Reduction of the number of material parameters by ANN approximation

Modern industrial standards require advanced constitutive modeling to obtain satisfactory numerical results. This approach however, is causing significant increase in number of material parameters which can not be easily obtained from standard and commonly known experimental techniques. Therefore, it is desirable to introduce procedure decreasing the number of the material parameters. This reduction however, should not lead to misunderstanding the fundamental physical phenomena. This paper proposes the reduction of the number of material parameters by using ANN approximation. Recently proposed viscoplasticity formulation for anisotropic solids (metals) developed by authors is used as an illustrative example. In this model one needs to identify 28 material parameters to handle particular metal behaviour under adiabatic conditions as reported by Glema et al (J Theor Appl Mech 48:973–1001, 2010), (Int J Damage Mech 18:205–231, 2009) and Sumelka (Poznan University of Technology, Poznan, 2009). As a result of proposed approach, authors decreased the number of material parameters to 19.