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A hyperconstrained packing is statically underdetermined, since there are multiple ways to resolve almost any applied load. In this case constitutive (elastic) laws need to be invoked to determine the forces. A hypoconstrained packing, on the other hand, is statically overdetermined, and as such is considered unstable in the classical literature on mechanical structures.
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A hyperconstrained packing is statically underdetermined, since there are multiple ways to resolve almost any applied load. In this case constitutive (elastic) laws need to be invoked to determine the forces. A hypoconstrained packing, on the other hand, is statically overdetermined, and as such is considered unstable in the classical literature on mechanical structures.
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Specifically, a packing of stiff particles will have only as many contacts closed as there are degrees of freedom, M≤ Nf. The additional single degree of freedom due to the density does not count unless the packing is compressed to close the additional one contact that is discussed in Sec. 4 2. Closing more than M= Nf +1 contacts will require further compression and significantly larger deformation of the particles.
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Specifically, a packing of stiff particles will have only as many contacts closed as there are degrees of freedom, M≤ Nf. The additional single degree of freedom due to the density does not count unless the packing is compressed to close the additional one contact that is discussed in Sec. 4 2. Closing more than M= Nf +1 contacts will require further compression and significantly larger deformation of the particles.
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Note that in our notation a self-stress has dimensions of force, rather than force per unit area as in the engineering literature.
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There is some ambiguity in defining the pair-correlation function for bi-dispersed packings, leading to ambiguity in the exponent.
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There is some ambiguity in defining the pair-correlation function for bi-dispersed packings, leading to ambiguity in the exponent.
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