1. Reference problem#

1.1. Geometry#

The cyclic shear test is carried out on a single Gauss point. The test is therefore checked in its entirety in terms of constraints and deformations imposed.

1.2. Material properties#

1.2.1. Hujeux and Iwan models of behavior#

The isotropic elastic properties of the material are \(E=619.33\) MPa and \(\nu =0.3\).

The anelastic parameters specific to the Hujeux model (modeling A) are:

  • \(n=0.4\), \(\mathrm{\beta }=24\), \(b=0.2\), \(d=2.5\).

  • \(\mathrm{\varphi }=33°\), \(\mathrm{\psi }=33°\), \({P}_{c0}=-1\) MPa, \({P}_{\mathit{ref}}=-1\) MPa

  • \({a}_{\mathit{cyc}}=1\times10^{-4}\), \({a}_{\mathit{mon}}=8\times10^{-3}\)

  • \({c}_{\mathit{cyc}}=9\times10^{-2}\), \({c}_{\mathit{mon}}=1.8\times10^{-1}\)

  • \({r}_{\mathit{ela}}^{d}=5\times10^{-3}\), \({r}_{\mathit{ela}}^{i}=1\times10^{-3}\), \({r}_{\mathit{ela}}^{d,c}=5\times10^{-3}\), \({r}_{\mathit{ela}}^{i,c}=1\times10^{-3}\)

  • \({r}_{\mathit{hys}}=5\times10^{-2}\), \({r}_{\mathit{mob}}=9\times10^{-1}\)

  • \({x}_{m}=1\), \(\alpha=1\)

The anelastic parameters of the Iwan model (modeling B) are for their part \(\gamma_{\mathrm{ref}}=2\times10^{-4}\) and \(n=0.78\).

1.2.2. Behaviour model CSSM#

The parameters specific to the model CSSM [r7.01.44] are grouped together in the Section 1.3 concerning the C modeling.

1.3. Boundary conditions and loads#

The use of the SIMU_POINT_MAT command makes it possible to directly impose a field of deformations and/or constraints.

A zero evolution during loading is imposed for the following components of the stress and strain tensors:

  • \({\mathrm{d}\sigma}_{xx}={\mathrm{d}\sigma}_{yy}={\mathrm{d}\sigma}_{zz}=0\)

  • \({\mathrm{d}\varepsilon}_{yz}={\mathrm{d}\varepsilon}_{zx}=0\)

We impose the evolution of Fig. 1.1 for the shear stress \(\sigma_{xy}\):

_images/1000000000000254000001A800AC136C4523B6E1.png

Fig. 1.1 Imposed load schedule for constraint component \(\sigma_{xy}\). The evolution with micro-discharges is defined by the function F 1, the one without microdischarge by the function F 2.#

The validation is carried out by comparison with the solution obtained for the loading path without the micro-discharges.

1.4. Initial conditions#

The initial stress state is isotropic and corresponds to a pressure equal to \(50\) kPa.