Mechanical parameters identification of keloid and surrounding healthy skin using Digital Image Correlation measurements in vivo

Scientific Conference (2019, December 09)

The human skin behaves as an elastic membrane initially prestressed but not uniformly. The presence of anatomical sites favorable to the appearance of some tumors, a keloid in our case, while other sites ... [more ▼]

The human skin behaves as an elastic membrane initially prestressed but not uniformly. The presence of anatomical sites favorable to the appearance of some tumors, a keloid in our case, while other sites never develop them attests to the importance of the mechanical environment of the tissue. Thus, a mechanical characterization of the tumored skin is necessary to understand the keloid expansion from a mechanical point of view. Our case study consists in modeling a bi-material structure composed of a keloid skin surrounded by healthy skin located on upper left arm of a young female. From the experimental measurements in vivo, by combining force sensor, displacement sensor and Digital Image Correlation techniques, we perform a mechanical analysis to characterize the mechanical stress fields over the entire area and on the interface ‘healthy skin/keloid skin’. Since the mechanical behavior of the tumorous skin is unknown, many physical models can be implemented and assessed very easily inside the specific digital software to fit with the real data. Once a set of mechanical parameters for both the healthy skin and the keloid skin are identified, the stress fields around the keloid are calculated. Next steps consist in determining matching preferential directions in order to define as precisely as possible the specifications of a device for preventing the growth of keloids. [less ▲]

Fracture mechanism simulation of inhomogeneous anisotropic rocks by extended finite element method

in Theoretical and Applied Fracture Mechanics (2019), 104

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores ... [more ▼]

The vast majority of rock masses is anisotropic due to factors such as layering, unequal in-situ stresses, joint sets, and discontinuities. Meanwhile, given the frequently asymmetric distribution of pores, grain sizes or different mineralogical compounds in different locations, they are often classified as inhomogeneous materials. In such materials, stress intensity factors (SIFs) at the crack tip, which control the initiation of failure, strongly depend on mechanical properties of the material near that area. On the other hand, crack propagation trajectories highly depend on the orthotropic properties of the rock mass. In this study, the SIFs are calculated by means of anisotropic crack tip enrichments and an interaction integral are developed for inhomogeneous materials with the help of the extended finite element method (XFEM). We also use the T-stress within the crack tip fields to develop a new criterion to estimate the crack initiation angles and propagation in rock masses. To verify and validate the proposed approach, the results are compared with experimental test results and those reported in the literature. It is found that the ratio of elastic moduli, shear stiffnesses, and material orientation angles have a significant impact on the SIFs. However, the rate of change in material properties is found to have a moderate effect on these factors and a more pronounced effect on the failure force. The results highlight the potential of the proposed formulation in the estimation of SIFs and crack propagation paths in inhomogeneous anisotropic materials. [less ▲]

An Implicit boundary approach for viscous compressible high Reynolds flows using hybrid remeshed particle hydrodynamics method

in Journal of Computational Physics (2019), 391

A stochastic Galerkin cell-based smoothed finite element method (SGCS-FEM)

in International Journal of Computational Methods (2019), 17(8),

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the ... [more ▼]

In this paper, the cell based smoothed finite element method is extended to solve stochastic partial diff erential equations with uncertain input parameters. The spatial field of Young's moduli and the corresponding stochastic results are represented by Karhunen-Lo eve expansion and polynomial chaos expansion, respectively. The Young's Modulus of structure is considered to be random for stochastic static as well as free vibration problems. Mathematical expressions and the solution procedure are articulated in detail to evaluate the statistical characteristics of responses in terms of static displacements and free vibration frequencies. The feasibility and eff ectiveness of the proposed SGCS-FEM method in terms of accuracy and lower requirement on the mesh size in the solution domain over that of conventional FEM for stochastic problems are demonstrated by carefully chosen numerical examples. From the numerical study, it is inferred that the proposed framework is computationally less demanding without compromising accuracy. [less ▲]

Structural shape optimization of three dimensional acoustic problems with isogeometric boundary element methods

in Computer Methods in Applied Mechanics and Engineering (2019), 355

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to ... [more ▼]

The boundary element method (BEM) is a powerful tool in computational acoustics, because the analysis is conducted only on structural surfaces, compared to the finite element method (FEM) which resorts to special techniques to truncate infinite domains. The isogeometric boundary element method (IGABEM) is a recent progress in the category of boundary element approaches, which is inspired by the concept of isogeometric analysis (IGA) and employs the spline functions of CAD as basis functions to discretize unknown physical fields. As a boundary representation approach, IGABEM is naturally compatible with CAD and thus can directly perform numerical analysis on CAD models, avoiding the cumbersome meshing procedure in conventional FEM/BEM and eliminating the difficulty of volume parameterization in isogeometric finite element methods. The advantage of tight integration of CAD and numerical analysis in IGABEM renders it particularly attractive in the application of structural shape optimization because (1) the geometry and the analysis can be interacted, (2) remeshing with shape morphing can be avoided, and (3) an optimized solution returns a CAD geometry directly without postprocessing steps. In the present paper, we apply the IGABEM to structural shape optimization of three dimensional exterior acoustic problems, fully exploiting the strength of IGABEM in addressing infinite domain problems and integrating CAD and numerical analysis. We employ the Burton–Miller formulation to overcome fictitious frequency problems, in which hyper-singular integrals are evaluated explicitly. The gradient-based optimizer is adopted and shape sensitivity analysis is conducted with implicit differentiation methods. The design variables are set to be the positions of control points which directly determine the shape of structures. Finally, numerical examples are provided to verify the algorithm. [less ▲]

