Multiscale design of nonlinear materials using a shape optimization scheme based on an interface-enriched GFEM

Motivated by key advances in manufacturing techniques, the tailoring of materials with specific macroscopic properties has been the focus of active research in mechanical engineering and materials science over the past decade. The key challenge in this line of work is how to optimize the material microstructure to achieve a desired macroscopic constitutive response. The overwhelming majority of this type of inverse design work relies on topology optimization based, primarily, on linear theory. In this work, we develop and implement a method to design particulate composites at the mesoscale using a shape optimization scheme to minimize or maximize a nonlinear cost function at the macroscale while satisfying a set of constraints associated, for example, with the volume fraction of inclusions or with the manufacturing technique. The optimization method relies on three key ‘modules’: multiscale modeling, sensitivity analysis, and optimization. The multiscale modeling is based on a nonlinear finite element solver, which combines a classical homogenization scheme with a NURBS-based Interface-enriched Generalized Finite Element Method (NIGFEM) used to capture accurately and efficiently the displacement field in a heterogeneous material with a finite element discretization that does not conform to the material interfaces. Damage evolution is captured using a three-parameter isotropic damage model able to simulate a wide range of failure responses. The proposed gradient-based shape optimization scheme relies on the stationary nature of the non-conforming meshes used to discretize the periodic unit cell, thereby avoiding mesh distortion issues that plague conventional finite-element-based shape optimization studies. In the current approach, the finite element approximation space used in the NIGFEM is augmented with NURBS to allow for the accurate capture of the weak discontinuity present along complex, curvilinear material interfaces. NURBS are also used to parameterize the design geometry precisely and compactly by a small number of design variables. To compute the derivatives of the cost and constraint functions with respect to the design variables, we also formulate an analytic nonlinear sensitivity, which is simplified by the fact that only the enrichment control points on material interfaces move, appear or disappear during the shape optimization process. The derivations uncover subtle but important new terms involved in the sensitivity of shape functions and their spatial derivatives. Our analytic nonlinear shape sensitivity avoids the technical difficulties encountered in the finite difference or semi-analytical schemes when the boundary intersects an element very close to a node in a non-conforming mesh. In these situations, the boundary may move to another element during the design perturbation step, resulting in changes of the mesh topology, making the differentiation of the stiffness matrix and load vector problematic. We apply the NIGFEM shape optimization scheme to several 2D and 3D structural problems including some benchmark and application examples to demonstrate the performance and accuracy of the method. Based on the multiscale approach, we also design the microstructure of a periodic particulate composite to optimize the volume fraction and distribution of the inclusions for a desired macroscopic nonlinear stress-strain curve

Shape optimization of microvascular composites used in active cooling applications

Inspired by microchannels networks in biological systems, microvascular composites are being used for various applications including active cooling, autonomic healing, and sensing. The recent development of a manufacturing technique for microvascular composites based on a sacrificial fiber approach has enabled the creation of complex networks of microchannels embedded in composite parts [1]. Motivated by these recent improvements in manufacturing of microvascular composites, we study design of an actively cooled composite plate. We examine the impact of microchannels configuration on the thermal response of the microvascular composite. Here, the composite plate is subjected to a heat flux that causes a high surface temperature in the absence of the active cooling by microchannels. The objective of this study is to determine the optimal configuration of the microchannels to maximize the thermal efficiency of microchannels to keep the domain temperature below a critical temperature value. We present a new gradient-based Isogeometric Interface-enriched Generalized Finite Element Method (IIGFEM) [2–4] optimization scheme that allows for the accurate and efficient extraction of the sensitivity of objective functions and constraints on the design parameters that define the geometry of the microchannels. At the heart of the modeling effort, the IIGFEM allows for the very accurate and efficient capture of the thermal impact of the embedded microchannel network on the thermal field in the composite part. Because the microchannels diameters are typically much smaller than other characteristic dimensions of the problem, we model microchannels as line (or curve) sinks. The IIGFEM solver allows for the capture of curved and branched microchannels over a mesh that does not conform to the geometry of the microchannels. One of the key challenges associated with the conventional finite element-based shape optimization of microvascular composites is the large mesh distortion that often takes place during the optimization process, as the finite element mesh must conform to the evolving microstructural elements. This mesh distortion may affect the accuracy of the optimum solution. Because of the stationary nature of the nonconforming mesh used by the IIGFEM, the issue of mesh distortion disappears. In this study, we adopt an isogeometric IGFEM-based adjoint shape sensitivity approach, which is simplified by the fact that only the enrichment (interface) nodes move, appear or disappear during the shape optimization process. To demonstrate the performance of the method, a set of microstructural shape optimization problems for the design of microvascular composites are presented

