KASPAR J. WILLAM (1940-2024)

BY JOSEF EBERHARDSTEINER, HERBERT A. MANG,
EKKEHARD RAMM, STEIN STURE, YUNPING XI,
IGNACIO CAROL, ROBERTO BALLARINI, JEREMY
ISENBERG, AND ZDENĚK P. BAŽANT

KASPAR JODOKUS WILLAM, an eminent professor of civil engineering at the University of Colorado, Boulder, passed away on Jan. 7, 2024, in Bezau, Austria. Renowned for his seminal contributions to computational mechanics, failure analysis of structures, and constitutive modeling of brittle and quasibrittle materials, with special emphasis on concrete, he was a leading figure in structural engineering. His work significantly advanced the quality of predictive modeling for material behavior and structural failure. His theoretical and computational contributions to finite element analysis had a global impact, shaping modern approaches to material and structural integrity assessment.

Kaspar was born in Vienna on Dec. 20, 1940. During World War II, his family relocated to Bezau, in the westernmost part of Austria. His formative years were shaped by the rigorous traditional education of his homeland, which emphasized academic achievement with scientific excellence. He studied civil engineering at the Vienna University of Technology, known as TU Wien, earning the degree of Dipl.-Ing. in 1964, comparable to an M.S. degree. TU Wien was home to leading scholars in civil engineering, including Ernst Melan, Karl Girkmann, and Otto Karl Fröhlich, all members of the Austrian Academy of Sciences. Their work left a profound impression on Kaspar’s intellectual trajectory. During his time at TU Wien, he conducted advanced research in structural mechanics, elasticity, and plasticity, refining his expertise in continuum mechanics and laying the groundwork for his later success in numerical simulation. His rigorous analytical mindset and commitment to interdisciplinary research became hallmarks of his career.

Driven by a growing interest in computational methods, Kaspar relocated to the United States to deepen his expertise in numerical analysis and structural mechanics. He earned an M.S. degree in 1966 from California State University, San Jose, where, as a student of William Lorell, he completed a thesis titled “An experimental study of combined torsion and bending of reinforced concrete beams.” During this period, he began working on numerical approaches to nonlinear material behavior. This marked the beginning of his lifelong engagement with finite element methods, leading to his doctoral studies at the University of California, Berkeley. Under the mentorship of Alex Scordelis (NAE 1978), Kaspar completed his Ph.D. in 1969 with a dissertation on “Finite element analysis of cellular structures,” focusing on box girder bridges. That research eventually contributed to the development of the CELL program used by the California Department of Transportation in Sacramento. His research at Berkeley was instrumental in the early application of computational methods to complex engineering problems, integrating novel numerical strategies to improve predictive accuracy in structural performance analysis. Additional mentors in his doctoral research included Ed Wilson (NAE 1985) and Karl Pister (NAE 1980), whose support helped lay the groundwork for Kaspar’s later advances in nonlinear material modeling and multiscale simulations.

Returning to Europe, he joined the University of Stuttgart, Germany, as a research scientist under John H. Argyris (NAE 1986). His work in Stuttgart was integral to the development of the SMART finite element code, a pivotal tool in the analysis of prestressed concrete reactor vessels.¹ The intellectually rigorous environment at the University of Stuttgart provided a platform for Kaspar to delve into new subareas of nonlinear mechanics, culminating in his habilitation in 1980 with the scientific work “Finite element discretization of quasistatic problems in space and time.” His tenure there also allowed him to expand his research on adaptive numerical methods, further enhancing the accuracy of computational simulations in engineering applications.

In 1981, Kaspar joined the University of Colorado Boulder, where he would spend the majority of his academic career. He briefly served as head of the Institute of Mechanics at the University of Karlsruhe from 1988 to 1990 before returning to Boulder to continue his pioneering work in constitutive modeling, failure mechanics, and multiscale analysis of materials. His contributions to the use of plasticity in computational modeling of concrete were transformative. With his Stuttgart colleague E.P. Warnke, he developed the “Willam-Warnke” five-parameter plasticity model for concrete under multiaxial stress,² which accounted for the effect of the intermediate principal stress and became a cornerstone in the field. The model was later extended to include a second yield surface to correct for excessive dilatancy due to adherence to the normality rule of plasticity.

