Elastoplastic analysis of compact and thin-walled structures using classical and refined beam finite element models

The paper presents results on the elastoplastic analysis of compact and thin-walled structures via refined beam models. The application of Carrera Unified Formulation (CUF) to perform elastoplastic analysis of isotropic beam structures is discussed. Particular attention is paid to the evaluation of local effects and cross-sectional distortions. CUF allows formulation of the kinematics of a one-dimensional (1D) structure by employing a generalized expansion of primary variables by arbitrary cross-section functions. Two types of cross-section expansion functions, TE (Taylor expansion) and LE (Lagrange expansion), are used to model the structure. The isotropically work-hardening von Mises constitutive model is incorporated to account for material nonlinearity. A Newton–Raphson iteration scheme is used to solve the system of nonlinear algebraic equations. Numerical results for compact and thin-walled beam members in plastic regime are presented with displacement profiles and beam deformed configurations along with stress contour plots. The results are compared against classical beam models such as Euler–Bernoulli beam theory and Timoshenko beam theory, reference solutions from literature, and three-dimensional (3D) solid finite element models. The results highlight: (1) the capability of the present refined beam models to describe the elastoplastic behavior of compact and thin-walled structures with 3D-like accuracy; (2) that local effects and severe cross-sectional distortions can be detected; (3) the computational cost of the present modeling approach is significantly lower than shell and solid model ones

Progressive delamination of laminated composites via 1D models

This paper presents a novel numerical framework to simulate the progressive delamination in laminated structures based on 1D component-wise models. The proposed numerical tool is a part of the virtual testing platform built within the Carrera Unified Formulation, a hierarchical, higher-order structural framework to generate theories of structures via a variable kinematic approach. Formulated within the Lagrange polynomial CUF models, the component-wise approach models the components of a complex structure through 1D CUF models at reduced computational costs and 3D-like accuracies. The effectiveness of CUF-CW models to capture accurate 3D transverse fields are of interest to solve delamination problems by integrating a class of higher-order cohesive elements to simulate the cohesive mechanics among the various components of the structure. The present framework adopts a bilinear constitutive law based on the mixed-mode delamination propagation and an efficient arc-length solver based on an energy-dissipation constraint. The numerical results aim to verify the accuracy and computational efficiency of CUF-CW models through benchmark composite delamination problems including multiple delamination fronts and comparisons with reference literature solutions and standard 3D FEM models. The outcomes show multi-fold improvements in the analysis times, good matches with experimental results, and promising enhancements of the meshing process due to the absence of aspect ratio constraints

A global-local approach for the elastoplastic analysis of compact and thin-walled structures via refined models

A computationally efficient framework has been developed for the elastoplastic analysis of compact and thin-walled structures using a combination of global-local techniques and refined beam models. The theory of the Carrera Unified Formulation (CUF) and its application to physically nonlinear problems are discussed. Higher-order models derived using Taylor and Lagrange expansions have been used to model the structure, and the elastoplastic behavior is described by a von Mises constitutive model with isotropic work hardening. Comparisons are made between classical and higher-order models regarding the deformations in the nonlinear regime, which highlight the capabilities of the latter in accurately predicting the elastoplastic behaviour. The concept of global-local analysis is introduced, and two versions are presented - the first where physical nonlinearity is considered for both the global and local analyses, and the second where nonlinearity is considered only for the local analysis. The second version results in reasonably accurate results compared to a full 3D finite element analysis, with a twofold reduction in the number of degrees of freedom

Computationally Efficient Concurrent Multiscale Framework for the Linear Analysis of Composite Structures

This paper presents a novel multiscale framework based on higher-order one-dimensional finite element models. The refined finite element models (FE) originate from the Carrera Unified Formulation (CUF), a novel and efficient methodology to develop higher-order structural theories hierarchically via a variable kinematic approach. The concurrent multiscale framework consists of a macroscale model to describe the structural level components interfaced with efficient CUF micromechanical models. Such micromechanical models can take into account the detailed architecture of the microstructure with high fidelity. The framework derives its efficiency from the capability of CUF models to detect accurate 3D-like stress fields at reduced computational costs. This paper also shows the ability of the framework to interface with different classes of representative volume elements (RVE) and the benefits of parallel implementations. The numerical cases focus on composite and sandwich structures and demonstrate the high-fidelity and feasibility of the proposed framework. The efficiency of the framework stems from comparisons with the analysis time and memory requirement against traditional multiscale implementations. The present paper is a companion of a linked work dealing with nonlinear material implementations

Wave propagation in compact, thin-walled, layered, and heterogeneous structures using variable kinematics finite elements

