The article presents a novel strain-based finite element family for the analysis of material softening of planar frame structures. In our case, the softening zone is described by a discrete crack, ...which is considered as an ‘excluded’ finite element point, i.e., the deformation quantities in the crack are considered separately from the deformation quantities of the element. They are connected to the element only through kinematic quantities, used to describe the crack opening. The criterion for crack initiation is defined as the limit axial-bending resistance of the cross-section. The advantage of the presented model is that it is not necessary to define cracks or softening zones in advance and that the solution is mesh-independent in the sense that no further densification of the mesh is needed purely on account of capturing material softening. The accuracy and efficiency of the presented finite element family is illustrated by the example of a clamped–simply supported concrete beam and a portal concrete frame. The examples demonstrate that even with a minimum number of finite elements of suitable accuracy, sufficiently accurate results are obtained for normal engineering practice.
•A novel strain-based FEM is presented for analysis of softening of planar frames.•Softening zone is described by a discrete crack considered as ‘excluded’ FE point.•Axial-bending resistance of the cross-section is considered in crack initiation.•The softening zones need not be defined in advance.•Results are independent of the finite element mesh.
In this paper, we propose a novel computational formulation capable of solving the problem of material softening and the emerging localisation of strains in spatial frame-like structure, a common ...phenomenon for brittle heterogeneous materials. This study adopts the embedded strong discontinuity approach within our original velocity-based framework. The velocity-based formulation is thus enhanced with additional capabilities of detection of critical load level and critical cross-section and introduction of the jump-like variables at the level of velocities and angular velocities to enable more realistic description of strain localisation. A modified consistency condition is derived using the method of weighted residuals in complete accordance with the theoretical concept of strong discontinuity. One of the key advantages of the proposed method is its computational efficiency, which is preserved even after detecting cross-sectional singularities and handling post-critical localised strains. The numerical examples show the effectiveness and robustness of the proposed approach.
•The problem of material softening and strain localization is addressed.•The primary unknowns are velocities and angular velocities.•The field of unknowns is enriched with additional shape functions.•The solution procedure enables possible discontinuities and localisms.•The updated strains are obtained using kinematic compatibility equations.•We surpass the singularity of cross-sectional constitutive equations.
Variation of cyclic loading effect on fatigue crack growth is investigated under plane strain and small scale yielding (SSY) conditions. The material is characterized by a finite strain elastic ...viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Displacements corresponding to the isotropic linear elastic mode I crack field are prescribed on a remote boundary. The influence of cyclic stress intensity factor range (
), load ratio (R), number of cycles (N), plastic compressibility (
overload and material softening on near tip deformation was studied in detail. For comparison purpose, a few results pertaining to plastically incompressible solids are also considered. The crack tip opening displacement (CTOD), plastic crack growth, deformed crack tip shape, plastic zone shape and size near the crack tip appear to depend significantly on
R, N,
overload and material softening. The overload produces strong plastic deformation ahead of the crack tip and decreases the fatigue crack growth substantially.
Highlights
Variation of cyclic loading effect on fatigue crack growth is investigated for materials characterized by a finite strain elastic viscoplastic constitutive model with hardening and hardening-softening-hardening hardness functions. Both plastically compressible and incompressible solids are considered.
The influence of cyclic stress intensity factor range (
), load ratio (R), number of cycles (N), plastic compressibility (
overload and material softening on near tip deformation was studied in detail.
The crack tip opening displacement, plastic crack growth, plastic zone shape and size near the crack tip appear to depend significantly on
R, N,
overload and material softening.
The combination of softening or softening-hardening material response and plastic compressibility leads to major deviations in crack tip blunting and fatigue crack growth from those that prevail for a hardening material.
This work deals with the modelling and numerical simulation of aluminium stiffened panels, assembled by means of friction stir welding (FSW) operations, and subjected to compressive loads that can ...catastrophically induce buckling (global or local) unstable modes and, subsequently, overall failure. Due to their geometrical complexity, added to localized thermo-mechanical effects that typically come from joining by welding, approximation methods such as the Finite Element Method are typically used in such nonlinear analyses, having proved to be useful to designers focused on the prediction of the behaviour (before and post buckling) of such structures. Being grounded on previous contributions from the authors, the present paper aims to bring a number of innovative aspects to the current state of the art by considering in the developed models the simultaneous influence of residual stress fields, material softening effects and geometrical imperfections. Doing so, it is possible to infer about the singular and combined influence of these effects in the overall structural performance of stiffened panels, building up a useful and comprehensive methodology for design stages.
