The goal of this research is to establish fundamental microstructure-property understanding needed for the development of a new generation of bio-engineered materials characterized by wavy microstructures, whose targeted performance is attained through micro-structural evolution based on the survival-of-the-fittest principles. Toughness, extensibility and adaptability may be realized through the exploitation of various arrangements of wavy microstructures, yet fundamental understanding of these architectural features vis-a-vis material response is lacking. Recent micro-structural simulation studies by the PI and co-workers demonstrated that layer thickness has a substantial impact on the homogenized response of periodic multi-layers with wavy microstructures in the inelastic domain. The proposed investigation addresses this recently discovered effect, and related effects, for the first time in engineered materials that mimic biological material response in the finite-deformation domain, including certain tissues. In particular, the investigation will answer the following questions, which have not been yet addressed, in the analysis and development of engineered materials with stiffening characteristics for bio-medical applications: (1) what is the effect of layer thickness on the homogenized and local responses of a wavy periodic multilayer in the finite-deformation domain?; (2) can targeted response of an engineered material with wavy microstructure be achieved using more than one microstructure?; (3) can connection between complexity and simplicity be established through an evolutionary design? The investigation employs a computational approach based on a novel homogenization technique called the parametric finite-volume direct averaging micromechanics (FVDAM) theory developed by the PI, his students and collaborators. This theory is particularly well suited for robust analysis, simulation and optimization of heterogeneous materials with accuracy comparable to the finite-element method, which presently is the computational standard, but with substantially greater efficiency. Experimentally measured response of three types of mitral valve chordea tendinea, which exhibit different levels of stiffening caused by different crimp patterns of the fibril bundles arranged in wavy layers, is employed in support of the verification and microstructural optimization component of the investigation. The intellectual merit stems both from the knowledge that will be generated and from further development of the theoretical tools necessary to accomplish it. Very little work based on first principles has been reported which is aimed at addressing the effect of microstructure in biological tissues on the overall response. The investigation will establish this connection for a particular material system that plays a significant role in biomedical applications. Further, the proposed theoretical enhancements of the parametric FVDAM theory will produce a paradigm shift in the theory's evolution, with the potential to replace the prevailing computational standard in the analysis and design of heterogeneous materials. The resulting computational technology will be readily employed in applications across several interdisciplinary boundaries, including traditional and emerging engineered materials with bio-inspired architectures. The theoretical enhancements involve the incorporation of finite-deformation capability into the FVDAM framework and the concomitant development of stable and accurate algorithms for the solution of structural mechanics problems in the finite-deformation domain, which continue to be a focus of the numerical engineering community. The proposed research is an important step in the parametric FVDAM theory?s continued development needed to realize its full potential across disciplinary boundaries. The broader impacts stem from the wide range of applications in which materials and structural components with wavy multilayer patterns are utilized across several scales and disciplines, ranging from corrugated structural panels to the rapidly developing nanotechnology areas. Microstructures with wavy architectures can potentially enhance certain performance characteristics such as stiffness, thermal stability and toughness. Yet, little systematic data is available addressing these issues in both the infinitesimal and finite-deformation domains. Moreover, the developed computational technology will be made available to the pertinent communities in the form of a Graphical User Interface to facilitate analysis, design and development of material systems for a wide range of applications, enabling material scientists and structural mechanicians alike to investigate what-if scenarios in pursuit of optimized and durable material microstructures. Concurrently, it will serve a greater educational purpose through training of both undergraduate and graduate students. Undergraduate students recruited from traditionally under-represented groups through the PI?s contact as an instructor in undergraduate courses, as well as through the well-known Center for Diversity at the University of Virginia, will be involved in the GUI?s testing and applications as summer interns who will further exploit this experience in their senior theses.
with wavy architectures that stiffen with increasing stretch, mimicking certain connecting tissues. Its goal was to establish fundamental microstructure-property understanding needed for the development of a new generation of bio-engineered materials with wavy microstructures, whose target performance is attained through microstructural evolution based on survival-of-the-fittest principles. The specific questions the investigation strove to answer in the analysis and development of engineered materials with stiffening characteristics for bio-medical applications were: Q1- What is the effect of material and geometric parameters of a wavy multilayer architecture on the multilayer’s stiffening response? Q2- Can targeted performance characteristics of an engineered material be achieved using more than one microstructure? Q3- Can a connection between complexity and simplicity be established through an evolutionary design? To address these questions, a novel computational technique had been developed, further generalized and combined with an evolutionary optimization algorithm that mimics the behavior of a swarm of birds searching for a target. The computational technique is well suited for robust analysis, simulation and optimization of heterogeneous materials with accuracy comparable to the present computational standard based on the finite-element method, but with substantially greater flexibility. It has also been demonstrated to facilitate simulation of damage evolution in heterogeneous materials based on a unified framework developed and implemented in this investigation that admits crack growth and interfacial separation between dissimilar materials. Experimentally measured response of three types of mitral valve chordae tendineae, which exhibit different stiffening characteristics due to differences in the collagen fibril waviness, was employed in support of the verification and microstructural optimization component of the investigation. The developed computational tools may be used in a wide range of applications, thereby broadening their impact. Three PhD students and one undergraduate student from an underrepresented group participated in this project, two of whom received their PhD degrees and are continuing as post-doctoral research associates in related areas elsewhere. The undergraduate student is now pursuing a medical degree at Virginia Tech. An important outcome of this study is the demonstration that the response of three types of mitral valve chordae tendineae characterized by complex microstructures of crimped bundles of collagen fibrils may be mimicked very accurately using simple, wavy planar multilayer architectures comprised of alternating stiff and soft layers. The roles of the amplitude and wavelength of the multilayers, microstructural refinement and the elastic properties of the constituent phases in controlling the unfolding and subsequent stiffening of the wavy microstructures have been elucidated, thereby providing design guidance for fabricating bio-inspired architectures that accurately mimic the response of chordae tendineae for heart-valve replacement purposes. These outcomes follow from the parametric and optimization studies enabled by the development of novel computational tools, and they fully address questions Q1 and Q2. In a broader setting, the generated simulation results provide guidance in the development and design of artificial tissues for this category of biological materials. Moreover, the extent of defect criticality of these multilayers vis-à-vis mimicking the response of the actual chordae tendineae to within an acceptable error also has been addressed and shown to depend on the wavelength of the crimp pattern. At small amplitude-to-wavelength ratios which lead to small extensibilities, as observed in the response of marginal chordae, up to 7 fractures in stiff layers in a unit cell comprised of 9 soft and 8 stiff layers may be tolerated without too much departure from the targeted response. This is due to the relatively high stiffness of the soft matrix phase which controls the unfolding of the wavy microstructure, and also transmits stress from the fractured layer into surrounding layers through the well-known shear-lag mechanism. For unit cells that mimic the response of basal and strut chordae which stiffen at much higher stretches, fewer stiff layer fractures (up to 3 for the unit cell with 8 stiff layers) may be tolerated owing to the low modulus of the soft phase which is required to ensure that the wavy microstructure unfolds without too much resistance. The low modulus of the soft phase is not effective in transferring stress to the intact fibers through shearing action. The conducted defect criticality study partially addresses the third question Q3 that strives to establish a connection between simplicity and complexity through an evolutionary process. Specifically, the study suggests that a complex microstructure that is comprised of both continuous and discontinuous stiff phases may produce comparable results as a simpler microstructure comprised solely of continuous layers. The evolution of the complex microstructure from the simpler one remains to be addressed. The development of a unified damage evolution methodology is a key to addressing this question upon identification of appropriate criteria and mechanisms which lead to local fractures/failures.
