We present recent results on the modeling and nu-merical simulation of reservoir stimulation in Hot Dry Rocks. Our approach is based on a mechanisti-cally faithful yet mathematically sound model, gener-alizing Griffiths idea of competition between bulk and surface energies. At each time increment, the fracture and displacement configuration of a reservoir is sought as the minimizer of a global energy. In do-ing so, the variational approach allows full crack path identification, interaction between multiple cracks, crack initiation and branching in two and three space dimensions. The numerical approach is based on building a regularized energy where cracks are repre-sented by a smooth function, similar in spirit to a phase-field approach. In this paper, we focus on thermal stimulation.

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