In the 1980s, Kaspar’s model was extensively used at many institutions — including at his alma mater, the Institute of Strength of Materials at TU Wien — for the mechanical modeling of concrete subjected to three-dimensional states of stress. For several decades, the model was also used in the design of protective military structures. His extensive research on fracture-energy-based constitutive formulations enabled engineers to predict structural failure with greatly improved accuracy.

Among his most consequential contributions was the refinement of failure models for quasibrittle materials, including the “Pramono-Willam” model in 1989³ and the “Extended Leon Model” in the early 1990s,^4,5 named after Alfons Leon, a professor at Graz University of Technology, in Austria. One endeavor, conducted with Pramono and Sture in 1989,⁶ became known as the Willam Test, which helped clarify the rotating versus smeared crack concepts. In this test, tensile loading was applied up to the strength limit, followed by a second load stage of tension where principal strains were in the ratio 1:1.5:1. The principal axes initially rotated rapidly, then more slowly, eventually stabilizing near an angle of 52 degrees. At the time, this test became a benchmark for anisotropic softening models of quasibrittle materials⁷ (part II). These models offered enhanced predictive capacity for simulating failure mechanisms under extreme loading conditions, significantly influencing engineering design and safety standards. Kaspar’s pioneering work in computational plasticity introduced innovative numerical integration algorithms for complex material models,^8,9 which vastly improved the efficiency and reliability of finite element analysis. His research on adaptive computational frameworks also provided a pathway for optimized engineering designs, enabling more rigorous assessments of material durability and structural resilience. Frequent visits of Zdeněk Bažant (NAE 1996) on his way from Evanston to ski or hike always led to animated technical discussions with Kaspar.

During 1998-99, while spending his sabbatical at the University of Stuttgart in the group led by Ekkehard Ramm (NAE 2008), Kaspar extended his work to failure modeling of elastoplastic materials at different levels of observation.¹⁰ His research on localization analysis had a profound impact on the understanding of fracture propagation and damage mechanics. He contributed to the development of mesh-independent numerical techniques, helping ensure the reliability of computational models in engineering applications.¹¹ His investigation into the thermomechanical degradation of concrete under high-temperature conditions played a critical role in advancing fire-resistant design methodologies and the development of robust nuclear containment structures.¹² His work on fracture propagation and multiscale material modeling led to significant advancements in seismic-resistant infrastructure, directly influencing contemporary earthquake engineering practices.

In collaboration with Steinmann, Dietsche, and Iordache in 1995,¹³ Kaspar extended the micropolar continuum to finite strain plasticity using von Mises and Drucker-Prager yield criteria, and further advanced localization analysis in 1991 based on the acoustic tensor by introducing a second localization condition.¹⁴ In 1998, he proposed a novel approach for characterizing nonsymmetric stress using a Mohr circle centered outside the horizontal axis.¹⁵ Kaspar also pioneered micromechanical material simulations for structural analysis in 1989, which led to a doctoral dissertation by T. Stankowski at the University of California, Berkeley in 1991.¹⁶ Though primarily a theorist, experimental studies were central to some of his work in the late 1980s — including direct tension and triaxial compression testing^17,18 and ultrasound measurement of progressive damage of concrete in 1996.¹⁹ His influence in earthquake, nuclear, and aerospace engineering enhanced the safety and durability of critical infrastructure worldwide. His collaborations across disciplines facilitated the integration of theoretical frameworks with practical engineering applications, bridging fundamental research with technological innovation. Kaspar’s contributions to continuum damage mechanics with Carol and Rizzi in 1994,²⁰ and extension of that work to anisotropic damage using his concept of pseudo-logarithmic tensor rate (2001-2002), were also noteworthy²¹ (see also fn. 7). So too was his 1996 analysis of associated localization properties²² and the extension to energy conservation during cycles of principal stress axis rotation.²³ These ideas were later combined with plasticity in work by Hansen and colleagues in 2001²⁴ and Salari and colleagues in 2004.²⁵

In 2010, he moved to the University of Houston as the Hugh Roy and Lillie Cranz Cullen Distinguished Professor, a position he held until his retirement in 2017. He also served as the interim department chair from 2013 to 2014. In Houston, together with Reza Mousavi and Giovanna Xotta in 2018,²⁶ he extended his work on the effect of the third stress invariant on plasticity to the modeling of structural steel.