Simulation of the microlevel damage evolution in polymer matrix composites

A 3D Isogeometric Interface-Enriched Generalized Finite Element Method (IIGFEM) is developed to analyze problems with complex, discontinuous gradient fields commonly observed in the structural analysis of heterogeneous materials including polymer matrix composites [1]. In the proposed approach, the mesh generation process is significantly simplified by utilizing simple structured meshes that do not conform to the complex microstructure of the heterogeneous media. Non-Uniform Rational B-Splines, commonly used in computer-aided design, are adopted in the IIGFEM to augment the finite element approximation space and capture the weak discontinuity present along material interfaces. The IIGFEM offers many advantages, such as the simplicity and accuracy of numerical integration, the straightforward implementation of essential boundary conditions, and the flexibility in the choice of the local solution refinement The ability to model complex material interfaces and the mesh independence are two of key features of the IIGFEM that enable it to tackle problems with evolving material response, such as computational study of damage in solids. Here, we utilize the IIGFEM scheme to study the impact of microstructural details on the initiation and evolution of the damage in polymer matrix composites. For this purpose, in this study, we incorporate a three-parameter isotropic damage model [2] into our IIGFEM solver to capture the fracture response of the matrix in a unidirectional composite layer. To bypass numerical issues associated with mesh bias, we use a viscous regularization scheme proposed by Simo and Ju [3]. The numerical stability of the proposed approach is studied and its advantages and limitations are discussed in detail. Finally, a number of numerical examples are presented to demonstrate the effect of RVE size and filler volume fraction on the damage behavior of fiber-reinforced polymer matrix composites. REFERENCES [1] Safdari, M., Najafi, A.R., Sottos, N.R., Geubelle, P.H. An Isogeometric Interface-Enriched Generalized Finite Element Method (IGFEM) for problems with complex discontinuous gradient field. Submitted (2014). [2] Matous, K., Kulkarni, M.G., Geubelle, P.H. Multiscale cohesive failure modeling of heterogeneous adhesives. Journal of the Mechanics and Physics of Solids. 2008, 56, 1511–1533. [3] Simo, J.C., Ju, J.W. Strain- and stress-based continuum damage models—ii. computational aspects. International Journal of Solids and Structures. 1987, 23(7), 841–869

An interface-enriched generalized finite-element method for efficient electromagnetic analysis of composite materials

An interface-enriched generalized FEM is presented for analyzing electromagnetic problems involving composite materials. To avoid of generating conformal meshes in highly inhomogeneous domains, enriched vector basis functions are introduced over the intersections of material interfaces and the nonconforming elements to capture the normal derivative discontinuity of the tangential field component. These enrichment functions are directly constructed from a linear combination of the vector basis functions of the subelements. Several numerical examples are presented to verify the algorithm with analytical solutions and demonstrate its h-refinement convergence rate. Finally, two illustrative examples, involving multiple microvascular channels and circular inclusions, are solved

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

BackgroundDisorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021.MethodsWe estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined.FindingsGlobally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer.InterpretationAs the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed

Global, regional, and national burden of disorders affecting the nervous system, 1990–2021: a systematic analysis for the Global Burden of Disease Study 2021

