### Nadia Lapusta

###### Lawrence A. Hanson, Jr., Professor of Mechanical Engineering and Geophysics

*Dipl., Kiev State University, 1994; M.S., Harvard University, 1996; Ph.D., 2001. Assistant Professor of Mechanical Engineering, Caltech, 2002-03; Assistant Professor of Mechanical Engineering and Geophysics, 2003-08; Associate Professor, 2008-10; Professor, 2010-19; Hanson Professor, 2019-.*

Research Summary

Professor Lapusta's interdisciplinary research group works in the areas of computational mechanics of geomaterials, earthquake source processes, fundamentals of friction and fracture, solid-fluid interactions, and seismology.

#### Research Options

Geophysics;

Ae/Ge/ME 160 ab. Continuum Mechanics of Fluids and Solids.
9 units (3-0-6); first, second terms., 2023-24.
Elements of Cartesian tensors. Configurations and motions of a body. Kinematics-study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics-balance laws. Linear and angular momentum, force, traction stress. Cauchy's theorem, properties of Cauchy's stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius-Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic Navier-Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws.

Instructors: Lapusta, Bhattacharya

Instructors: Lapusta, Bhattacharya

ME/CE/Ge 174. Mechanics of Rocks.
9 units (3-0-6); third term, 2023-24.
Prerequisites: Ae/Ge/ME 160 a.
Basic principles of deformation, strength, and stressing of rocks. Elastic behavior, plasticity, viscoelasticity, viscoplasticity, creep, damage, friction, failure mechanisms, shear localization, and interaction of deformation processes with fluids. Engineering and geological applications.

Instructor: Lapusta

Instructor: Lapusta

ME/Ge/Ae 266 ab. Fracture and Frictional Faulting.
9 units (3-0-6); second, third terms, 2022-23.
Prerequisites: Ae/AM/CE/ME 102 a or Ae/Ge/ME 160 a or instructor's permission.
Introduction to elastodynamics and waves in solids. Fracture theory, energy concepts, cohesive zone models. Friction laws, nucleation of frictional instabilities, rupture of frictional interfaces. Radiation from moving cracks. Thermal effects during dynamic fracture and faulting. Interaction of faulting with fluids. Applications to engineering phenomena a physics and mechanics of earthquakes.

Instructor: Lapusta

Instructor: Lapusta

Ae/Ge/ME 160 ab. Continuum Mechanics of Fluids and Solids.
9 units (3-0-6); first, second terms, 2021-22.
Elements of Cartesian tensors. Configurations and motions of a body. Kinematics-study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics-balance laws. Linear and angular momentum, force, traction stress. Cauchy's theorem, properties of Cauchy's stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius-Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic Navier-Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws.

Instructors: Rosakis, Lapusta

Instructors: Rosakis, Lapusta

ME/CE/Ge 174. Mechanics of Rocks.
9 units (3-0-6); second term, 2021-22.
Prerequisites: Ae/Ge/ME 160a.
Basic principles of deformation, strength, and stressing of rocks. Elastic behavior, plasticity, viscoelasticity, viscoplasticity, creep, damage, friction, failure mechanisms, shear localization, and interaction of deformation processes with fluids. Engineering and geological applications. Not offered 2021-2022.

ME/Ge/Ae 266 ab. Dynamic Fracture and Frictional Faulting.
9 units (3-0-6); third term, 2021-22.
Prerequisites: Ae/AM/CE/ME 102 abc or Ae/Ge/ME 160 ab or instructor's permission.
Introduction to elastodynamics and waves in solids. Dynamic fracture theory, energy concepts, cohesive zone models. Friction laws, nucleation of frictional instabilities, dynamic rupture of frictional interfaces. Radiation from moving cracks. Thermal effects during dynamic fracture and faulting. Crack branching and faulting along nonplanar interfaces. Related dynamic phenomena, such as adiabatic shear localization. Applications to engineering phenomena and physics and mechanics of earthquakes.

Instructor: Lapusta

Instructor: Lapusta

Ae/Ge/ME 160 ab. Continuum Mechanics of Fluids and Solids.
9 units (3-0-6); first, second terms, 2020-21.
Elements of Cartesian tensors. Configurations and motions of a body. Kinematics-study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics-balance laws. Linear and angular momentum, force, traction stress. Cauchy's theorem, properties of Cauchy's stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius-Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic Navier-Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws. Part a will be offered in 2020-21.

Instructor: Lapusta

Instructor: Lapusta