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

A NURBS-based interface-enriched generalized finite element scheme for the computational analysis and design of high temperature microvascular composites

Computational studies on multifunctional microvascular composite materials for high temperature application have focused on simple microchannel geometries [1–2]. Motivated by recent advances in the manufacturing of microvascular composites based on a sacrificial fiber technique that allows a complex network of curved microchannels to be embedded in the material [3], we develop an Interface Enriched Generalized Finite Element Method (IGFEM) [4] with Non-Uniform Rational B-Splines (NURBS) to analyze the impact of the microchannel network on the thermal field in the composite component [5]. By capturing the gradient discontinuity present at the microchannels, the method is able to simulate efficiently and accurately the thermal response of the microvascular composite without the need for a mesh that conforms to the geometry of the microchannels. We show that near-optimal convergence rate can be achieved and that IGFEM is more accurate than standard finite element method for coarse meshes when the enrichment functions are constructed using the NURBS description of the curved microchannels. Verification studies conducted against a detailed multiphysics model based on the Navier–Stokes equation for the fluid shows that the much simpler line source/sink model is very accurate for problems involving microvascular plates and fins. Various application problems are presented to demonstrate the efficiency, flexibility and accuracy of the proposed method. REFERENCES [1] Soghrati, S., Thakre, P.R., White, S.R., Sottos, N.R., Geubelle, P.H. Computational modeling and design of actively-cooled microvascular materials. Int. J. Heat Mass Transfer. 2012, 55, 5309–5321 [2] Soghrati, S., Najafi, A.R., Hughes, K.M., Lin, J.H., White, S.R., Sottos, N.R., Geubelle, P.H. Computational analysis of actively-cooled 3D woven microvascular composites using a stabilized interface-enriched generalized finite element method. Int. J. Heat Mass Transfer. 2013, 65, 153–164. [3] Esser-Kahn, A.P., Thakre, P.R., Dong, H., Patrick, J.F., Vlasko-Vlasov, V.K., Sottos, N.R., Moore, J.S., White, S.R. Three-dimensional microvascular fiber-reinforced composites. Advanced Materials. 2011, 23, 3654–3658. [4] Soghrati, S., Aragón, A.M., Duarte, C.A., Geubelle, P.H. An interface-enriched generalized FEM for problems with discontinuous gradient fields. Int. J. Numer. Methods Eng. 2012, 89, 991–1008. [5] Tan, M.H.Y., Safdari, M., Najafi, A.R., Geubelle, P.H. A NURBS-based interface-enriched generalized finite element scheme for the thermal analysis and design of microvascular composites. 2014 (submitted)

Interplay between Process Zone and Material Heterogeneities for Dynamic Cracks

Using an elastodynamic boundary integral formulation coupled with a cohesive model, we study the problem of a dynamic rupture front propagating along an heterogeneous plane. We show that small-scale heterogeneities facilitate the supershear transition of a mode-II crack. The elastic pulses radiated during front accelerations explain how microscopic variations of fracture toughness change the macroscopic rupture dynamics. Perturbations of dynamic fronts are then systematically studied with different microstructures and loading conditions. The process zone size is the intrinsic length scale controlling heterogeneous dynamic rupture. The ratio of this length scale to asperity size is proposed as an indicator to transition from quasihomogeneous to heterogeneous fracture. Moreover, we discuss how the shortening of the process zone size with increasing crack speed brings the front to interact with smaller details of the microstructure. This study shines new light on recent experiments reporting perturbations of dynamic rupture fronts, which intensify with crack propagation speed

Supershear bursts in the propagation of a tensile crack in linear elastic material

Since the early years of the linear elastic theory of fracture [linear elastic fracture mechanics (LEFM)], scientists have sought to understand and predict how fast cracks grow in a material or slip fronts propagate along faults. While shear cracks can travel faster than the shear wave speed, the Rayleigh wave speed is the limiting speed theoretically predicted for tensile failure. This work uncovers the existence of supershear episodes in the tensile (mode I) rupture of linearly elastic materials beyond the maximum allowable (sub-Rayleigh) speed predicted by the classical theory of dynamic fracture. While the admissible rupture speeds predicted by LEFM are verified for smooth crack fronts, we present numerically how a supershear burst can emerge from a discontinuity in crack front curvature. Using a spectral formulation of the three-dimensional elastodynamic equations coupled with a cohesive model of fracture, we study how these short-lived bursts create shock waves persisting far from the discontinuity site. This study provides insight on crack front instabilities present in the rapid tensile failure of brittle materials due to large distortions of the rupture front

Impact Response of Elasto-Plastic Granular Chains Containing an Intruder Particle

Wave propagation in homogeneous granular chains subjected to impact loads causing plastic deformations is substantially different from that in elastic chains. To design wave tailoring materials, it is essential to gain a fundamental understanding of the dynamics of heterogeneous granular chains under loads where the effects of plasticity are significant. In the first part of this work, contact laws for dissimilar elastic-perfectly plastic spherical granules are developed using finite element simulations. They are systematically normalized, with the normalizing variables determined from first principles, and a unified contact law for heterogeneous spheres is constructed and validated. In the second part, dynamic simulations are performed on granular chains placed in a split Hopkinson pressure bar (SHPB) setup. An intruder particle having different material properties is placed in an otherwise homogeneous granular chain. The position and relative material property of the intruder is shown to have a significant effect on the energy and peak transmitted force down the chain. Finally, the key nondimensional material parameter that dictates the fraction of energy transmitted in a heterogeneous granular chain is identified

Frontal Polymerizations: From Chemical Perspectives to Macroscopic Properties and Applications

The synthesis and processing of most thermoplastics and thermoset polymeric materials rely on energy-inefficient and environmentally burdensome manufacturing methods. Frontal polymerization is an attractive, scalable alternative due to its exploitation of polymerization heat that is generally wasted and unutilized. The only external energy needed for frontal polymerization is an initial thermal (or photo) stimulus that locally ignites the reaction. The subsequent reaction exothermicity provides local heating; the transport of this thermal energy to neighboring monomers in either a liquid or gel-like state results in a self-perpetuating reaction zone that provides fully cured thermosets and thermoplastics. Propagation of this polymerization front continues through the unreacted monomer media until either all reactants are consumed or sufficient heat loss stalls further reaction. Several different polymerization mechanisms support frontal processes, including free-radical, cat- or anionic, amine-cure epoxides, and ring-opening metathesis polymerization. The choice of monomer, initiator/catalyst, and additives dictates how fast the polymer front traverses the reactant medium, as well as the maximum temperature achievable. Numerous applications of frontally generated materials exist, ranging from porous substrate reinforcement to fabrication of patterned composites. In this review, we examine in detail the physical and chemical phenomena that govern frontal polymerization, as well as outline the existing applications