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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.

SUMMARYIn this paper a new eight-node (brick) solid-shell finite element formulation based on the concept of reduced integration with hourglass stabilization is presented. The work focuses on static problems. The starting point of the derivation is the three-field variational functional upon which meanwhile established 3D enhanced strain concepts are based. Important additional assumptions are made to transfer the approach into a powerful solid-shell. First of all, a Taylor expansion of the first Piola-Kirchhoff stress tensor with respect to the normal through the centre of the element is carried out. In this way the stress becomes a linear function of the shell surface co-ordinates whereas the dependence on the thickness co-ordinate remains non-linear. Secondly, the Jacobian matrix is replaced by its value in the centre of the element. These two assumptions lead to a computationally efficient shell element which requires only two Gauss points in the thickness direction (and one Gauss point in the plane of the shell element). Additionally three internal element degrees-of-freedom have to be determined to avoid thickness locking. One important advantage of the element is the fact that a fully three-dimensional stress state can be modelled without any modification of the constitutive law. The formulation has only displacement degrees-of-freedom and the geometry in the thickness direction is correctly displayed.

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SUMMARYThe paper discusses the derivation and the numerical implementation of a finite strain material model for non-linear kinematic and isotropic hardening. The kinematic hardening component represents a continuum extension of the classical rheological model of Armstrong-Frederick kinematic hardening. In addition, a comparison between several numerical algorithms for the integration of the evolution equations is conducted. In particular, a new form of the exponential map that preserves the plastic volume and the symmetry of the internal variables, as well as two modifications of the backward Euler scheme are discussed. Finally, the applicability of the model for springback prediction is demonstrated by performing simulations of the draw-bending process and a comparison with experiments. The results show an excellent agreement between simulation and experiment.

SUMMARYIn this paper we address the extension of a recently proposed reduced integration eight-node solid-shell finite element to large deformations. The element requires only one integration point within the shell plane and at least two integration points over the thickness. The possibility to choose arbitrarily many Gauss points over the shell thickness enables a realistic and efficient modeling of the non-linear material behavior. Only one enhanced degree-of-freedom is needed to avoid volumetric and Poisson thickness locking. One key point of the formulation is the Taylor expansion of the inverse Jacobian matrix with respect to the element center leading to a very accurate modeling of arbitrary element shapes. The transverse shear and curvature thickness locking are cured by means of the assumed natural strain concept. Further crucial points are the Taylor expansion of the compatible cartesian strain with respect to the center of the element as well as the Taylor expansion of the second Piola-Kirchhoff stress tensor with respect to the normal through the center of the element.