrichment functions through the partition of unity method. NURBS basis functions with their inherent arbitrary high order smoothness permit the C1 requirement of the HSDT model. The material properties of the FGM plates vary continuously through the plate thickness according to an exponent function. The effects of gradient index, crack length, crack location, length to thickness on the natural frequencies and mode shapes of simply supported and clamped FGM plate are studied. Numerical examples are provided to show excellent performance of the proposed method compared with other published solutions in the literature.

This paper presents an effective formulation to study the response of laminated composites based on isogeometric approach (IGA) and Carrera unified formulation (CUF). The IGA utilizes the non-uniform rational B-spline (NURBS) functions which allows to construct higher order smooth functions with less computational effort. The static bending and the free vibration of thin and moderately thick laminates plates are studied. The present approach also suffers from shear locking when lower order functions are employed and the shear locking is suppressed by introducing a modification factor. The combination of the IGA with the CUF allows a very accurate prediction of the field variables. The effectiveness of the formulation is demonstrated through numerical examples.

We propose in this paper a novel inverse tangent transverse shear deformation formulation for functionally graded material (FGM) plates. The isogeometric finite element analysis (IGA) of static, free vibration and buckling problems of FGM plates is then addressed using a refined plate theory (RPT). The RPT enables us to describe the non-linear distribution of shear stresses through the plate thickness without any requirement of shear correction factors (SCF). IGA utilizes basis functions, namely B-splines or non-uniform rational B-splines (NURBS), which achieve easily the smoothness of any arbitrary order. It hence satisfies the C1 requirement of the RPT model. The present method approximates the displacement field of four degrees of freedom per each control point and retains the computational efficiency while ensuring the high accuracy in solution.

A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational expenses while using traditional finite element methods. The isogeometric analysis heterogeneous multiscale method (IGA-HMM) investigated in this paper is regarded as an alternative approach to the standard Finite Element Heterogeneous Multiscale Method (FE-HMM) which is currently an effective framework to solve these problems. The method utilizes non-uniform rational B-splines (NURBS) in both macro and micro levels instead of standard Lagrange basis. Beside the ability to describe exactly the geometry, it tremendously facilitates high-order macroscopic/microscopic discretizations thanks to the flexibility of refinement and degree elevation with an arbitrary continuity level provided by NURBS basis functions. A priori error estimates of the discretization error coming from macro and micro meshes and optimal micro refinement strategies for macro/micro NURBS basis functions of arbitrary orders are derived. Numerical results show the excellent performance of the proposed method.

We present in this paper a rigorous theoretical framework to show stability, convergence and accuracy of improved edge-based and face-based smoothed finite element methods (bESFEM and bFS-FEM) for nearly-incompressible elasticity problems. The crucial idea is that the space of piecewise linear polynomials used for the displacements is enriched with bubble functions on each element, while the pressure is a piecewise constant function. The meshes of triangular or tetrahedral elements required by these methods can be generated automatically. The enrichment induces a softening in the bilinear form allowing the weakened weak (W2)procedure to produce a high-quality solution, free from locking and that does not oscillate. We prove theoretically that both methods confirm the uniform inf-sup and convergence conditions. Four numerical examples are given to validate the reliability of the bES-FEM and bFS-FEM., Comment: 37 pages, 0 figures