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SUMMARYIn this paper a new reduced integration eight-node solid-shell finite element is presented. The enhanced assumed strain (EAS) concept based on the Hu-Washizu variational principle requires only one EAS degree-of-freedom to cure volumetric and Poisson thickness locking. One key point of the derivation is the Taylor expansion of the inverse Jacobian with respect to the element center, which closely approximates the element shape and allows us to implement the assumed natural strain (ANS) concept to eliminate the curvature thickness and the transverse shear locking. The second crucial point is a combined Taylor expansion of the compatible strain with respect to the center of the element and the normal through the element center leading to an efficient and locking-free hourglass stabilization without rank deficiency. Hence, the element requires only a single integration point in the shell plane and at least two integration points in thickness direction. The formulation fulfills both the membrane and the bending patch test exactly, which has, to the authors' knowledge, not yet been achieved for reduced integration eight-node solid-shell elements in the literature. Owing to the three-dimensional modeling of the structure, fully three-dimensional material models can be implemented without additional assumptions.

We extend the Data-Driven formulation of problems in elasticity of Kirchdoerfer and Ortiz [1] to inelasticity. This extension differs fundamentally from Data-Driven problems in elasticity in that the material data set evolves in time as a consequence of the history dependence of the material. We investigate three representational paradigms for the evolving material data sets: i) materials with memory, i. e., conditioning the material data set to the past history of deformation; ii) differential materials, i. e., conditioning the material data set to short histories of stress and strain; and iii) history variables, i. e., conditioning the material data set to ad hoc variables encoding partial information about the history of stress and strain. We also consider combinations of the three paradigms thereof and investigate their ability to represent the evolving data sets of different classes of inelastic materials, including viscoelasticity, viscoplasticity and plasticity. We present selected numerical examples that demonstrate the range and scope of Data-Driven inelasticity and the numerical performance of implementations thereof.