ECCOMAS 2024

Regularized four-field variational formulation for thermo-elastodynamics and thermo-plasticity

  • Suljevic, Samir (University of Sarajevo (UNSA))
  • Ibrahimbegovic, Adnan (University of Technology Compiegne (UTC))
  • Dolarevic, Samir (University of Sarajevo (UNSA))

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This paper presents a novel mixed method to problem solving in coupled thermomechanics. The main objective is to achieve a superior accuracy for stress and heat-flux computed results and ensure stability in long-term computations, such as those required for failure analysis under fires for long-term thermal loading. To accomplish this, several innovation have been introduced at all stages of the finite element solution. The first innovation focuses on providing a robust variational formulation suitable for long term simulations in thermo-elastodynamics and thermo-plasticity, along with a regularization technique that guarantees stability. The first innovation focuses on providing a robust variational formulation suitable for long-term simulations in thermo-elastodynamics and thermo-plasticity, along with a regularization technique that guarantees stability. The regularization technique allows us to eliminate the independent rotation field, resulting in a four-field variational formulation that includes independent fields for displacement, temperature, stress, and heat-flux. The second innovation is the corresponding discrete approximation, which ensures the continuity of stress vectors and flux components across element boundaries. This leads to enhanced finite elements, where the displacement and temperature fields are approximated using standard linear shape functions, while the stress vectors and flux components are approximated using the lowest-order Raviart–Thomas vector space interpolations. This approach ensures continuity and enables smooth propagation of waves and heat flow. The final innovative development for enhanced finite elements in dynamic analysis involves the corresponding time integration scheme for long term computations. The mid-point time integration scheme and algorithmic constitutive equations allow us to control energy decay from thermal, plastic, and algorithmic dissipation, providing the scheme with higher stability and robustness in long-term computations.