Session: 07-19-01: Symposium on the Anniversary of the Timoshenko-Ehrenfest Beam Model and Other Refined Theories and Vibrations of Continuous Systems

Paper Number: 150610

150610 - Inverse Rod Model to Investigate How Atomistic Details Govern Non-Homogeneous Constitutive Laws of Biological Filaments 

Introduction: Conventional studies on the mechanical properties of biological and synthetic filaments have largely relied on linear and homogeneous constitutive laws derived from noisy experimental data through parameter fitting. This approach overlooks the inherent non-homogeneity and nonlinearity due to the intricate atomic configurations of these filaments that not only vary along their lengths but also change as they deform. This research introduces a sophisticated computational framework to explore these variations using simulations of discrete structures, thus transcending the limitations of simplified empirical models.

Contribution: Our study significantly advances biomechanical modeling by integrating three pivotal advancements: leveraging both static and dynamic deformation data, employing an unbiased approach for estimating constitutive laws, and incorporating uncertainty quantification to address non-homogeneous properties. This holistic method enables a comprehensive characterization of constitutive laws as complex nonlinear functions, directly informed by the dynamic responses of the structures rather than through presupposed assumptions.

Methodology: We developed an inverse rod model that utilizes dynamic deformation datasets to estimate constitutive laws, which is more informative than just static equilibria. We present and evaluate this inverse approach using synthetic data from simulations of artificially designed discrete structures that exhibit non-homogeneous and potentially nonlinear behaviors by design. By focusing on dynamic rather than static data, our method captures a fuller range of mechanical responses, offering profound insights into the underlying mechanics governing filament behavior.

Results: The model has been rigorously tested with synthetic data from discrete structure simulations, demonstrating its capacity to accurately derive complex constitutive laws. Both rigorous testing and robustness analysis confirm the model's effectiveness in handling data with inherent noise and variability, ensuring reliability across diverse simulation scenarios. Sensitivity analysis shows the critical role of data quality in constitutive law estimation. Smooth and accurate data sets significantly enhance the estimation process compared to sparse data. The robustness analysis further revealed that the algorithms were more sensitive to noise in curvature than to noise in linear and angular velocities. Overall, these findings highlight the model's robustness and reliability across different scenarios, emphasizing the importance of data quality and appropriate noise mitigation strategies in accurately estimating constitutive laws.

Conclusions: This research not only enhances the understanding of filament mechanics but also lays the groundwork for designing materials with specific mechanical properties tailored through precise atomic configurations. By enabling a deeper comprehension of how discrete arrangements influence overall deformability, our work paves the way for innovations in biomaterials and synthetic structures. Furthermore, the integration of this research into educational tools represents a significant stride in teaching complex biomechanical interactions, fostering an interdisciplinary understanding of science and engineering. This dual focus on research and education bridges critical gaps in current engineering practices, enhancing both academic and practical approaches to material science.

Presenting Author: Muhammad Hassaan Ahmed University of California Merced

Presenting Author Biography: In 2018, I earned my B.E. degree in Mechanical Engineering from the National University of Science and Technology (NUST), Pakistan, securing GPA-based scholarships throughout all eight semesters. During my academic journey, I also served as a Research Assistant (RA) at the National Centre of Robotics and Automation (NCRA). My diverse research interests encompass biomedical devices, robotics, and computational dynamics, with a particular focus on microscope biological systems.
The crux of my research revolves around investigating the impact of constitutive laws on slender structures, modeled as continuum beams or rods, and their dynamics of deformation in bending and torsion. Specifically, I will delve into scenarios where the constitutive law exhibits non-linear and/or non-homogeneous characteristics. This exploration is propelled by a fundamental question: how do the features of non-linearity and non-homogeneity in constitutive laws influence the dynamics of deformation in biological filaments, subsequently shaping their biological activity or functions?
Although the exact application of this study may be elusive, I plan to define mechanics-based problems that intricately address engineering and mathematical challenges. This strategic approach serves as a foundational stepping stone toward achieving the overarching goal of understanding the intricate relationship between the structure and function of biological filaments.
Moreover, my research aims to develop inverse methods for identifying the constitutive laws governing slender filaments. To achieve this, I will leverage experimental data from real systems, employing it to discern the constitutive laws. The accuracy of these identified laws will be rigorously validated through molecular dynamics simulations on software platforms, ensuring the reliability and applicability of the research outcomes.

Authors:

Muhammad Hassaan Ahmed University of California Merced
Soheil Fatehiboroujeni Colorado State University
Sachin Goyal University of California Merced