In the presence of the strong material nonlinearity caused by post-peak strain softening of dense sandy soils

the solution of traditional finite element method (FEM) with implicit algorithm often becomes intractable. The dynamic relaxation (DR) method has a great reputation in solving highly nonlinear equations. A new dynamic relaxation-finite element method (DR-FEM) for strong nonlinearity caused by post-peak strain softening of sands is proposed

which takes into account the advantages of DR and FEM together. According to the explicit nature of DR and the central difference technique

the general governing equations of DR-FEM has been derived. The way of tracing the whole equilibrium curve in the stress-strain space has also been presented; and then the DR method is implemented into a general nonlinear finite element codes. The return mapping algorithm is used for stress updating

which is a first-order approximated Euler backward integration. Therefore

the strong material nonlinearity caused by post-peak strain softening of sandy soils can be simulated by the proposed DR-FEM combined with the corresponding material model. The DR-FEM is validated by simulating the result of physical plane strain compression test performed on sands. It is shown that the DR method has a superiority to solve the material nonlinearity.