Transient analysis of trusses considering nonlinear elastic and viscoelastic material models Débora Cristina Brandt, Pablo Andrés Muñoz-Rojas Latin American Journal of Solids and Structures, 2024 The use of simple bar elements in nonlinear structural finite element formulations has the academic advantage of uncoupling element technology issues, normally present in continuum finite elements, from the structural phenomena to be observed. Motivated by this feature, we present a finite element setting for the formulation of different nonlinear elastic and viscoelastic truss models applied to transient analyses. Nonlinear elasticity is considered by studying two material model families: the first one stablishes a Hooke-like linear relationship between different pairs of nonlinear measures of stress and strain (Saint-Venant-Kirchhoff materials, for example); the second family considers hyperelastic behavior, where we adopt Ogden's model. Viscoelasticity is introduced as an extension of the above, using a generalized Kelvin rheological model to account for strain rate effects. The finite kinematics is set in a corotational total Lagrangian description where the virtual work is described using the Second Piola-Kirchhoff and the Green Lagrange measures. Although the derivation is omitted, the consistent tangent moduli are given for all these cases. Transient analysis is solved by means of the average acceleration method. A simple and efficient algorithm for integration of viscous strain is then introduced and numerical problems involving simultaneously different truss models are studied. While, on one hand, we discuss some non-intuitive aspects found, on the other hand we believe that the results are valuable as benchmarks since little comparative data is found in literature.
Aspects on viscoelasticity modeling of HDPE using fractional derivatives: Interpolation procedures and efficient numerical scheme T.C. da Costa-Haveroth, G.A. Haveroth, A. Kühl, J.L. Boldrini, M.L. Bittencourt, et al. Mechanics of Advanced Materials and Structures, 2022 Among the wide range of structural polymers currently available, this work deals with high-density polyethylene (HDPE). The typical viscoelastic behavior of this material is not trivial to model and has already been investigated by many authors. We employ the fractional Zener model to fit our experimental creep results of HDPE evaluated at different stress levels. This model produces fractional constitutive equations with excellent curve-fitting properties and fewer parameters to be identified in relation to traditional models. The results are compared with those ones provided by the application of the Prony series method. The first novelty of this paper is the application of the time-stress equivalence principle (TSEP), coupled to the fractional model, to estimate creep at intermediate stress levels, that in turn, were not measured experimentally but lie within the stress range used to calibrate the model. We compare the results provided by this method with those based on linear interpolation of the parameters. Although there is clear benefits requiring fewer parameters, fractional derivatives render costly computations due to their history memory. To cope with this, we propose a new algorithm, called GPE, which shows a compromise between enhanced efficiency and accuracy when compared with other proposals of the literature. These features are verified with simulations for simple functions, and a long term creep test with the fractional Zener model. The combined application of fractional derivatives, TSEP and the new GPE algorithm results in a novel efficient and effective alternative to account for the creep modeling of HDPE.
Second-order design sensitivity analysis using diagonal hyper-dual numbers Vitor Takashi Endo, Eduardo Alberto Fancello, Pablo Andrés Muñoz‐Rojas International Journal for Numerical Methods in Engineering, 2021 Although sensitivity analysis provides valuable information for structural optimization, it is often difficult to use the Hessian in large models since many methods still suffer from inaccuracy, inefficiency, or limitation issues. In this context, we report the theoretical description of a general sensitivity procedure that calculates the diagonal terms of the Hessian matrix by using a new variant of hyper‐dual numbers as derivative tool. We develop a diagonal variant of hyper‐dual numbers and their arithmetic to obtain the exact derivatives of tensor‐valued functions of a vector argument, which comprise the main contributions of this work. As this differentiation scheme represents a general black‐box tool, we supply the computer implementation of the hyper‐dual formulation in Fortran. By focusing on the diagonal terms, the proposed sensitivity scheme is significantly lighter in terms of computational costs, facilitating the application in engineering problems. As an additional strategy to improve efficiency, we highlight that we perform the derivative calculation at the element‐level. This work can contribute to many studies since the sensitivity scheme can adapt itself to numerous finite element formulations or problem settings. The proposed method promotes the usage of second‐order optimization algorithms, which may allow better convergence rates to solve intricate problems in engineering applications.
Application of a master curve and the modified superposition principle for modeling creep and loading rate effects at small strains in high-density polyethylene A. Kühl, P. A. Muñoz-Rojas Mechanics of Advanced Materials and Structures, 2021 Studying the nonlinear viscoelastic behavior of high-density polyethylene (HDPE) at small strains and stresses is still a matter of interest in engineering applications such as laying submerged pipelines. Although sound modeling of such behavior requires complex phenomenological or micromechanical constitutive laws, many works have focused on the development of simplified procedures for approximating this type of nonlinear response. Usually, when these simplified methods are employed to reproduce creep behavior, they are not capable to simultaneously provide good estimates for traction tests even at constant stress or strain rates. This work describes a methodology, which has shown a good compromise to reproduce both types of responses within a given stress range. The procedure can be understood as an interpolative approach based on a master curve and the modified superposition principle to account for nonlinear effects. With this strategy, it is possible to predict the nonlinear creep behavior for an HDPE sample subjected at any constant stress level within a given experimental range. Once this predictive capability is achieved, we use an incremental algorithm based on the modified superposition principle to simulate traction tests at constant strain rates. We show that the combined application of the proposed master curve approach and the modified superposition principle results in good approximations for creep tests and simultaneously leads to remarkable agreement with experimental traction tests reported in the literature.
