A new volumetric and shear locking‐free 3D enhanced strain element

Abstract

This paper focuses on the development of a new class of eight-node solid ®nite elements, suitable for the treatment of volumetric and transverse shear locking problems. Doing so, the proposed elements can be used ef®ciently for 3D and thin shell applications. The starting point of the work relies on the analysis of the subspace of incompressible deformations associated with the standard (displacement-based) fully integrated and reduced integrated hexahedral elements. Prediction capabilities for both formulations are de®ned related to nearly-incompressible problems and an enhanced strain approach is developed to improve the performance of the earlier formulation in this case. With the insight into volumetric locking gained and bene®ting from a recently proposed enhanced transverse shear strain procedure for shell applications, a new element conjugating both the capabilities of ef®cient solid and shell formulations is obtained. Numerical results attest the robustness and ef®ciency of the proposed approach, when compared to solid and shell elements well-established in the literature.

On the comparison of two solid-shell formulations based on in-plane reduced and full integration schemes in linear and non-linear applications

“…The incremental displacement U can be calculated according to (25), and thus the displacement U can be updated. Subsequently the increment Δα can be calculated with (24) using the incremental displacement U and then it will be used to update the EAS parameter α .…”

“…For instance, the reduced integration or the selective reduced integration schemes are often used to avoid volumetric locking issues for hexahedral elements with an isochoric or nearly isochoric material behavior. Despite their efficiency in term of locking treatment and computational time, reduced integration schemes have certain drawbacks such as the rank deficiency of the stiffness matrix, which can lead to no solution at all, or erroneous solutions in (25); thereby to the element instability which is known as 'hourglass effect'. In the development of a solid-shell element dedicated to the modeling of thin-walled structures, an improved integration scheme with a large number of integration points along the thickness direction was considered.…”

“…The plate is subjected to a concentrated force F=16.367 at the center. It is considered as a classical shell example, hence it is presented in several research works (see [12,25,28]). The material parameters used for this example are an elasticity modulus E=10000 and Poisson's ratios ѵ=0.3 or 0.499.…”

“…The EAS procedure was also applied directly to enhance the GreenLagrange strain tensor E in several works (e.g. Klinkel et al [23,24], Vu-Quoc and Tan [6,7], Alves de Sousa et al [1,25], Parente et al [26], Schwarze et al [27], among others). Comparing these different ways to introduce the EAS technique is not obvious.…”

“…Therefore, the choice of the optimal EAS parameters is a crucial matter for several published works (e.g. Betsh et al [29], Andelfinger and Ramm [28], Vu-Quoc and Tan [6], Klinkel et al [18], Alves de Sousa et al [25], Miehe [16], Rah et al [12]). This choice should depend on the type of analysis for which the element is used.…”