Inf-sup testing of some three-dimensional low-order finite elements for the analysis of solids

•We assess some 8-node hexahedral three-dimensional solid elements using inf-sup testing.•The test is for coercivity using displacement degrees of freedom only.•Insight into the element capacity to not lock in volumetric, shear, membrane, and pinching actions is obtained.•The novel 3D-MITC8 element is tested and found to perform well. We assess some 8-node hexahedral three-dimensional (3D) solid elements using inf-sup tests focusing on locking behavior in volumetric, shear, membrane, and pinching actions. Inf-sup tests have been widely used to see whether a finite element discretization is effective. In this paper we use a rather simple approach to inf-sup testing for the coercivity of the discretization to obtain insight into the convergence behavior of the standard displacement-based element, the 8-node element with incompatible modes, and the 3D-MITC8 element, and include geometric nonlinear analysis. We see that the 3D-MITC8 element performs better than the incompatible modes element in plate bending problems and can also be used with a small modification in the solution of thick or moderately thick curved shell structures.