The article investigates wave propagation characteristics for a class of structures using higher-order one-dimensional (1D) models. 1D models are based on the Carrera Unified Formulation (CUF), a hierarchical formulation which provides a framework to obtain refined structural theories via a variable kinematics description. Theories are formulated by employing arbitrary expansions of the primary unknowns over the beam cross-section. Two classes of beam models are employed in the current work, namely Taylor Expansion (TE) and Lagrange Expansion (LE) models. Using the principle of virtual work and finite element method, the governing equations are formulated. The direct time integration of equation of motion is carried through an implicit scheme based on the Newmark method and a dissipative explicit method based on the Tchamwa–Wielgosz scheme. The framework is validated by comparing the response for the stress wave propagation in an isotropic beam to an analytical solution available in the literature. The capabilities of the proposed model are demonstrated by presenting results for wave propagation analysis of a sandwich beam and a layered annular cylinder structure. The ability of CUF models to detect 3D-like behavior with a reduced computational overhead is highlighted

CONTACT MODELLING OF COMPOSITE STRUCTURES USING ADVANCED STRUCTURAL THEORIES

The current work deals with the development of contact modelling capabilities in the framework of the Carrera Unified Formulation (CUF), which is a generalised framework for the development of advanced structural theories. The current modelling approach uses 1D elements with Lagrange polynomials being used to enhance the cross-section kinematic field, leading to a layer-wise model and involving purely displacement degrees of freedom. Such a modelling approach results in 3D-like accuracy of the solution, at a significantly reduced computational effort compared to standard 3D – FEA. The current work considers normal, frictionless contact with a node-to-node discretisation, and the penalty approach is used to enforce the contact constraints. The resulting nonlinear analysis is implicitly solved using the Newton-Raphson method. The use of layer-wise modelling in CUF results in a high-fidelity solution which is capable of accurately evaluating the interlaminar stress fields, as well as accounting for transverse stretching. The development is extended to the case of dynamic contact, which uses a combination of node-to-node discretisation and Lagrange Multiplier constraints to model contact. Initial assessments consider elastic impact between two bodies and demonstrate the capability of CUF models in accurately modelling contact/impact

Nonlinear analysis of compact and thin-walled metallic structures including localized plasticity under contact conditions

This work presents the numerical analysis of elastoplastic contact problems of compact and thin-walled metallic structures. The emphasis is on the use of higher-order 1D elements with pure displacement variables and based on the Carrera Unified Formulation (CUF) to capture localized effects and cross-sectional distortions. Contact interactions are normal and frictionless via a node-to-node contact algorithm with the penalty approach for contact enforcement. The analysis considers the material nonlinearity via the von Mises constitutive law. Numerical assessments compare the CUF solutions with 3D finite element analysis concerning the solution quality, computational size, and analysis time. The results show the ability of 1D CUF models of accurately evaluating localized deformations and plasticity. The CUF results are in good agreement with reference 3D finite element solutions, and require an order of magnitude fewer degrees of freedom and analysis time, making them computationally efficient

Computationally Efficient Concurrent Multiscale Framework for the Nonlinear Analysis of Composite Structures

This paper presents a computationally efficient concurrent multiscale platform to undertake the nonlinear analysis of composite structures. The framework exploits refined 1D models developed within the scheme of the Carrera Unified Formulation (CUF), a generalized hierarchical formulation that generates refined structural theories via a variable kinematic description. CUF operates at the macro and microscale, and the macroscale interfaces with a nonlinear micromechanical toolbox. The computational efficiency derives from the ability of the CUF to obtain accurate 3D-like stress fields with a reduced computational cost. The nonlinearity is at the matrix level within the microscale, and its effect scales up to the macroscale through homogenization. The macro tangent matrix adopts a perturbation-based method to have meliorated performances. The numerical results demonstrate that the framework requires some $50$ of the computational time and $10$ of memory usage of traditional 3D finite elements (FE). Very detailed local effects at the microscale are detectable, and there are no restrictions concerning the complexity of the geometry. The present paper is a companion of a linked work dealing with linear material implementations

Accurate evaluation of failure indices of composite layered structures via various FE models

The objective of the current work is to perform a failure evaluation of fiber composite structures based on failure indices computed using the Hashin 3D failure criterion. The analysis employs 1D and 3D finite elements. 1D elements use higher-order structural theories from the Carrera Unified Formulation based on Lagrange expansions of the displacement field. The 3D model analysis exploits ABAQUS. Attention is paid to the free-edge effects, the mode of failure initiation - matrix or fiber tension, delamination -, and the loads at which first ply failure occurs. The results underline the paramount importance of out-of-plane stress components for accurate prediction and the computational efficiency of refined 1D models. In fact, 1D models lead from one to twofold reductions of the CPU time if compared to 3D models