Next week: SPECIAL SEMINAR: Arnav Gupta, 24-Mar-26, 12:20pm Central
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Ellad Tadmor
Mar 17, 2026, 9:21:10 AM (15 hours ago) Mar 17
to aem-solid...@umn.edu
AEM Mechanics Research Seminar
Tuesday 24-Mar-2026, 12:20pm Central
Mr. Arnav Gupta
Theoretical and Applied Mechanics, Cornell University
Title: Brittle fracture using the inverse-deformation approach
Abstract: Many industrial and biological materials function under large deformations. A central obstacle in modeling their fracture is the presence of cracks as discontinuities in the deformation map. We overcome this issue by solving for the inverse-deformation that maps points on the deformed body to the reference domain. This map is continuous and is amenable to analysis and reliable computations even in the presence of cracks. We propose a non-convex energy density that asymptotes to a constant as the local volumetric change approaches infinity. In the inverse-deformation formulation, this energy appears as a two-well potential. A higher-gradient term is incorporated that introduces a surface energy in the model. The method predicts spontaneous nucleation and propagation of cracks without using damage/phase variables or pre-existing flaws. We derive an irreversibility condition for quasistatic motions of a one-dimensional bar using the second law of thermodynamics. We prove conditions for local stability that incorporate these restrictions. Their numerical implementation shows that all broken equilibria of the elastic bar are locally stable. For two-dimensional solids, we present numerical results obtained using FEM-based bifurcation/continuation methods. Fracture occurs at a critical load due to an elastic instability. On further stretching, the cracks open and propagate at their tips. The crack faces are sharp that precisely delineate the solid material from empty space.
For more information, visit the AEM Mechanics Research Seminar website:
Tuesday 24-Mar-2026, 12:20pm Central
In-person: Room 321, Mechanical Engineering, University of Minnesota
Online: Webinar registration link
Theoretical and Applied Mechanics, Cornell University
Title: Brittle fracture using the inverse-deformation approach
Abstract: Many industrial and biological materials function under large deformations. A central obstacle in modeling their fracture is the presence of cracks as discontinuities in the deformation map. We overcome this issue by solving for the inverse-deformation that maps points on the deformed body to the reference domain. This map is continuous and is amenable to analysis and reliable computations even in the presence of cracks. We propose a non-convex energy density that asymptotes to a constant as the local volumetric change approaches infinity. In the inverse-deformation formulation, this energy appears as a two-well potential. A higher-gradient term is incorporated that introduces a surface energy in the model. The method predicts spontaneous nucleation and propagation of cracks without using damage/phase variables or pre-existing flaws. We derive an irreversibility condition for quasistatic motions of a one-dimensional bar using the second law of thermodynamics. We prove conditions for local stability that incorporate these restrictions. Their numerical implementation shows that all broken equilibria of the elastic bar are locally stable. For two-dimensional solids, we present numerical results obtained using FEM-based bifurcation/continuation methods. Fracture occurs at a critical load due to an elastic instability. On further stretching, the cracks open and propagate at their tips. The crack faces are sharp that precisely delineate the solid material from empty space.
For more information, visit the AEM Mechanics Research Seminar website:
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Ellad B. Tadmor, Ph.D.
Russell J. Penrose Professor
Department of Aerospace Engineering and Mechanics
University of Minnesota
https://dept.aem.umn.edu/~tadmor/
Russell J. Penrose Professor
Department of Aerospace Engineering and Mechanics
University of Minnesota
https://dept.aem.umn.edu/~tadmor/
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