SUMMARYThe now classical enhanced strain technique, employed with success for more than 10 years in solid, both 2D and 3D and shell ÿnite elements, is here explored in a versatile 3D low-order element which is identiÿed as HIS. The quest for accurate results in a wide range of problems, from solid analysis including near-incompressibility to the analysis of locking-prone beam and shell bending problems leads to a general 3D element. This element, put here to test in various contexts, is found to be suitable in the analysis of both linear problems and general non-linear problems including ÿnite strain plasticity. The formulation is based on the enrichment of the deformation gradient and approximations to the shape function material derivatives. Both the equilibrium equations and their variation are completely exposed and deduced, from which internal forces and consistent tangent sti ness follow. A stabilizing term is included, in a simple and natural form. Two sets of examples are detailed: the accuracy tests in the linear elastic regime and several ÿnite strain tests. Some examples involve ÿnite strain plasticity. In both sets the element behaves very well, as is illustrated in numerous examples.

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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.

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SUMMARYThe degenerated approach for shell elements of Ahmad and co-workers is revisited in this paper. To avoid transverse shear locking e ects in four-node bilinear elements, an alternative formulation based on the enhanced assumed strain (EAS) method of Simo and Rifai is proposed directed towards the transverse shear terms of the strain ÿeld. In the ÿrst part of the work the analysis of the null transverse shear strain subspace for the degenerated element and also for the selective reduced integration (SRI) and assumed natural strain (ANS) formulations is carried out. Locking e ects are then justiÿed by the inability of the null transverse shear strain subspace, implicitly deÿned by a given ÿnite element, to properly reproduce the required displacement patterns. Illustrating the proposed approach, a remarkably simple single-element test is described where ANS formulation fails to converge to the correct results, being characterized by the same performance as the degenerated shell element. The adequate enhancement of the null transverse shear strain subspace is provided by the EAS method, enforcing Kirchho hypothesis for low thickness values and leading to a framework for the development of shear-lockingfree shell elements. Numerical linear elastic tests show improved results obtained with the proposed formulation.

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This paper presents the extension of a previously developed formulation for shell elements in order to account for non-linear geometric effects, particularly in the presence of large rotations. To eliminate transverse shear locking, the developed shell formulation provides an enlargement of the transverse shear strain field coming from the usual degenerated concept. Doing so, additional transverse shear strain terms are included into the original displacement-based functional, following the enhanced strain approach. To reproduce the behavior of shell structures under large rotations and displacements, a rotation-free configuration is considered, where constitutive relations are stated. Dealing with finite incremental rotations, a singularity-free procedure is employed, characterizing the evolution of normal vectors to shell's mid-surface. Representative non-linear examples are considered, providing the validation of the enhanced shell element as well as the algorithmic procedures implemented, when compared to other formulations in the literature.

This contribution is devoted to the formulation and numerical implementation of a ductile damage constitutive model enriched with a thermodynamically consistent nonlocal theory of integral type. In order to describe ductile deformation, the model takes finite strains into account. To model elasticity, a Hencky-like hyperelastic free energy potential coupled with nonlocal damage is adopted. The thermodynamic consistency of the model is ensured by applying the first and second thermodynamical principles in the global form and the dissipation inequality can be re-written in a local form by incorporating a nonlocal residual that accounts for energy exchanges between material points of the nonlocal medium. The thermodynamically consistent nonlocal model is compared with its associated classical formulation (in which nonlocality is merely incorporated by averaging the damage variable without resorting to thermodynamic potentials) where the thermodynamical admissibility of the classical formulation is demonstrated. Within the computational scheme, the nonlocal constitutive initial boundary value problem is discretized over pseudo-time where it is shown that well established numerical integration strategies can be straightforwardly extended to the nonlocal integral formulation. A modified NewtonRaphson solution strategy is adopted to solve the nonlinear complementarity problem and its numerical implementation, regarding the proposed nonlocal constitutive model, is presented in detail. The results of two-dimensional finite element analyses show that the model is able to eliminate the pathological mesh dependence inherently present under the softening regime if the local theory is considered.