Dr Joseph Ghaffari Motlagh

This paper presents an approach for computationally efficient inverse material characterization using Physics-Informed Neural Networks (PINNs) based on partial-field response measurements. PINNs reconstruct the full spatial distribution of the system's response from the measured portion of the response field and estimate the spatial distribution of unknown material properties. The primary computational expense in this approach is the one-time generation of potential responses for the PINNs, resulting in significant computational efficiency. Furthermore, this study utilizes PINNs to train a model based on the underlying physics described by differential equations, and to quantify aleatoric uncertainty arising from noisy data. We demonstrate several one-dimensional and two-dimensional examples where the elastic modulus distribution is characterized based on static partial-field displacement response measurements. The inversion procedure efficiently provides accurate estimates of material property distributions, showcasing the potential of PINNs in practical applications.

We present deep learning phase‐field models for brittle fracture. A variety of physics‐informed neural networks (PINNs) techniques, for example, original PINNs, variational PINNs (VPINNs), and variational energy PINNs (VE‐PINNs) are utilized to solve brittle phase‐field problems. The performance of the different versions is investigated in detail. Also, different ways of imposing boundary conditions are examined and are compared with a self‐adaptive PINNs approach in terms of computational cost. Furthermore, the data‐driven discovery of the phase‐field length scale is examined. Finally, several numerical experiments are conducted to assess the accuracy and the limitations of the discussed deep learning schemes for crack propagation in two dimensions. We show that results can be highly sensitive to parameter choices within the neural network.

Summary

A recently proposed phase‐field model for cohesive fracture is examined. Previous investigations have shown stress oscillations to occur when using unstructured meshes. It is now shown that the use of nonuniform rational B‐splines (NURBS) as basis functions rather than traditional Lagrange polynomials significantly reduces this oscillatory behavior. Moreover, there is no effect on the global structural behavior, as evidenced through load‐displacement curves. The phase‐field model imposes restrictions on the interpolation order of the NURBS used for the three different fields: displacement, phase field, and crack opening. This holds within the Bézier element, but also at the boundaries, where a reduction to ‐continuity yields optimal results. Application to a range of cases, including debonding of a hard fiber embedded in a soft matrix, illustrates the potential of the cohesive phase‐field model.

This paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al. (2016) to include isotropic hardening of the yield surfaces. The approach allows any smooth isotropic yield envelope to be represented by a NURBS surface. The key extension provided by this paper is that the yield surface can expand or contract through the movement of control points linked to the level of inelastic straining experienced by the material. The model is integrated using a fully implicit backward Euler algorithm that constrains the return path to the yield surface and allows the derivation of the algorithmic consistent tangent to ensure optimum convergence of the global equilibrium equations. This provides a powerful framework for elasto-plastic constitutive models where, unlike the majority of models presented in the literature, the underlying numerical algorithm (and implemented code) remains unchanged for different yield surfaces. The performance of the algorithm is demonstrated, and validated, using both material point and boundary values simulations including plane stress, plane strain and three-dimensional examples for different yield criteria.

In numerical analysis the failure of engineering materials is controlled through specifying yield envelopes (or surfaces) that bound the allowable stress in the material. However, each surface is distinct and requires a specific equation describing the shape of the surface to be formulated in each case. These equations impact on the numerical implementation, specifically relating to stress integration, of the models and therefore a separate algorithm must be constructed for each model. This paper presents, for the first time, a way to construct yield surfaces using techniques from non-uniform rational basis spline (NURBS) surfaces, such that any isotropic convex yield envelope can be represented within the same framework. These surfaces are combined with an implicit backward-Euler-type stress integration algorithm to provide a flexible numerical framework for computational plasticity. The algorithm is inherently stable as the iterative process starts and remains on the yield surface throughout the stress integration. The performance of the algorithm is explored using both material point investigations and boundary value analyses demonstrating that the framework can be applied to a variety of plasticity models.

We present an application of the residual-based variational multiscale modeling methodology to the computation of laminar and turbulent concentric annular pipe flows. Isogeometric analysis is utilized for higher-order approximation of the solution using Non-Uniform Rational B-Splines (NURBS). The ability of NURBS to exactly represent curved geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through annular channels. We demonstrate the applicability of the methodology to both laminar and turbulent flow regimes.

This study proposes a new sample-independent mixing index, termed the Coefficient of Blending Performance (CBP), for monitoring the formation of undesired API (Active Pharmaceutical Ingredient) agglomerates in continuous mixing processes. The proposed index is examined for the blending of pharmaceutical powders in a simulated twin-screw mixer using Discrete Element Method (DEM). Model excipient and API particles with physical and mechanical properties within the typical range of pharmaceutical powders are used in simulations. Results suggest that the CBP is an effective index for monitoring the formation of API agglomerates in the mixer. Using this index, DEM results suggest a high possibility of formation of API agglomerates during the first stage of twin screw mixing. The results show that adding a kneading zone to the twin screw mixer enhances the blending quality by breaking the API agglomerates, making the mixture ready for the next operating unit.

