Thermo-elastic extended meshfree method for fracture without crack tip enrichment

This is the first manuscript presenting an extended meshfree method for thermo- elastic fracture which does not exploit a crack tip enrichment. The crack is modeled by partition of unity enrichment of the displacement and temperature field. Only a step function is employed that facilitates the implementation. To ensure that crack tip is at the correct position, a Lagrange multiplier field ahead of the crack tip is introduced along a line. The Lagrange multiplier nodal parameters are discretised with the available meshfree functions. Two benchmark examples illustrate the efficiency of the method.