Data-Driven Finite Elasticity
We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti et al. (Arch Ration Mech Anal 229:79–123, 2018). The main focus of this paper concerns the formulation of a suitable framework in which the Data-Driven problem of finite elasticity is well-posed in the sense of existence of solutions. We confine attention to deformation gradients F ∈ L^p(Ω;R^(n x n)) and first Piola-Kirchhoff stresses P ∈ L^q(Ω;R^(n x n)), with (p,q) ∈ (1, ∞) and 1/p + 1/q = 1. We assume that the material behavior is described by means of a material data set containing all the states (F, P) that can be attained by the material, and develop germane notions of coercivity and closedness of the material data set. Within this framework, we put forth conditions ensuring the existence of solutions. We exhibit specific examples of two- and three-dimensional material data sets that fit the present setting and are compatible with material frame indifference.
© 2020 Springer Nature. Received 15 January 2020. Accepted 27 January 2020. Published 13 March 2020. This work was partially Funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via Project 211504053 - SFB 1060 and Project 390685813 - GZ 2047/1 - HCM.
Accepted Version - 1912.02978.pdf