"I, a universe of atoms,
an atom in the universe"
— Richard P. Feynman

Our research interests focus on the formation of mathematical models and the employment of atomistic and multiscale computational modeling to understand the mechanics of materials, including biomaterials and engineering materials. We aim to integrate nanoscale approaches to provide novel solutions to complex engineering problems based on the principles of statistical and continuum mechanics.

We are always looking for prosperctive students who are interested in our research activities. To discuss available positions in the lab, please contact Prof. Shu-Wei Chang at

Multiscale modeling of Mechanobiology: Understanding
How Mechanical Forces Influence Biological Materials

Biomechanical forces play a critical role in our body. The musculoskeletal system generates, absorbs and transmits force, enabling the functional movement of our body. Collagenous tissues in tendon, bone and articular cartilage provide mechanical stability, elasticity and strength to the human skeleton. Collagenous tissues are “smart” materials that have the ability to adapt their properties in response to mechanical forces through altering their structures from the molecular level up. They are able to convert mechanical forces into biochemical signals that control many biological and pathological processes such as wound healing and tissue remodeling. For example, appropriate physical training can increase the tensile strength of tendons, while inappropriate mechanical forces can lead to many diseases such as tendon injuries, bone fractures and osteoarthritis (OA). Despite a clear clinical relevancy of understanding the mechanobiology, how the collagenous tissues convert the biomechanical forces into the signaling that regulates the cells during development and adulthood remains to be elucidated. Understanding these relationships is crucial for the developing of the skeletal regenerative medicine or preventative strategies for the related diseases. We take an innovative in silico approach to investigate the mechanobiology of biological materials from a bottom up approach. Since the mechanobiology of biological materials involves the material properties of the matrix, the mechanotransduction of cells and the molecular mechanisms of the extracellular matrix degradation, our research focus on investigating the mechanobiology from these three aspects, with an aim to elucidate the role of mechanical forces in biological materials and related diseases.

Articular cartilage is connective tissue that forms a slippery load-bearing joint surface between bones. With outstanding mechanical properties, it plays an essential role in cushioning impact and protecting the ends of bones. Abnormal mechanical stimulation, such as repetitive overloading or chondral injury, induces excessive cartilage extracellular matrix (ECM) degradation, leading to osteoarthritis and other joint disorders. A disintegrin and metalloproteinase with thrombospondin motifs-5 (ADAMTS-5) is an aggrecanase that dominates the catalysis of aggrecan, the major proteoglycan in the cartilage ECM. Intriguingly, unlike its critical cleavage site Glu373–374Ala, another potential cleavage site, Glu419-420Ala, composed of the same amino acids in the aggrecan interglobular domain, is not a major cleavage site. It remains unclear how ADAMTS-5 distinguishes between them and hydrolyzes the correct scissile bonds. This research introduces a bottom-up in silico approach to reveal the molecular mechanism by which ADAMTS-5 recognizes the cleavage site on aggrecan. It is hypothesized that the sequence in the vicinity assists ADAMTS-5 in positioning the cleavage site. Specific residues were found to serve as binding sites, helping aggrecan bind more stably and fit into the enzyme better. The findings provide insight into the substrate binding and recognition mechanism for cartilage ECM degradation from a brand new atomic-scale perspective, laying the foundation for prophylaxis and treatment of related joint diseases.

Mechanical force plays a critical role in the remodeling and degradation of cartilage tissues. The cartilage tissue generates, absorbs, and transmits mechanical force, enabling specific biological processes in our body. A moderate intensity mechanical force is necessary for cartilage tissue remodeling and the adaptation of biomechanical properties, but a high intensity mechanical force can lead to pathological degradation of cartilage tissue. However, the molecular mechanism of cartilage degradation is still unclear. We use full atomistic simulations with SMD simulations to investigate whether the magnitude of mechanical force affects the unbinding pathway of the MMP8-Aggrecan_IGD complex. We find that when the pulling velocity is slow, the mechanical force required to unbind the Aggrecan_IGD from MMP8 is higher, and a three-step unbinding pathway is observed. On the other hand, when the pulling velocity is fast, the mechanical force required to unbind the Aggrecan_IGD from MMP8 is lower, and a two-step unbinding pathway is observed. Our results help us to understand how the magnitude of the mechanical force affects the unbinding pathway of the enzyme-ligand complex in cartilage tissue at the molecular level.

