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535.663.81 - Biosolid Mechanics

Mechanical Engineering

Spring 2024

Description

This class will introduce fundamental concepts of statics and solid mechanics and apply them to study the mechanical behavior bones, blood vessels, and connective tissues such as tendon and skin. Topics to be covered include the structure and mechanical properties of tissues, such as bone, tendon, cartilage and cell cytoskeleton; concepts of small and large deformation; stress; constitutive relationships that relate the two, including elasticity, anisotropy, and viscoelasticity; and experimental methods for measuring mechanical properties.

Instructor

Thomas Metzger

This course contains content produced by faculty members other than the listed instructors including: Dr. Thao Nguyen.

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the course menu. The modules run for a period of seven (7) days and are made available the Thursday prior. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. You should regularly check the Calendar and Announcements for assignment due dates.

It is expected that each module will take approximately 8–9 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 1–2 hours per week) as well as some outside reading, listening to the audio annotated slide presentations (approximately 1-2 hours per week), and homework and projects (approximately 4–5 hours per week).

Timely feedback on students' performance is an established learning tool, so we will endeavor to grade and return to you, as quickly as possible, all material that you submit. Homework will normally be graded and returned via the website within a week. If you do not receive a grade on homework that you have turned in, please ask of its whereabouts; it may need to be resubmitted.

Course Topics

Module #	Module Title	Module Overview	Learning Activities and Assessments	Module Resources
1	Review of Statics	Review concepts of free body diagrams and equilibrium in the form of balance of forces and moments	HW 1	Required: Humphrey – Chapter 1 Lecture notes
2	Concepts of Stress	Introduce and define concepts of traction and stress. Derive the formulas for stress transformation based on static equilibrium and define the state of stress and principal stresses.	HW 2	Required: Humphrey – Chapter 2.1-2.4 Lecture notes
3	Concepts of Strain	Introduce and define concepts of deformation gradient, Green-Lagrange, and small strain. We will also derive formulas for Strain transformation and states of strain.	HW3	Required: Humphrey – Chapter 2.5 Lecture notes
4	Bone and constitutive equations for hard tissues	Introduce structure and mechanical properties of bone; Generalized Hooke’s Law for isotropy, transverse isotropy and orthotropy. Introduce structure of bone.	HW4 Midterm Project is Assigned	Required: Textbook Humphrey – Chapter 2.6-2.7 Lecture notes Recommended Rho et al. 1998, “Mechanical properties and the hierarchical structure of bone” Oftadeh et al. 2015, “ Biomechanics and Mechanobiologyof Trabecular Bone: A Review”
5	Axial Loaded Rods and torsion	Understand concepts of boundary value problems. Derive force-displacement response for an axially loaded rod and the torque-angle of twist for torsion.	HW5	Required: Humphrey – Chapter 3.1-3.3 and 4.1-4.6, Appendix 4 Lecture notes
6	Blood Vessels and Pressure Vessels	Introduction to blood vessels Derive Laplace’s law for thin-walled cylindrical pressure vessel with different end conditions and spherical pressure vessels. Derive stress response for thick-walled pressure vessel. Discover the relationships between the two.	HW6	Required: Humphrey – Chapter 3.3-3.6 Lecture notes
7a	Cell cytoskeleton and Beam bending part 1	Introduce concepts of cell cytoskeleton and methods developed to measure the stiffness of cytoskeletal fibers and cellular contractility. Derive the equilibrium equations relating lateral forces, shear forces and moments. Introduce model for the strain-curvature relationship. Derive the stress-moment relationship from equilibrium	HW7a	Required: Humphrey – Chapter 5.1-5.2, 5.4 Lecture notes Recommended S. Park and Y. Chen “Mechanics of Biological Systems 3.9.2 Atomic Force Microscopy 4.6.4 Microbead-based traction force microscopy 4.6.5 Micropillar-based traction force microscopy
7b	Beam bending part 2	Derive the beam bending equations for the lateral deflection. Derive the theory of beam buckling	HW7b Midterm Project is due	Required: Textbooks 5.3., 5.5, 5.6 Appendix 5 Lecture notes Recommended Kis et al. 2002 “Nanomechanics of Microtubules” Kinisho and Yanagida (1998) “Force measurements by micromanipulation a single actin filament by glass needles Kurachi et al. (1995) “Buckling of a single microtubule by optical trapping forces.. “
8	Introduction to collagenous soft tissues Stress and strains for large deformation	Introduce structure of collagenous soft tissues Introduce concepts of true stress and true strain. Introduce finite deformation kinematics and models of traction and stress.	HW8 Final Project is assigned	Required: Humphrey – Chapter 6.1 Fung Chapter 7.1-7.4 Lecture notes
9a	Hyperelasticity: part 1	Introduce concepts of hyperelasticity, Fung’s model, and incompressible hyperelastic model	HW 8	Required: Humphrey – Chapter 6.2-6.6 Lecture notes
9b	Hyperelasticity: part 2	Introduce structure tensor models of soft tissues, distributed fiber models, Gasser, Ogfen and Holzapfel model.	HW9b	Required: J. Merodio and R. W. Ogden (2005) “Mechanical response of fiber-reinforced incompressible non-linearly elastic solids”. Gasser et al. (2006) “Hyperelastic modelling of arterial layers with distributed collagen fibre orientations” Tonge et al. (2013), “Full-field bulge test for planar anisotropic tissues: Part II – A thin shell method for determining material parameters and comparison of two distributed fiber modeling approaches”
10	Viscoelasticity: Applications to soft tissues	Introduce small-strain theory of viscoelasticity and the resulting time-dependent and frequency dependent behaviors.	Work on your research paper	Required: Fung Chapter 2.11-2.13, 7.6 Lecture notes
11	Cartilage and Poroelastcity:	Introduction to structure of cartilage Introduction to small strain theory of poroelasticity and application to unconfined compression,		Required: Lecture notes
12	Final		Final Project is due

