  Dense non-Brownian suspensions including both the hydrodynamic interactions
and the frictional contacts between particles are numerically studied under
simple and oscillatory shears in terms of the lattice Boltzmann method. We
successfully reproduce the discontinuous shear thickening (DST) under a simple
shear for bulk three-dimensional systems. For our simulation of an oscillatory
shear in a quasi-two-dimensional system, we measure the mechanical response
when we reduce the strain amplitude after the initial oscillations with a
larger strain amplitude. Here, we find the existence of the shear-jammed state
under this protocol in which the storage modulus $G^{\prime}$ is only finite
for high initial strain amplitude $\gamma_0^{I}$. We also find the existence of
the fragile state in which both fluid-like and solid-like responses can be
detected for an identical area fraction and an initial strain amplitude
$\gamma_0^{I}$ depending on the initial phase $\Theta$ (or the asymmetricity of
the applied strain) of the oscillatory shear. We also observe the DST-like
behavior under the oscillatory shear in the fragile state. Moreover, we find
that the stress anisotropy becomes large in the fragile state. Finally, we
confirm that the stress formula based on the angular distribution of the
contact force recovers the contact contributions to the stress tensors for both
simple and oscillatory shears with large strains.
