Material similarity of scaled models

When different strain hardening, strain-rate sensitive and temperature softening materials are used for scaled model and prototype, the traditional similarity laws of solid mechanics will be broken. Although research works in the last twenty years have developed the correction methods of initial conditions to compensate for the similarity distortion, their basic correction factors are practically impeded for their inherent non-direct (depending on unknown structural responses) and inexact (having significant similarity errors) defects. In this paper, a more complete framework of material similarity is developed. Based on the similarity analysis of thermo-visco-plastic constitutive equation, the material dimensionless numbers are suggested to represent the objective similarity of strain hardening, strain-rate sensitive and temperature softening effects. The universal direct and exact solution of the basic correction factors is further proved when the material numbers of the scaled model and the prototype are equal, which overcomes the previous inherent defects radically. And the simple and practical phase diagram of ‘material numbers - strain/strain-rate/temperature’ curves are proposed to design the optimum similitude materials. Three impacted structure are numerically verified: circular plate, crooked plate, and Taylor bar. The results show that the proposed material numbers control the similarity behavior of different materials. When the proposed direct and exact methods are used by the designed optimum similitude materials, the completely different materials can behave acceptable exact similarity of strain, strain-rate, temperature, stress and displacement responses in time and space fields.