TY - JOUR

T1 - Constitutive equations for an elastic material with anisotropic rigid particles

AU - Sagis, L.M.C.

AU - Ramaekers, M.

AU - van der Linden, E.

PY - 2001

Y1 - 2001

N2 - In this paper we have derived constitutive equations for an elastic material with anisotropic rigid particles. We have included a dependence on the Finger tensor B and the orientation tensor Q in the expression for the free energy of the system. With this expression for the free energy we have derived an expression for the stress tensor up to second order in both these variables. We have shown that the elastic modulus in this expression depends on Q, and this dependence leads to an effective elastic modulus that depends on the strain. We have calculated the explicit form of the equation for the stress tensor for a deformation in the xy plane with a strain equal to –. For fully isotropic materials with Q = 0 this expression reduces to an equation containing only odd powers of . The inclusion of a non-zero value for the orientation tensor leads to an additional set of terms in the equation, all proportional to Qxy (the xy component of the tensor Q), and all proportional to even powers of . We have qualitatively compared these expressions with Fourier transform (FT) rheological measurements of xanthan gels, at concentrations above and below the order-disorder transition. In FT rheometry an oscillatory deformation is applied in the nonlinear regime, and the resulting stress response is analyzed in Fourier space. In the 2øw/w) xanthan system (disordered state) only odd harmonics were found in the stress response, whereas in the 4øw/w) xanthan gel (ordered state) even harmonics could be detected. As predicted by our theory, the intensity of these even harmonics first increased with increasing , until a maximum value was reached. Beyond this maximum the intensity decreased continuously with increasing

AB - In this paper we have derived constitutive equations for an elastic material with anisotropic rigid particles. We have included a dependence on the Finger tensor B and the orientation tensor Q in the expression for the free energy of the system. With this expression for the free energy we have derived an expression for the stress tensor up to second order in both these variables. We have shown that the elastic modulus in this expression depends on Q, and this dependence leads to an effective elastic modulus that depends on the strain. We have calculated the explicit form of the equation for the stress tensor for a deformation in the xy plane with a strain equal to –. For fully isotropic materials with Q = 0 this expression reduces to an equation containing only odd powers of . The inclusion of a non-zero value for the orientation tensor leads to an additional set of terms in the equation, all proportional to Qxy (the xy component of the tensor Q), and all proportional to even powers of . We have qualitatively compared these expressions with Fourier transform (FT) rheological measurements of xanthan gels, at concentrations above and below the order-disorder transition. In FT rheometry an oscillatory deformation is applied in the nonlinear regime, and the resulting stress response is analyzed in Fourier space. In the 2øw/w) xanthan system (disordered state) only odd harmonics were found in the stress response, whereas in the 4øw/w) xanthan gel (ordered state) even harmonics could be detected. As predicted by our theory, the intensity of these even harmonics first increased with increasing , until a maximum value was reached. Beyond this maximum the intensity decreased continuously with increasing

U2 - 10.1103/PhysRevE.63.051504

DO - 10.1103/PhysRevE.63.051504

M3 - Article

VL - 63

SP - 051504.1-051504.8

JO - Physical Review. E, Statistical nonlinear, and soft matter physics

JF - Physical Review. E, Statistical nonlinear, and soft matter physics

SN - 1539-3755

IS - 5

ER -