The variational structure of a dynamic system with general internal dissipative mechanisms is discretized in time by applying the Optimal Transportation theory, while material points and nodes are introduced for the spatial discretization. The HOTM method combines the Optimal Transportation Meshfree (OTM) method and the variational thermomechanical constitutive updates.
We present a monolithic incremental Lagrangian framework based on meshfree methods, the Hot Optimal Transportation Meshfree (HOTM) method, for a robust and efficient solution of the dynamic response of materials under extreme thermomechanical conditions, possibly involving extremely large deformation, phase transition and multiphase mixing.
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