Background Disorders affecting the nervous system are diverse and include neurodevelopmental disorders, late-life neurodegeneration, and newly emergent conditions, such as cognitive impairment following COVID-19. Previous publications from the Global Burden of Disease, Injuries, and Risk Factor Study estimated the burden of 15 neurological conditions in 2015 and 2016, but these analyses did not include neurodevelopmental disorders, as defined by the International Classification of Diseases (ICD)-11, or a subset of cases of congenital, neonatal, and infectious conditions that cause neurological damage. Here, we estimate nervous system health loss caused by 37 unique conditions and their associated risk factors globally, regionally, and nationally from 1990 to 2021. Methods We estimated mortality, prevalence, years lived with disability (YLDs), years of life lost (YLLs), and disability-adjusted life-years (DALYs), with corresponding 95% uncertainty intervals (UIs), by age and sex in 204 countries and territories, from 1990 to 2021. We included morbidity and deaths due to neurological conditions, for which health loss is directly due to damage to the CNS or peripheral nervous system. We also isolated neurological health loss from conditions for which nervous system morbidity is a consequence, but not the primary feature, including a subset of congenital conditions (ie, chromosomal anomalies and congenital birth defects), neonatal conditions (ie, jaundice, preterm birth, and sepsis), infectious diseases (ie, COVID-19, cystic echinococcosis, malaria, syphilis, and Zika virus disease), and diabetic neuropathy. By conducting a sequela-level analysis of the health outcomes for these conditions, only cases where nervous system damage occurred were included, and YLDs were recalculated to isolate the non-fatal burden directly attributable to nervous system health loss. A comorbidity correction was used to calculate total prevalence of all conditions that affect the nervous system combined. Findings Globally, the 37 conditions affecting the nervous system were collectively ranked as the leading group cause of DALYs in 2021 (443 million, 95% UI 378–521), affecting 3·40 billion (3·20–3·62) individuals (43·1%, 40·5–45·9 of the global population); global DALY counts attributed to these conditions increased by 18·2% (8·7–26·7) between 1990 and 2021. Age-standardised rates of deaths per 100 000 people attributed to these conditions decreased from 1990 to 2021 by 33·6% (27·6–38·8), and age-standardised rates of DALYs attributed to these conditions decreased by 27·0% (21·5–32·4). Age-standardised prevalence was almost stable, with a change of 1·5% (0·7–2·4). The ten conditions with the highest age-standardised DALYs in 2021 were stroke, neonatal encephalopathy, migraine, Alzheimer's disease and other dementias, diabetic neuropathy, meningitis, epilepsy, neurological complications due to preterm birth, autism spectrum disorder, and nervous system cancer. Interpretation As the leading cause of overall disease burden in the world, with increasing global DALY counts, effective prevention, treatment, and rehabilitation strategies for disorders affecting the nervous system are needed. Funding Bill & Melinda Gates Foundation

Pervaporation separation of azeotrope water–isopropanol mixtures through poly(vinyl alcohol)-based membranes incorporated with modified CNTs

Although carbon nanotubes possess unique characteristics to be used for separation purposes, one of the most challenging problems affecting the preparation of carbon nanotubes-incorporated-mixed matrix membranes has been ascribed to Van der Waals interactions among carbon nanotubes walls, which hinder the pristine nanotubes’ ability to make good interfacial interactions within the polymer matrix. To overcome this challenge, herein, poly (styrene sulfonic acid)-grafted- multi-walled carbon nanotubes were prepared via in-situ radical polymerisation and then incorporated into poly (vinyl alcohol), resulting in enhanced pervaporation performance of poly (vinyl alcohol) membranes. The observed results indicated that poly (styrene sulfonic acid)-modified carbon nanotubes could effectively vanquish the Van der Waals forces between nanotube walls. In general, our experiments revealed that the attachment of a bulky polymer containing hydrophilic sulfonic groups could improve the pervaporation performance of a poly (vinyl alcohol) membrane.</p