The material point method is ideally suited to modelling problems involving large deformations where conventional mesh-based methods would struggle. However, total and updated Lagrangian approaches are unsuitable and non-ideal, respectively, in terms of formulating equilibrium for the method. This is due to the basis functions, and particularly the derivatives of the basis functions, of material point methods normally being defined on an unformed, and sometimes regular, background mesh. It is possible to map the basis function spatial derivatives using the deformation at a material point but this introduces additional algorithm complexity and computational expense. This paper presents a new Lagrangian statement of equilibrium which is ideal for material point methods as it satisfies equilibrium on the undeformed background mesh at the start of a load step. The formulation is implemented using a quasi-static implicit algorithm which includes the derivation of the consistent tangent to achieve optimum convergence of the global equilibrium iterations. The method is applied to a number of large deformation elasto-plastic problems, with a specific focus of the convergence of the method towards analytical solutions with the standard, generalised interpolation and CPDI2 material point methods. For the generalised interpolation method, different domain updating methods are investigated and it is shown that all of the current methods are degenerative under certain simple deformation fields. A new domain updating approach is proposed that overcomes these issues. The proposed material point method framework can be applied to all existing material point methods and adopted for implicit and explicit analysis, however its advantages are mainly associated with the former.

Winglets can reduce effect of wingtip vortices on the wind turbine performance can be reduced by diffusing the vortices from the blade tips. Unlike non-rotating wings, winglets have not been widely investigated for moving blades of wind turbines, while there is a potential they could enable the wind turbine rotor to capture more kinetic energy from wind. There have been a number of studies on the effect of winglet parameters and configurations on the wind turbine performance, however a combined effect of winglet planform and airfoil has not been investigated in details. The present work reports on the study of the effect of winglet planform and winglet airfoil on the wind turbine performance using Computational Fluid Dynamics (CFD). The National Renewable Energy Laboratory (NREL) phase VI rotor with 10 m diameter was used as the baseline and the CFD results were validated with the available experimental data on the output power and pressure coefficients. Different designs of winglet with different heights, cant angles, planforms and airfoils have been numerically tested and optimised. The best improvement in the performance is achieved when a 15 cm rectangular winglet with the S809 airfoil and 45° cant angle is used.

This paper extends the non-uniform rational basis spline (NURBS) plasticity framework of Coombs et al. (2016) and Coombs and Ghaffari Motlagh (2017) to include non-associated plastic flow. The NURBS plasticity approach allows any smooth isotropic yield envelope to be represented by a NURBS surface whilst the numerical algorithm (and code) remains unchanged. This paper provides the full theoretical and algorithmic basis of the non-associated NURBS plasticity approach and demonstrates the predictive capability of the plasticity framework using both small and large deformation problems. Wherever possible errors associated with the constitutive formulation are specified analytically and if not numerical analyses provide this information. The rate equations within the plasticity framework are integrated using an efficient and stable implicit stress update algorithm which allows for the derivation of the algorithmic consistent tangent which ensures optimum convergence of the global out of balance force residual when used in boundary value simulations. The important extension provided by this paper is that the evolution of plastic strain is decoupled from the yield surface normal. This allows the framework to model more realistic material behaviour, particularly in the case of frictional plasticity models where an associated flow rule is known to significantly overestimate volumetric dilation leading to spurious results. This paper therefore opens the door for the NURBS plasticity formulation to be used for a far wider class of material behaviour than is currently possible.

We present a residual-based isogeometric variational multiscale method to solve laminar and turbulent channel flow. Residual-based variational multiscale method is a new finite element formulation for solving turbulent flows using a large-eddy simulation type modeling. Isogeometric analysis, a new finite element method using CAD blending functions as its basis functions, is employed for higher order approximation of the solution. First, laminar flow with Reτ 0.55 = through flat channel is considered and linear, quadratic and cubic basis functions, which are C0, C1, and C2-continuous across element boundaries, respectively are employed and their accuracy is presented by the comparison with analytical result. Next, same methodology is applied to the turbulent channel flow with Rer = 180. Current results are validated by the comparison of turbulence statistics using available DNS data.

We present an application of the Residual-based variational multiscale (RBVMS) methodology to the computation of laminar eccentric annular pipe flow with eccentricities of 0.5 and 1. Isogeometric analysis is utilized for higher order approximation of the geometry and solution using Non-uniform rational B-splines (NURBS) functions. The ability of NURBS exactly representing curved circular geometries makes NURBS-based isogeometric analysis attractive for the application to the flow through the eccentric annuli. By using the exact representation of circular boundary, the limiting case of the eccentricity, i.e. the inner circular wall actually touches the outer circular wall, is successfully demonstrated.