Thomas Heuzé (IRDL, ENI Brest)

Many engineering applications require to carry out numerical simulations of impacts on dissipa- tive solids, such as dynamic forming processes, crash or ballistic impacts. In these applications, thermal effects are generally solved in addition to mechanical ones, and allow to account for equations of state, as well as thermomechanical coupling on the shear part via e.g. temperature increase due to plastic strains, thermal softening, and so on. Hyperbolic models dedicated to high levels of pressure usually embed the conservation of total energy, and it is interesting to extend such approach also for applications involving moderate levels of pressure, for which shear strength is still important. It thus requires efficient constitutive updates compatible with that equation, together with accounting for temperature-dependent constitutive response.

This talk aims at presenting the interest of variational approaches dedicated to the description of dissipative and thermally-coupled constitutive response of solids, especially in the context of fast solid dynamics, which are compatible with the solution of the conservation of total energy. First, the variational constitutive update recently introduced [1] is recalled, which admits the internal energy density as input data, and is then particularized to hyperelastic-plastic flow using the concept of pseudo-stresses [2]. Second, in case of repeated impacts like Laser Shock Peening, local cyclic loadings can yield Bauschinger and/or ratchetting effects, such that non-linear kinematic hardening becomes important. The previous variational framework is thus extended to include a kinematic tensorial internal variable while ensuring material frame indifference of the modeling. Two consistent Eulerian and Lagrangian hyperbolic modelings of thermo-hyperelastic-plastic solids are built and coupled with a non-linear kinematic hardening in finite strains [3]. At last, we examine the interest of using such variational approach to build efficient solver of the source term in hyperbolic modeling of gradient damage, recently introduced in [4].

REFERENCES

[1] Heuzé, T. and Stainier, L. A variational formulation of thermomechanical constitutive up- date for hyperbolic conservation laws. Computer Methods in Applied Mechanics and Engi- neering. 394, 114893, (2022).

[2] Mosler, J. and Bruhns, O. On the implementation of rate-independent standard dissipa- tive solids at finite strain–Variational constitutive updates, Computer Methods in Applied Mechanics and Engineering. 199 (9-12), 417–429, (2010).

[3] Heuzé, T. and Favrie, N. Consistent Eulerian and Lagrangian variational formulations of non-linear kinematic hardening for solid media undergoing large strains and shocks. Com- puter Methods in Applied Mechanics and Engineering, 433, 117480, (2025).

[4] Favrie, N. and Renaud, A. and Kondo, D. Hyperbolic modeling of gradient damage and one-dimensional finite volume simulationsComputer Methods in Applied Mechanics and En- gineering. 419, 116643, (2024).