CD44 is widely expressed in most vertebrate cells, whereas the expression of CD44v6 is restricted to only a few tissues and has been considered to be associated with tumor progression and metastasis. Thus, CD44v6 has been recognized as a promising prognostic biomarker and therapeutic target for various cancers for more than a decade. However, despite many experimental studies, the structural dynamics and differences between CD44s and CD44v6, particularly in their stem region, still remain elusive. Here, a computational study was conducted to address these problems. We found that the stem of CD44s adopted predominantly two conformations, one featuring antiparallel β-sheets and the other featuring parallel β-sheets, whereas the stem of CD44v6 adopted mainly one conformation with relatively highly suppressed β-sheet contents. Moreover, Phe215 was found to be essential in the β-sheets of both CD44s and CD44v6. We finally found intramolecular Phe215–Trp224 hydrogen-bonding interactions and hydrophobic interactions with Phe215 that cooperatively drove conformational differences upon the addition of the v6 region to CD44. Our study elucidated the structural differences between the stem regions of CD44s and CD44v6 and thus can offer useful structural information for drug design to specifically target CD44v6 in promising clinical applications.

The transient receptor potential (TRP) channel TRPV4 is a calcium-permeable cation channel protein which plays a mechanosensory and osmosensory role in several musculoskeletal tissues. Previous studies have shown that some specific mutations in the ankyrin repeat domain (ARD) of TRPV4 can reduce channel activity and further cause the osteoarthropathy related disease. Mutations in this region probably influence the constitutive activity of the channel, which mainly regulated by the binding of a small ligand such as adenosine triphosphate (ATP). These findings suggest that it is crucial to understand the fundamental mechanisms regulated by chemical ligands such as ATP binding with the ankyrin repeat domain (ARD) of TRPV4. However, how these mutations at the molecular level resulting in the related diseases are still unclear. Here we use full atomistic simulations to investigate the mutation induced conformational changes and ATP binding ability differences of TRPV4-ARD. Conformation characteristics of different mutations of TRPV4-ARD are explored. Optimal communication paths are studied to explain how a point mutation away from aim region (Finger 3) can cause a significant alteration on the conformation. We identify two molecular mechanisms through the conformation of Finger 3 and through alter the ATP binding mechanism correspondently to explain these unknowns. Our study provides fundamental insights into the mutation induced structural changes of the TRPV4-ARD and helps to explain how the mutations alter the ATP binding ability of the TRPV4-ARD.

Bio-inspired Structural Materials for Engineering Applications

Cellular composites found in nature have provided fruitful inspirations for their exceptional toughness with merely a few building blocks of base constituents. The infructescence of Liquidambar formosana, which has porous cells arranged in spherical Fibonacci spirals, demonstrates high compressive stiffness and strength albeit lightweight and high porosity. In this work, we propose a Fibonacci composite inspired by Liquidambar formosana. The stress–strain response and fracture modes of bio-inspired cellular composites are simulated to show that the structural geometry of stiff skeleton and soft inclusion governs the toughening performance of cellular composites. The Fibonacci composite outperforms other studied geometries in terms of specific stiffening, strengthening, and toughening because of its high degree of isotropy to arrest and deflect the cracks across multiple length scales.

Fractals, mathematically defined as “self-similar subsets at different scales”, are ubiquitous in nature despite their complexity in assembly and formulation. Fractal geometry formed by simple components has long been applied to many fields, from physics and chemistry to electronics and architecture. The Sierpiński carpet (SC), a fractal with a Hausdorff dimension of approximately 1.8933, has two-dimensional space-filling abilities and therefore provides many structural applications. However, few studies have investigated its mechanical properties and fracture behaviors. Here, utilizing the lattice spring model (LSM), we constructed SC composites with two base materials and simulated tensile tests to show how fractal iterations affect their mechanical properties and crack propagation. From observing the stress–strain responses, we find that, for either the soft-base or stiff-base SC composites, the second iteration has the optimal mechanical performance in the terms of stiffness, strength, and toughness compared to the composites with higher hierarchies. The reason behind this surprising result is that the largest stress intensities occur at the corners of the smallest squares in the middle zone, which consequently induces crack nucleation. We also find that the main crack tends to deflect locally in SC composites with a soft matrix, but in global main crack behavior, SC composites with a stiff matrix have a large equivalent crack deflection. Furthermore, considering the inherent anisotropy of SC composites, we rotated the samples by 45°. The results show that the tensile strength and toughness of rotated SC composites are inferior and the crack propagating behaviors are distinct from the standard SC composites. This finding infers advanced engineering for crack control and deflection by adjusting the orientation of SC composites. Overall, our study opens the door for future engineering applications in stretchable devices, seismic metamaterials, and structural materials with tunable properties and hierarchies.

