The procedure for reuse of finite element method (FEM) programs for heat transfer and structure analysis to solve advanced thermo-mechanical problems is presented as powerful algorithm applicable for coupling of other physical fields (magnetic, fluid flow, etc.). In this case, nonlinear Block-Gauss-Seidel partitioned algorithm strongly couples the heat transfer and structural FEM programs by a component-based software engineering. Component template library provides possibility to exchange the data between the components which solve the corresponding subproblems. The structural component evaluates the dissipative energy induced by inelastic strain. The heat transfer component computes the temperature change due to the dissipation. The convergence is guaranteed by posing the global convergence criterion on the previously locally converged coupled variables. This enables reuse of software and allows the numerical simulation of thermo-sensitive problems.Communicated by Andreas Öchsner.V. Dunić (B) · N. Busarac · V. Slavković · R. Slavković · M. Živković

The phenomenological SMA material model proposed by Lagoudas [1] is modified and implemented in finite element software PAK [2]. Critical thermodynamic force is derived to match implicit integration method. All variables are derived to depend on effective values of stress, strain and martensitic volume fraction. One scalar equation need to be solved in the integration point using trial stress direction for each time step. The integration in the trial deviatoric stress direction provides possibility to solve large strain problems using the algorithms developed for small strains. Two one-dimensional and one non-proportional large strain example verified accuracy of proposed modifications.

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Abstract. Shape memory alloys (SMA) material is widely used in many applications of interest where it is necessary to recover permanent strains. There are many constitutive models which describe that phenomenon. The SMA model described by Lagoudas in [1] and [2] is modified and implemented into the PAK software package [3]. Development of this model is motivated by previous papers of Lagoudas and Auricchio groups and it considers governing parameter method applied on phenomenological behavior of SMA materials. All variables are derived to depend on effective values of stress and strain and now we have only one scalar equation to solve in the integration point. Critical thermodynamic force is also modified to match new integration method. Integration is done for the deviatoric and mean stress using trial stress direction for each time step. Difference between the return mapping algorithm and the integration in the trial deviatoric stress direction can be neglected for nearly proportional loading [2]. The second case provide possibility to solve large strain problems in the similar manner, using the same constitutive model relations. One dimensional loaded examples of super-elasticity, shape memory and thermally induced phase transformation effect proposed by Lagoudas group are verified by modified governing parameter method using the PAK software. Several large strain examples are examined under uniaxial and non-proportional loading and the results are compared with the experimental results proposed in referenced papers.