Hentschel H G E, Karmakar Smarajit, Lerner Edan, Procaccia Itamar
Department of Chemical Physics, The Weizmann Institute of Science, Rehovot, Israel.
Phys Rev E Stat Nonlin Soft Matter Phys. 2011 Jun;83(6 Pt 1):061101. doi: 10.1103/PhysRevE.83.061101. Epub 2011 Jun 2.
We study the elastic theory of amorphous solids made of particles with finite range interactions in the thermodynamic limit. For the elastic theory to exist, one requires all the elastic coefficients, linear and nonlinear, to attain a finite thermodynamic limit. We show that for such systems the existence of nonaffine mechanical responses results in anomalous fluctuations of all the nonlinear coefficients of the elastic theory. While the shear modulus exists, the first nonlinear coefficient B(2) has anomalous fluctuations and the second nonlinear coefficient B(3) and all the higher order coefficients (which are nonzero by symmetry) diverge in the thermodynamic limit. These results call into question the existence of elasticity (or solidity) of amorphous solids at finite strains, even at zero temperature. We discuss the physical meaning of these results and propose that in these systems elasticity can never be decoupled from plasticity: the nonlinear response must be very substantially plastic.
我们研究了在热力学极限下由具有有限范围相互作用的粒子构成的非晶态固体的弹性理论。为使弹性理论存在，要求所有弹性系数，包括线性和非线性的，都能达到有限的热力学极限。我们表明，对于这类系统，非仿射力学响应的存在会导致弹性理论中所有非线性系数出现反常涨落。虽然剪切模量存在，但第一非线性系数B(2)具有反常涨落，第二非线性系数B(3)以及所有更高阶系数（由于对称性不为零）在热力学极限下发散。这些结果对有限应变下非晶态固体弹性（或固态性）的存在提出了质疑，即使在零温度下也是如此。我们讨论了这些结果的物理意义，并提出在这些系统中弹性永远无法与塑性解耦：非线性响应必定在很大程度上是塑性的。
