FE Realization of a Thermo-Visco-Plastic Constitutive Model using VUMAT in ABAQUS/Explicit Program

ABAQUS software has provided many kinds of element types and material models in its program for users. But with the rapid development of industrial technology the material models in existed material library cannot well describe some special problems such as ultra-high-speed cutting. Fortunately, ABAQUS provides the redevelopment function for users by allowing them introduce user materials subroutine (UMAT) into the main program to solve their practical problems accurately. In this paper, the method of how to realize a user-defined material model in ABAQUS/Explicit by the explicit user materials subroutine (VUMAT) is presented in details. Compared with UMAT in ABAQUS/Standard, VUMAT adopts explicit difference integration (like Euler methods) as its stress updating algorithm, so it doesn’t need iterations and Jacobian but requires a stable limit ( Δt max ) determined by minimum characteristic element length and elastic wave speed of the material. Although the examples of user subroutine for isotropic and kinematic hardening models have been given in ABAQUS manual, the realization of the more complex constitutive models that consider rate effect and thermal softening effect is still uninvestigated and remains difficult to users. For this thermal-coupled rate-typed constitutive model, the general expression of one-dimensional form can be written as $$ \sigma = (A + B\bar \varepsilon _p^n )f(\mathop {\bar \varepsilon }\limits^. _p ,T) $$ . Here $$ \bar \varepsilon _p $$ is equivalent plastic strain; $$ f(\mathop {\bar \varepsilon }\limits^. _p ,T) $$ means rate effect and thermal softening effect. The integration procedures can be formulated based on the basic governing equations. The elastic part obeys generalized Hooke’s law in which stress is expressed in Jaumann rate form in a co-rotational framework. The plastic part is similar to that of isotropic hardening model except that two new state variables, strain rate and temperature, must be introduced here. Mises yield criterion and plastic flow law are still usable. The strain increment is obtained approximately by $$ \Delta \bar \varepsilon _p = (\bar \sigma _{trial} - \sigma _y )/(3\mu + h) $$ (plastic hardening $$ h = d\sigma _y /d\bar \varepsilon _p $$ ). The FORTRAN code of VUMAT can then be written after the integration procedures using vector-formed state variables. Finally, initial testing on a single element model with prescribed impact loading must be carried to validate the coding of user subroutine. Johnson-Cook model, already in ABAQUS material library, is selected first to be realized using VUMAT so that its numerical test results can be verified with those of ABAQUS itself.