An extended multiscale finite element method (Emsfem) analysis of periodic truss metamaterials (ptmm) designed by asymptotic homogenization Elias Jagiello, Pablo Andrés Muñoz-Rojas Latin American Journal of Solids and Structures, 2021 Asymptotic Homogenization (AH) and the Extended Multiscale Finite Element Method (EMsFEM) are both procedures that allow working on a structural macroscale that incorporates the effect of averaged microscopic heterogeneities, thus resulting in computationally efficient strategies. EMsFEM works directly on coupled finite micro and macroscales using numerically built discrete interpolation functions. Periodic Truss Metamaterials (PTMMs) are cellular materials formed by the periodic repetition of a truss-like unit cell and engineeringly tailored to show a given macroscopic response. In this work we analyze the numerical behavior of selected PTMMs that were designed for extreme Poisson ratios using AH theory. As a first issue, we study macroscopic structures made of finite unit cells and verify how close their average behavior coincides with the material properties predicted by AH. For comparison, we solve the macroscopic plane stress associate problems that employ the elastic constitutive tensor obtained by AH. The second issue is concerned with the ability of EMsFEM to reproduce the structural behavior of the full macro-micro model. We employ two versions of the EMsFEM, adopting linear (LBC) and periodic (PBC) boundary conditions to build the numerical interpolation functions. The third and most important aspect discussed in this research concerns evaluation of the EMsFEM downscaled displacement fields. We observe that according to the layout of the AH designed unit cell, to the use of LBC or PBC and, depending on the boundary conditions present in the macroscopic problem, spurious downscaled displacements might occur. Such spurious displacements are due to excessive compliance of the corresponding unit cell and can be detected when building the numerical interpolation functions. We conclude that the layout optimization of PTMM using AH must be carefully interpreted and that EMsFEM is a good tool to detect a macroscopic excessively compliant response at an early design stage.
Dynamic analysis of a coupled high-speed train and bridge system subjected to sea wave hydrodynamic load Amin Razzaghi Kalajahi, Morteza Esmaeili, Jabbar Ali Zakeri Latin American Journal of Solids and Structures, 2021 IN THIS STUDY, THE DYNAMIC BEHAVIOR OF THE 3D TRAIN–BRIDGE SYSTEM SUBJECTED TO DIFFERENT HYDRODYNAMIC LOADS (TBW MODEL) IS ESTABLISHED. BY TAKING A CONTINUOUS BRIDGE (32 + 48 + 32) M WITH BOX GIRDERS AS A CASE STUDY, THE DYNAMIC RESPONSES OF THE BRIDGE WHICH IS UNDER TRAIN PASSING AND SUBJECTED TO SEVERAL SEA HYDRODYNAMIC LOADS ARE ANALYZED. THE SUBSTRUCTURE OF THE VIADUCT INCLUDES FOUR CONCRETE SOLID PIERS WITH RECTANGULAR SECTIONS AND PIERS ARE FIXED AT SEABED. PIERS AND DECKS ARE DESIGNED AND ANALYZED BASED ON DYNAMIC FINITE ELEMENTS METHODS, AND HYDRODYNAMIC FORCES ARE APPLIED ON PIERS ACCORDING TO MORRISON'S THEORY. ALSO, CAR BODY IS MODELED BY A 27-DOFS DYNAMIC SYSTEM. MODEL VALIDATION HAS BEEN PERFORMED WITH OTHER RESEARCH BY CONSIDERING VESSEL COLLISION LOAD. IN CONTINUATION, THE DYNAMIC RESPONSES OF THE BRIDGE AND THE RUNNING SAFETY INDICES OF THE TRAIN ON THE BRIDGE UNDER SEVERAL TYPES OF SEA WAVE STATES AND SEVERAL TRAIN SPEEDS ARE ANALYZED. CONSEQUENTLY AN ASSESSMENT PROCEDURE IS PROPOSED FOR THE RUNNING SAFETY OF HIGH-SPEED TRAINS ON BRIDGES SUBJECTED TO WAVE LOADS, AND RELATED THRESHOLD CURVES FOR TRAIN SPEED VERSUS SEA STATES ARE DEFINED. RESULTS OF TBW'S SENSITIVE ANALYZES SHOWN THE IMPORTANCE OF SEA-STATES CONDITIONS FOR TRAIN SAFE AND COMFORTABLE RUNNING. THESE OUTPUTS INDICATES THAT IN STORMY CONDITIONS (WAVE HEIGHT ≥ 8.5 M), THE SPEED OF THE TRAIN CROSSING THE BRIDGES SHOULD BE REDUCED AND IT IS POSSIBLE FOR THE TRAIN TO PASS AT LOW SPEEDS (UNDER 200 KM/H) IN STORMY CONDITIONS.
Benchmark study on identification of inelastic parameters based on deep drawing processes using PSO - Nelder Mead hybrid approach Computational Plasticity Xii Fundamentals and Applications Proceedings of the 12th International Conference on Computational Plasticity Fundamentals and Applications Complas 2013, 2013
Materials Modeling-Challenges and Perspectives Miguel Vaz, Eduardo A. de Souza Neto, Pablo Andreś Muñoz‐Rojas Advanced Computational Materials Modeling from Classical to Multia Scale Techniques, 2010
Truss optimization in aerospace structures Hervandil Morosini Sant’Anna, Carlos Eduardo Marcos Guilherme, Jun Sérgio Ono Fonseca, Pablo Andrés Muñoz-Rojas SAE Technical Papers, 2001