In light of the demand for mechanically robust synthetic composites, researchers have adapted several toughening mechanisms of nacre, hardening through tablet sliding in particular has been in highlight till date. A few pioneers have reported an exclusive hardening phenomenon capable of amplifying the strength and toughness of staggered composites, however, works devoted to the tunability are limited to computation. Here, by employing design optimization, 3D-printing, and simulation, we demonstrate the evolution, and tunability of such deformation behavior. We discern two fracture mechanisms, columnar and non-columnar fractures, which elucidate hardening and toughening observed for interlocking and non-interlocking tablet topologies. Computation analyses at various fracture stages are conducted to unravel the change in stress concentrations, comprehending the fracture mechanisms in depth. We present vital insights on the multi-stage deformation behavior and its tunability in staggered composites, which currently has reached the pinnacle of interest for developing composites with superior mechanical properties.

Biological materials such as silk, nacre, and bone have superior mechanical properties due to their well-designed microstructures with dissimilar, namely soft and bulk, composites. It is widely believed that the unique microstructures result in high strength and toughness via a normal-shear-stress-coupling mechanism. Microcrack initiation in biological materials play a crucial role in triggering such a mechanism, and therefore further investigation of its initiating condition and microcrack propagation are needed. In this study, we first describe a staggered model from biological material and illustrate the effects under different microcrack patterns. We employ a Fast Fourier Transform based (FFT-based) homogenization method with linear elasticity and non-local damage theory to investigate the stress distribution and load transmission, as well as the microcrack propagation due to different structural designs of soft matrix geometry. The major implication of this paper is that the design of soft matrix geometry determines the microcrack initiating patterns and impacts the local transmission mechanism of biocomposites. This research provides insights into design strategies for microstructures to trigger normal-shear-stress-coupling behavior for biocomposites to achieve high toughness and strength.

Full Atomistic Modeling of Cementitious and
Metallic Materials

Variable stoichiometry and silicate polymorphism in calcium-silicate-hydrates (C-S-H) has impeded the revelation of point defects distribution in the silicate tetrahedral network of C-S-H, which resembles tobermorite crystal structure with some bridging tetrahedra (BT) and paired tetrahedra (PT) vacancies in dreierketten chains. Here we use a computational approach to characterize silicate polymorphism by introducing the vacancy ratio of BT to PT (α) and establishing a three-term empirical mean chain length (MCL) formula for different calcium-to‑silicon ratios (Ca/Si) ranging from 1.2 to 2.3. The formula identifies BT and PT controls at low and high α respectively and allows an inverse mapping of polymorphic range based on NMR experiments. The proposed computational framework quantitatively describes silicate polymorphs and links NMR-measured MCL to C-S-H atomistic configurations at the molecular level.

Mechanics of Nanostructures and Nanocomposites

Nanostructures and nanomaterials have been studied thoroughly due to their remarkable properties. With various sizes and shapes, they serve as highly functional sensors in nanoelectromechanical systems (NEMS), noninvasive medical diagnostic devices or drug delivers. Although the importance of surfaces has been recognized when it comes to the nanoscale, few researchers investigate nanostructures with multiple surface orientations. In this work, we propose a two-surface theoretical model for nanohoneycombs and verify the model by conducting molecular dynamics (MD) simulations on regular hexagonal Al nanohoneycombs with cell-wall thickness ranging from 5 nm to 30 nm. These numerical examples show excellent agreement with the proposed theory, proving the applicability of the two-surface model. The Al nanohoneycomb exhibits significant “positive” size dependence – it is 2.4 times stiffer compared with its large counterpart when the cell-wall thickness is 5.7 nm. In sum, this study improves the accuracy of the predicted in-plane Young’s moduli of nanohoneycombs by taking differently oriented surfaces into account and considering more comprehensive deformation mechanisms. By investigating nanosized honeycomb structure in-depth and providing a more general theoretical model, we aim to improve the accuracy of predicted mechanical properties and provide a guide for the applicability of various models for honeycombs. Furthermore, this study can help exploit the full potential of various nanoporous structures, not restricted to nanohoneycombs.