ADVANCES IN GEOMETRY INDEPENDENT APPROXIMATIONS

Scientific Conference (2019, April 11)

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no ... [more ▼]

We present recent advances in geometry independent field approximations. The GIFT approach is a generalisation of isogeometric analysis where the approximation used to describe the field variables no-longer has to be identical to the approximation used to describe the geometry of the domain. As such, the geometry can be described using usual CAD representations, e.g. NURBS, which are the most common in the CAD area, whilst local refinement and meshes approximations can be used to describe the field variables, enabling local adaptivity. We show in which cases the approach passes the patch test and present applications to various mechanics, fracture and multi-physics problems. [less ▲]

A unified polygonal locking-free thin/thick smoothed plate element

in Composite Structures (2019), 219

A novel cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields. The domain is discretized with arbitrary ... [more ▼]

A novel cell-based smoothed finite element method is proposed for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields. The domain is discretized with arbitrary polygons and on each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The plate is made of functionally graded material with effective properties computed using the rule of mixtures. The influence of various parameters, viz., the plate aspect ratio and the material gradient index on the static bending response and the first fundamental frequency is numerically studied. It is seen that the proposed element: (a) has proper rank; (b) does not require derivatives of shape functions and hence no isoparametric mapping required; (c) independent of shape and size of elements and (d) is free from shear locking. [less ▲]

Model order reduction accelerated Monte Carlo stochastic isogeometric method for the analysis of structures with high-dimensional and independent material uncertainties

in Computer Methods in Applied Mechanics and Engineering (2019), 349

Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially ... [more ▼]

Structural stochastic analysis is vital to engineering. However, current material related uncertainty methods are mostly limited to low dimension, and they mostly remain unable to account for spatially uncorrelated material uncertainties. They are not representative of realistic and practical engineering situations. In particular, it is more serious for composite structures comprised of dissimilar materials. Therefore, we propose a novel model order reduction via proper orthogonal decomposition accelerated Monte Carlo stochastic isogeometric method (IGA-POD-MCS) for stochastic analysis of exactly represented (composite) structures. This approach particularly enables high-dimensional material uncertainties wherein the characteristics of each element are independent. And the novelties include: (1) the structural geometry is exactly modeled thanks to isogeometric analysis (IGA), as well as providing more accurate deterministic and stochastic solutions, (2) we innovatively consider high-dimensional and independent material uncertainties by separating the stochastic mesh from the IGA mesh, and modeling different stochastic elements to have different (independent) uncertainty behaviors, (3) the classical Monte Carlo simulation (MCS) is employed to universally solve the high-dimensional uncertainty problem. However, to circumvent its computational expense, we employ model order reduction via proper orthogonal decomposition (POD) into the IGA coupled MCS stochastic analysis. In particular, we observe that this work decouples all IGA elements and hence permits independent uncertainty models easily, thereby the engineering problem is modeled to be more realistic and authentic. Several illustrative numerical examples verify the proposed IGA-POD-MCS approach is effective and efficient; and the larger the scale of the problem is, the more advantageous the method will become. [less ▲]

Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins

Learning material (2019)

Modelling Complex Systems: a primer - agent-based models, equation-based models, statistical models and Bayesian inference, digital twins

A one point integration rule over star convex polytopes

in Computers and Structures (2019), 215

In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it ... [more ▼]

In this paper, the recently proposed linearly consistent one point integration rule for the meshfree methods is extended to arbitrary polytopes. The salient feature of the proposed technique is that it requires only one integration point within each n-sided polytope as opposed to 3n in Francis et al. (2017) and 13n integration points in the conventional approach for numerically integrating the weak form in two dimensions. The essence of the proposed technique is to approximate the compatible strain by a linear smoothing function and evaluate the smoothed nodal derivatives by the discrete form of the divergence theorem at the geometric center. This is done by Taylor’s expansion of the weak form which facilitates the use of the smoothed nodal derivatives acting as the stabilization term. This translates to 50% and 30% reduction in the overall computational time in the two and three dimensions, respectively, whilst preserving the accuracy and the convergence rates. The convergence properties, the accuracy and the efficacy of the one point integration scheme are discussed by solving few benchmark problems in elastostatics. [less ▲]