Inelastic equation of state for solids

A complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration ene...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2021-03, Vol.375, p.113622, Article 113622
Main Author: Sanchez, J.J.
Format: Article
Language:English
Subjects:
Elasticity
Equation of state
Equations of state
Inelastic
Lattice vibration
Materials failure
Nonlinear equations
Solid mechanics
Temperature dependence
Thermo-mechanical
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Summary:A complete inelastic equation of state (IEOS) for solids is developed based on a superposition of thermodynamic energy potentials. The IEOS allows for a tensorial stress state by including an isochoric hyperelastic Helmholtz potential in addition to the zero-kelvin isotherm and lattice vibration energy contributions. Inelasticity is introduced through the nonlinear equations of finite strain plasticity which utilize the temperature dependent Johnson–Cook yield model. Material failure is incorporated into the model by a coupling of the damage history variable to the energy potentials. The numerical evaluation of the IEOS requires a nonlinear solution of stress, temperature and history variables associated with elastic trial states for stress and temperature. The model is implemented into the ALEGRA shock and multi-physics code and the applications presented include single element deformation paths, the Taylor anvil problem and an energetically driven thermo-mechanical problem. •A thermodynamically consistent inelastic equation of state (IEOS) is developed.•Numerical IEOS evaluation requires a novel nonlinear solution for stress and temperature.•Thermomechanical ALEGRA simulations demonstrate IEOS agreement with a traditional method.•IEOS predicts more physically realistic material failure than the traditional method.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2020.113622