Molecular Modeling of Biodegradable and
Self-healing Hydrogels

Chitosan is a natural polycationic linear polysaccharide deacetylated from chitin. Glycol chitosan is a derivative of chitosan and has been extensively investigated in the biomaterials and hydrogel field for many bioengineering applications because of their unique material and biological properties. However, the molecular structure and network of glycol chitosan hydrogels remain unclear. Here, we explored the molecular structures and network of glycol chitosan with different protonation percentages by using full atomistic simulations. Hydrogel and xerogel models are constructed to understand the interactions between the water molecules and glycol chitosan chains. We calculated the radius of gyration and radial distribution function of hydrogel and xerogel models to understand the swelling behavior from molecular level. We find that when the pH is close to neutral and becomes basic, greater flexibility of glycol chitosan chains leads to a high swelling ratio. The slight contracting behavior of glycol chitosan chains and the dispersive distribution above 40% protonation can be interpreted to indicate a poor swelling ratio. The protonated amino groups inhibit the hydrogen-bond formation between water molecules and adjacent oxygen-containing groups of glycol chitosan main chains. On the other hand, the glycol groups of glycol chitosan are not affected by the electrostatic interaction, and the number of hydrogen bonds between glycol groups and water molecules does not vary with pH. The van der Waals interaction between glycol chitosan chains is dominant when the protonation percentages are lower than 40%, while the electrostatic interaction of amino groups is dominant when the protonation percentages are higher than 40%. Our results explain the effects of pH on the molecular structures of glycol chitosan and provide useful information regarding the design strategy of novel glycol chitosan and its derivatives for biomedical applications.

Biodegradable hydrogels have become promising materials for many biological applications in the past years. Recently, novel waterborne biodegradable polyurethane (WDPU) nanoparticles have been synthesized by a green water-based process, and serve as fundamental building blocks to form materials with great biocompatibility, biodegradability, and mechanical properties. However, the molecular structures and mechanisms of the WDPU nanoparticles and the relationship between the chemical compositions of the polymer segments and the material properties of the biodegradable hydrogels at macro-scale are still not well understood. In this study, we explore the fundamental mechanisms of WDPU nanoparticles through a full atomistic simulation approach to understand how the chemical compositions at the molecular level affect the molecular structures and material properties of WDPU nanoparticles. Specifically, we compare two WDPUs, i.e. PCL75LL25 and PCL75DL25, of the same hard segment composition and very similar soft segment composition [75% poly(e-caprolatone) and 25% polylactide], except the lactide in the former is L-form and in the latter is D,L-form. Our results show that the material properties of the biodegradable hydrogel can be designed by tuning the chemical compositions of the polymer segments. We find that the PCL75DL25 and PCL75LL25 have distinct molecular structures and physical crosslinks within the nanoparticles. The molecular structure of WDPU with PDLLA as soft segments is more extended, leading to more physical crosslinks between PCL segments. This study provide fundamental insights into the molecular structures and mechanisms of WDPU nanoparticles and help enabling the design of material properties of biocompatible hydrogel.

In silico Investigation of Tendon and Bone
from Molecular Level

Collagenous tissues, made of collagen molecules, such as tendon and bone, are intriguing materials that have the ability to respond to mechanical forces by altering their structures from the molecular level up, and convert them into biochemical signals that control many biological and pathological processes such as wound healing and tissue remodeling. It is clear that collagen synthesis and degradation are influenced by mechanical loading, and collagenous tissues have a remarkable built-in ability to alter the equilibrium between material formation and breakdown. However, how the mechanical force alters structures of collagen molecules and how the structural changes affect collagen degradation at molecular level is not well understood. The purpose of this article is to review the biomechanics of collagen, using a bottom-up approach that begins with the mechanics of collagen molecules. The current understanding of collagen degradation mechanisms is presented, followed by a discussion of recent studies on how mechanical force mediates collagen breakdown. Understanding the biomechanics of collagen molecules will provide the basis for understanding the mechanobiology of collagenous tissues. Addressing challenges in this field provides an opportunity for developing treatments, designing synthetic collagen materials for a variety of biomedical applications, and creating a new class of ‘smart’ structural materials that autonomously grow when needed, and break down when no longer required, with applications in nanotechnology, devices and civil engineering.

Bone is a natural composite of collagen protein and the mineral hydroxyapatite. The structure of bone is known to be important to its load-bearing characteristics, but relatively little is known about this structure or the mechanism that govern deformation at the molecular scale. Here we perform full-atomistic calculations of the three-dimensional molecular structure of a mineralized collagen protein matrix to try to better understand its mechanical characteristics under tensile loading at various mineral densities. We find that as the mineral density increases, the tensile modulus of the network increases monotonically and well beyond that of pure collagen fibrils. Our results suggest that the mineral crystals within this network bears up to four times the stress of the collagen fibrils, whereas the collagen is predominantly responsible for the material’s deformation response. These findings reveal the mechanism by which bone is able to achieve superior energy dissipation and fracture resistance characteristics beyond its individual constituents.