Award Abstract # 2206114
Variational Fracture with Loads

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: WORCESTER POLYTECHNIC INSTITUTE
Initial Amendment Date: June 23, 2022
Latest Amendment Date: June 23, 2022
Award Number: 2206114
Award Instrument: Standard Grant
Program Manager: Pedro Embid
pembid@nsf.gov
 (703)292-4859
DMS
 Division Of Mathematical Sciences
MPS
 Direct For Mathematical & Physical Scien
Start Date: July 1, 2022
End Date: June 30, 2025 (Estimated)
Total Intended Award Amount: $271,932.00
Total Awarded Amount to Date: $271,932.00
Funds Obligated to Date: FY 2022 = $271,932.00
History of Investigator:
  • Christopher Larsen (Principal Investigator)
    cjlarsen@wpi.edu
Recipient Sponsored Research Office: Worcester Polytechnic Institute
100 INSTITUTE RD
WORCESTER
MA  US  01609-2247
(508)831-5000
Sponsor Congressional District: 02
Primary Place of Performance: Worcester Polytechnic Institute
100 Institute Rd
Worcester
MA  US  01609-2280
Primary Place of Performance
Congressional District:
02
Unique Entity Identifier (UEI): HJNQME41NBU4
Parent UEI:
NSF Program(s): APPLIED MATHEMATICS
Primary Program Source: 01002223DB NSF RESEARCH & RELATED ACTIVIT
Program Reference Code(s): 5918, 5920, 5936, 5946
Program Element Code(s): 1266
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

For a large range of applications, from civil infrastructure to national defense, understanding the failure of materials is critical. The ability to predict failure depends on modeling and on the mathematics available to formulate and analyze models, and to justify numerical methods. Over the last twenty years, there have been significant mathematical advances in this area, particularly in fracture mechanics, but these results are largely limited to models without applied forces. However, the inclusion of applied forces is relevant for applications. This project aims to improve the current mathematical formulation for fracture in materials in equilibrium with applied forces, to extend this formulation to models for material evolution, and to study certain features of these evolutions related to the presence of applied forces. The project offers training research opportunities for doctoral students.

The ability to accurately predict failure depends on the quality of the underlying mathematical modeling of defects, as well as on understanding fundamental properties of solutions. Until recently, variational models for static and quasi-static fracture have been limited to Dirichlet boundary conditions, since there do not exist solutions to the seemingly most natural formulation that includes Neumann boundary conditions, i.e., boundary loads. The aim of the project is to improve on a recently introduced static formulation for variational fracture with boundary loads which can have solutions, to extend this static model to the quasi-static case and show existence of solutions, and to study the possibility of existence of energy drops in quasi-static models.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

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