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- Publisher Website: 10.1103/PhysRevB.37.5500
- Scopus: eid_2-s2.0-0001553890
- WOS: WOS:A1988M824000014
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Article: Elastic fracture in random materials
Title | Elastic fracture in random materials |
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Authors | |
Issue Date | 1988 |
Citation | Physical Review B, 1988, v. 37, n. 10, p. 5500-5507 How to Cite? |
Abstract | We analyze a simple model of elastic failure in randomly inhomogeneous materials such as minerals and ceramics. We study a two-dimensional triangular lattice with nearest-neighbor harmonic springs. The springs are present with probability p. The springs can only withstand a small strain before they fail completely and irreversibly. The applied breakdown stress in a large, but finite, sample tends to zero as the fraction of springs in the material approaches the rigidity percolation threshold. The average initial breakdown stress, σb, behaves as σbμ[A(p)+B(p)ln(L)]-1, where L is the linear dimension of the system and the exponent μ is between 1 and 2. The coefficient B(p) diverges as p approaches the rigidity percolation threshold. The breakdown-stress distribution function FL(σ) has the form FL(σ)1-exp[-cL2exp(-k/σμ)]. The parameters c and k are constants characteristic of the microscopic properties of the system. The parameter k tends to zero at the rigidity percolation threshold. These predictions are verified by computer simulations of random lattices. The breakdown process can continue until a macroscopic elastic failure occurs in the system. The failure occurs in two steps. First, a number of springs fail at approximately the strain which causes the initial failure. This results in a system which has zero elastic modulus. Finally, at a considerably larger strain a macroscopic crack forms across the entire sample. © 1988 The American Physical Society. |
Persistent Identifier | http://hdl.handle.net/10722/303812 |
ISSN | |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Beale, Paul D. | - |
dc.contributor.author | Srolovitz, David J. | - |
dc.date.accessioned | 2021-09-15T08:26:04Z | - |
dc.date.available | 2021-09-15T08:26:04Z | - |
dc.date.issued | 1988 | - |
dc.identifier.citation | Physical Review B, 1988, v. 37, n. 10, p. 5500-5507 | - |
dc.identifier.issn | 0163-1829 | - |
dc.identifier.uri | http://hdl.handle.net/10722/303812 | - |
dc.description.abstract | We analyze a simple model of elastic failure in randomly inhomogeneous materials such as minerals and ceramics. We study a two-dimensional triangular lattice with nearest-neighbor harmonic springs. The springs are present with probability p. The springs can only withstand a small strain before they fail completely and irreversibly. The applied breakdown stress in a large, but finite, sample tends to zero as the fraction of springs in the material approaches the rigidity percolation threshold. The average initial breakdown stress, σb, behaves as σbμ[A(p)+B(p)ln(L)]-1, where L is the linear dimension of the system and the exponent μ is between 1 and 2. The coefficient B(p) diverges as p approaches the rigidity percolation threshold. The breakdown-stress distribution function FL(σ) has the form FL(σ)1-exp[-cL2exp(-k/σμ)]. The parameters c and k are constants characteristic of the microscopic properties of the system. The parameter k tends to zero at the rigidity percolation threshold. These predictions are verified by computer simulations of random lattices. The breakdown process can continue until a macroscopic elastic failure occurs in the system. The failure occurs in two steps. First, a number of springs fail at approximately the strain which causes the initial failure. This results in a system which has zero elastic modulus. Finally, at a considerably larger strain a macroscopic crack forms across the entire sample. © 1988 The American Physical Society. | - |
dc.language | eng | - |
dc.relation.ispartof | Physical Review B | - |
dc.title | Elastic fracture in random materials | - |
dc.type | Article | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1103/PhysRevB.37.5500 | - |
dc.identifier.scopus | eid_2-s2.0-0001553890 | - |
dc.identifier.volume | 37 | - |
dc.identifier.issue | 10 | - |
dc.identifier.spage | 5500 | - |
dc.identifier.epage | 5507 | - |
dc.identifier.isi | WOS:A1988M824000014 | - |