It is well known that the constitutive relation plays a key role in the nonlinear finite element analysis

and a time integration is particularly required to solve the problem whose stress response is deduced by its strain increment. The hypoplastic rate constitutive model is represented by Jaumann stress rate and deformation rate

and on the basis of this model

we develop adaptive implicit and explicit integration methods with local error control respectively. Meanwhile

the consistent tangent modulus is given for the implicit integration. Based on two different element tests

results of two types of numerical simulations of integration algorithm are compared by using ABAQUS. Moreover

a UMAT-VUMAT interface is developed to implement the transition from ABAQUS/Standard to ABAQUS/Explicit and then the flow chart of this development is presented. Therefore

the existing UMAT subroutine can be used for large deformation or high-degree dynamic problem analysis. Finally

the accuracy of numerical results is verified by a case study.