Throughout his career, Kaspar played a pivotal role in fostering international research collaborations. He chaired the American Society of Civil Engineers (ASCE) and American Concrete Institute (ACI) Committee 447 on Finite Element Analysis of Reinforced Concrete Structures and served on the editorial boards of several leading scientific journals. His research was funded by agencies including the National Science Foundation, Air Force Office of Scientific Research, U.S. Army Engineer Research and Development Center, Federal Highway Administration, German Research Foundation, Canadian Aeronautics and Space Institute, and the European Commission. He was active in numerous professional organizations, including ASCE, ACI, the American Society of Mechanical Engineers, the U.S. Association for Computational Mechanics, and the European Community on Computational Methods in Applied Sciences (EURO-C). In 1999, he organized the U.S. National Congress on Computational Mechanics (USNCCM) in Boulder, and in 1984, he organized FraMCoS-5, the fifth international conference on Fracture Mechanics of Concrete Structures, in Vail, Colorado — though the conference ski competition had to be cancelled due to rain. He published more than 160 peer-reviewed journal articles and delivered more than 140 keynote and invited lectures. His leadership in the USNCCM, in the EURO-C conference series hosted by TU Vienna in premier alpine locations, and the FraMCoS conferences helped foster global research partnerships. Kaspar’s contributions were recognized with numerous prestigious awards, including the Nathan M. Newmark Medal (2003), the Alexander von Humboldt Research Award (1998), the Science Award of the Japan Society for the Promotion of Science (1992), and election to the National Academy of Engineering in 2004. In recognition of his legacy, the University of Houston established the Kaspar J. Willam Professorship in the Civil Engineering Department.

Beyond his scholarly achievements, Kaspar was a mentor and a visionary educator. Known for his intellectual generosity and unwavering dedication to his students, he inspired a generation of engineers and researchers. He was a kind and charismatic person, always friendly and smiling — never one word too sharp, even in scientific disagreements. He made everyone around him feel better while encouraging hard work and excellence. His passion for knowledge extended far beyond academia. A lifelong lover of the mountains and skiing, he often merged academic conferences with alpine adventures, which typically included technical discussions on ski lifts. Whether skiing or hiking in Colorado — where the snow resembled dry champagne and the skies were blue — he shared memorable adventures with friends who, without his company, might not have risked skiing the out-of-bounds bowls in Breckenridge, descending untouched powder snow in Whistler, or making it safely to the top of Longs Peak in the summer. At the EURO-C conferences, often held in Austrian mountain resorts, Kaspar regularly competed in the mid-conference ski race, frequently placing among the top three in his age category. He also drew laughter with camaraderie with his après-ski anecdotes shared in local beer pubs.

Many of Kaspar’s scientific colleagues came to celebrate his 60th birthday in December 2000 in his hometown of Bezau, where the locals still affectionately called him “Kashpi.” A few months later, in March 2001, Ekkerhard Ramm — together with colleagues from Evanston, TU Kaiserslautern, and UPC Catalonia — organized a workshop in his honor at the Soellerhaus in Hirschegg, Kleinwalsertal, Austria, also a favorite skiing destination. All papers presented at the event were published in a special issue of the International Journal of Engineering Science (IJES), edited by Bažant, Steinmann, and Carol. At the U.S. National Congress on Computational Mechanics (USNCCM-9) in San Francisco in 2007, Ekkehard Ramm and Karl Pister organized a dinner to honor Kaspar’s contributions.

His ability to cultivate an environment of collaboration and inquiry ensured that his legacy would live on through the work of his students and colleagues. He will be remembered for his kindness, mentorship, and passion for advancing knowledge. The FraMCoS XII conference, held in April 2025 at TU Wien under the chairmanship of Bernhard Pichler, is dedicated to his legacy, ensuring that his pioneering work remains at the forefront of engineering science.

Kaspar was laid to rest in Bezau. His legacy will continue to inspire future generations of researchers and practitioners in civil engineering.

References