Course Goals

To learn about the structure and mechanical properties of tissue, understand how mechanics can be applied to measure the mechanical properties of tissues, and analyze for the stresses and deformation of tissues in response to mechanical loading.

Course Learning Outcomes (CLOs)

Explain about the microstructure and mechanical behavior of tissue structures.
Apply the fundamental concepts of stress and strain for infinitesimal and finite deformation kinematics.
Apply the constitutive models commonly applied for biological hard and soft tissues.
Solve static problems for common of biological tissue structures.

Textbooks

Biosolid mechanics is a diverse topic that spans the fracture of bones to the mechanotransduction of cells. I will rely mostly on class notes and assign reading from the required textbook: J.D. Humphrey. The textbook presents a rigorous non-tensor treatment of mechanics with relevant biological applications and is a great introductory textbook. I will also assign required reading from research papers and a few sections from the optional textbook by Y.C. Fung. These should be available in the course contents and from the library.

Humphrey, J. D., & O’Rourke, S. L. (2015). An Introduction to Biomechanics: Solids and Fluids, Analysis and Design. Springer. ISBN: 978-1-4939-2622-0 [e-version]

Optional
Fung, Y. C. (1993). Biomechanics: Mechanical Properties of Living Tissues. Springer. ISBN 978-1-4757-2257-4 [e-version]

Student Coursework Requirements

Homework Assignments: 50%
Midterm Project: 25%
Final Project 25%

Note that HW grades will be assigned based on the cumulative score and will be curved depending the grade distribution of the class unless everyone gets 80% and above. Then we will follow the grading policy below.

Extensions for HW and project deadlines must be requested at least 24 hours in advance. This is so I can time the release of HW solutions. Otherwise, late HW and projects are not accepted.

Grading Policy

EP uses a +/- grading system (see “Grading System”, Graduate Programs catalog, p. 10).

Score Range	Letter Grade
100-98	= A+
97-94	= A
93-90	= A−
89-87	= B+
86-83	= B
82-80	= B−
79-77	= C+
76-73	= C
72-70	= C−
69-67	= D+
66-63	= D
<63	= F

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically.

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity.

If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.