Events
Past Event
Stress-Sprain Crack Band Model Based on Lagrange Multiplier Constraint of Displacement Gradient
McCormick - Mechanical Engineering (ME)
11:00 AM
//
A230, Technological Institute
Details
Prof. Zdeněk P Bažant
Walter P. Murphy Professor of Civil and Environmental Engineering
Northwestern University
A preceding seminar on 1/12/23 argued that the resistance of a heterogeneous material to the displacement field curvature is the physically most realistic localization limiter for softening damage and fracture. The curvature was characterized by the second gradient of the displacement vector field, which includes the material rotation gradient, and was named the ‘sprain’ tensor (a force variable work-conjugate to ‘sprain’ tensor). Initially, the partial derivatives of the associated sprain energy density were used to obtain self-equilibrated sets of curvature-resisting nodal sprain forces. Some forces acted on nodes adjacent to the finite element, which led to enormous computational burden. This burden is now eliminated by formulating a finite element with linear shape functions for both the displacement vector and the approximate displacement gradient tensor. The derivatives of the latter then yield the tensor of displacement curvature (or hessian), obviating the need for sprain forces. The main idea is to use a Lagrange multiplier tensor to constrain the approximate gradients to the actual displacement gradients. A user element for Abaqus is formulated and used to demonstrate mesh-independent crack band growth, capturing the band width variation and smooth damage distribution across the crack band.
Born and educated in Prague (Ph.D. 1963), Bažant joined the Northwestern faculty in 1969, where he has been W.P. Murphy Professor since 1990 and simultaneously McCormick Institute Professor since 2002, and Director of Center for Geomaterials (1981-87). He has been inducted to the NAS, NAE, AAAS, Royal Soc. London and 8 other national academies, and has received the Austrian Cross of Honor for Science and the Art I. Class from the President of Austria, among many other awards and 9 honorary doctorates. He has authored nine books on structural stability, fracture, its probability, and concrete creep and hygrothermal effects. In 2019 Stanford University citation survey, he ranked worldwide no.1 in CE and no.2 in engineering overall. In 2015, ASCE established the Bažant Medal for Failure and Damage Prevention and in 2023, ASME established the Bažant Medal for contributions to mechanics.
Time
Thursday, December 14, 2023 at 11:00 AM - 12:00 PM
Location
A230, Technological Institute Map
Contact
Calendar
McCormick - Mechanical Engineering (ME)
The Chicago Cultural Stadium, Lou Raizin, Broadway in Chicago
Center for Robotics and Biosystems (CRB)
1:00 PM
//
Cohen Commons, 4th Floor, Technological Institute
Details
Speaker: Lou Raizin, President and CEO, Broadway in Chicago
Title: “The Chicago Cultural Stadium”
Date: Wednesday, May 14, 1:00 PM CT
Location: Tech, Cohen Commons, 4th Floor
Zoom: https://tinyurl.com/ArtAndRobotics
Abstract: Broadway in Chicago President and CEO Lou Raizin will visit Northwestern to convene people from across the university to learn more about his vision for the Cultural Stadium in Chicago: where he imagines the possibility of linking art and engineering with a kinetic or robotics-related sculpture to inspire wonder in the Loop.
The Cultural Stadium reimagines downtown Chicago as a vibrant, inclusive arena of cultural life—where every street, bridge, and building becomes a stage. Inspired by the scale and spirit of a stadium, the concept brings culture to the forefront through art, live performances, and creative community spaces. With projects like the LaSalle Street transformation, it blends affordable housing, artist studios, and public exhibitions to make culture accessible and alive. This vision calls for structural shifts—zoning, funding, and public-private collaboration—to turn downtown into a bold, living showcase of Chicago’s creativity and diversity. A place where culture isn’t background—it's center stage.
Co-sponsored by McCormick School of Engineering, Arts + Engagement Initiative and Center for Robotics and Biosystems
Bio: Lou Raizin has over 40 years of experience in the entertainment industry. As a founder and the prime mover behind Broadway In Chicago, a joint theatrical venture formed in 2000, his leadership propelled the transformation of Chicago from a short-term stop on “the road” to the third most important city in the world for theater. Encompassing the five premiere theater stages in the city, Broadway In Chicago has presented over 400 productions, bringing an economic impact of over $750 million annually to the City of Chicago and State of Illinois and supporting more than 9,200 local jobs.
Raizin’s focus on economic development, tourism and the support of culture in our City has led to the creation and continued sponsorship of the annual League of Chicago Theatre’s Emerging Theatre Award and the Illinois High School Musical Theatre Awards. Mr. Raizin has been named one of Chicago Magazine’s 100 Most Powerful Chicagoans and is a tireless advocate for Chicago as a cultural destination, having served as the Board Chair of the Chicago Loop Alliance leading the organization in the creation of Pop Up Art Loop, comprised of over 14 galleries and as well as the installation of a number of major public art projects in the city including the lighting and music display along State Street.
Outside of Broadway In Chicago, Raizin’s focus is often at the intersection of arts, culture and economic development to create jobs in the city. He had long served as Treasurer for Choose Chicago and on the Executive Committee of Choose Chicago and is a Board Member of the Magnificent Mile Association. He previously chaired the Chicago Loop Alliance and the State Street Commission for multiple terms, served as a member of the Economics Club as well as serving as a director of a number of other civic and not-for-profit organizations. He founded and chaired the Board of LUMA8 (Light Up My Arts), the entity that produces the Arts In The Dark Parade and the River Walk Lantern Festival. Raizin also served as the catalyst for both the $12M permanent light art installation on the back wall of the Merchandise Mart and a digital platform for tourism.
Time
Wednesday, May 14, 2025 at 1:00 PM - 2:00 PM
Location
Cohen Commons, 4th Floor, Technological Institute Map
Contact
Calendar
Center for Robotics and Biosystems (CRB)