•Geometrical imperfections, residual stress and material softening coming from FSW.•Distinct methodologies to model, simulate and characterize the welding effects.•How welding effects can influence buckling and collapse loads of stiffened panels.•Geometrical imperfections are critical for the behavior of welded structures.
The mechanical response of filled rubber depends on load history, strain rate and state, temperature and even direction of previous loading. Although there is a plurality of both physical and ...phenomenological models, only few are able to reproduce this rich spectrum of effects. Moreover, many of them suffer from physical or mathematical inconsistencies. We present a model, which is based on physical ideas and plausible assumptions about the material’s microstructure, while being designed for high efficiency and robustness in finite element applications. It is shown by fits to extensive experimental data that it reproduces almost the full phenomenology of filled rubbers, both at low and high strains, for different deformation states and rates, holding times, and at different temperatures. The main modeling paradigm is the stress-induced breakdown and reorganization of microscopic structures which defines the time-dependent behavior of the material and allows to reproduce logarithmic relaxation effects. Moreover, its nine fit parameters evolve in a physically reasonable way under variation of filler and cross-linker content. A static limiting case of the model is derived, reducing the number of parameters and computational effort wherever necessary. Finally, a FE-implementation using computer-generated subroutines is presented and tested against experimental data of a simplified bushing under torsional, radial, cardanic and axial loading.
Poly-Carbonate (PC) and Poly-Methyl-Methacrylate (PMMA) are lightweight and mechanically tough transparent glassy polymers. Their mechanical behavior at low to moderate strain rates has been well ...characterized; however, that at high strain rates needs additional work. We propose two modifications to existing pressure-dependent viscoplastic constitutive equations that enable one to simulate better mechanical deformations of PC and PMMA at high strain rates. First, the elastic moduli are taken to depend upon the current temperature and the current effective strain rate. Second, two internal variables are introduced to better characterize the strain softening of the material at high strain rates. A technique to find values of newly introduced material parameters is described. We compute the local temperature rise due to energy dissipated during plastic deformations. The true axial stress vs. the true axial strain curves in uniaxial compression from numerical simulations of the test configurations at high strain rates using the proposed constitutive equations are found to agree well with the experimental results available in the literature.
AerMet100 steel is a typical difficult-to-cut material, and laser-assisted milling (LAM) is a promising machining technology for this kind of material. In LAM process, the material is softened by the ...thermal effect of laser beam, which improves the machinability of the materials. And finally, the cutting forces are reduced compared with conventional milling (CM). This paper presents an analytical model considering material softening effect to predict the cutting force during LAM. The cutting force is produced by shearing and ploughing action. Both laser source and cutting tool are discretized into elements. Based on the Johnson-Cook (J-C) constitutive model and the thermal model due to laser beam and cutting action, the shear plane temperature and the shear flow stress considering the combined effects of laser heating and plastic deformation are calculated iteratively, and the influence of material softening effect on cutting force coefficients is taken into account. A series of experiments carried out on AerMet100 steel demonstrate the accuracy of the cutting force model, and the results show that the three-axis cutting force in LAM is reduced by up to 33.9%. Besides, the influence of laser parameters related to material softening effect on the cutting force is discussed based on the proposed model.
In forming processes, the material undergoes large and complex deformations that influence the shape and properties of the final component. Especially the local weakening of the microstructure in the ...form of ductile damage, defined as the nucleation, growth and coalescence of voids, has a significant impact on the component’s performance. To predict the void area fraction in a dual-phase steel, a data-driven model is used, which is trained with high-resolution scanning electron microscope data. The model provides good quantitative predictions of the void area fraction for various tensile and bending tests. In the next step, the model is coupled to the mechanical properties using the homogenization approach of effective stresses. The model is calibrated using force–displacement curves of various tensile tests. Besides the void area fraction, the model is able to predict the corresponding mechanical properties in the sense of the force–displacement response and to account for the material softening during air bending.
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