Research

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22 pages, 5745 KiB

Open AccessArticle

Development and Analysis of High-Modulus Asphalt Concrete Predictive Model

by Mikołaj Bartkowiak and Mieczysław Słowik

Materials 2023, 16(13), 4509; https://doi.org/10.3390/ma16134509 - 21 Jun 2023

Viewed by 659

The main purpose of this paper is to present the development of a new predictive model intended for the calculation of stiffness modulus |E*| determined by a four-point bending beam test (4PBB or 4PB-PR). The model developed, called model A, was based on [...] Read more.

The main purpose of this paper is to present the development of a new predictive model intended for the calculation of stiffness modulus |E*| determined by a four-point bending beam test (4PBB or 4PB-PR). The model developed, called model A, was based on the Witczak model, which was developed for the dynamic-modulus (DM) method. Most of the asphalt mixtures used to develop the model were high-modulus asphalt concrete (HMAC). The most commonly used methods for determining the stiffness modulus |E*| of asphalt mixtures were also discussed. The paper presents the results of the study for 10 asphalt mixtures but 8 of them were used to develop the predictive model. In addition, the results of complex shear modulus G* tests on neat and modified bituminous binders carried out in a dynamic shear rheometer (DSR), necessary for the development of a predictive model, are presented. The tests carried out in the dynamic shear rheometer had significant measurement uncertainties. The results of the volumetric parameters of the asphalt mixtures are also reported. The developed model A has maximum absolute errors e = 1930 MPa (p = 95%) and maximum relative errors re = 50% (p = 95%). The distribution of the absolute errors of the model, after discarding outliers, has a normal distribution as in the development of other models of this type, which was confirmed by appropriate statistical tests. On the basis of the tests and calculations carried out, it was concluded that, in order to increase the precision of the predictive models, it is advisable to reduce the measurement uncertainty of the bitumen complex shear modulus G*. For the developed model A, the limiting values of the stiffness modulus |E*| are also shown, within which the determined stiffness modulus should fall. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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14 pages, 3706 KiB

Open AccessArticle

Compressive Strength of Corrugated Paperboard Packages with Low and High Cutout Rates: Numerical Modelling and Experimental Validation

by Lajos Fehér, Damian Mrówczyński, Renáta Pidl and Péter Böröcz

Materials 2023, 16(6), 2360; https://doi.org/10.3390/ma16062360 - 15 Mar 2023

Cited by 2 | Viewed by 1736

Abstract

The finite element method is a widely used numerical method to analyze structures in virtual space. This method can be used in the packaging industry to determine the mechanical properties of corrugated boxes. This study aims to create and validate a numerical model [...] Read more.

The finite element method is a widely used numerical method to analyze structures in virtual space. This method can be used in the packaging industry to determine the mechanical properties of corrugated boxes. This study aims to create and validate a numerical model to predict the compression force of corrugated cardboard boxes by considering the influence of different cutout configurations of sidewalls. The types of investigated boxes are the following: the width and height of the boxes are 300 mm in each case and the length dimension of the boxes varied from 200 mm to 600 mm with a 100 mm increment. The cutout rates were 0%, 4%, 16%, 36%, and 64% with respect to the total surface area of sidewalls of the boxes. For the finite element analysis, a homogenized linear elastic orthotropic material model with Hill plasticity was used. The results of linear regressions show very good estimations to the numerical and experimental box compression test (BCT) values in each tested box group. Therefore, the numerical model can give a good prediction for the BCT force values from 0% cutout to 64% cutout rates. The accuracy of the numerical model decreases a little when the cutout rates are high. Based on the results, this paper presents a numerical model that can be used in the packaging design to estimate the compression strength of corrugated cardboard boxes. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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16 pages, 3303 KiB

Open AccessArticle

Influence of Imperfections on the Effective Stiffness of Multilayer Corrugated Board

by Damian Mrówczyński and Tomasz Garbowski

Materials 2023, 16(3), 1295; https://doi.org/10.3390/ma16031295 - 02 Feb 2023

Cited by 4 | Viewed by 1472

Abstract

There are many possible sources of potential geometrical inaccuracies in each layer of corrugated board during its manufacture. These include, among others, the processes of wetting the corrugated layers during profiling, the process of accelerated drying, the gluing process, and any mechanical impact [...] Read more.

There are many possible sources of potential geometrical inaccuracies in each layer of corrugated board during its manufacture. These include, among others, the processes of wetting the corrugated layers during profiling, the process of accelerated drying, the gluing process, and any mechanical impact of the pressure rollers on the cardboard. Work taking into account all the above effects in numerical modeling is not well described in the literature. Therefore, this article presents a simple and practical procedure that allows us to easily account for geometric imperfections in the calculation of the effective stiffness of corrugated board. As a main tool, the numerical homogenization based on the finite element method (FE) was used here. In the proposed procedure, a 3D model of a representative volumetric element (RVE) of a corrugated board is first built. The numerical model can include all kinds of geometrical imperfections and is used to calculate the equivalent tensile and bending stiffnesses. These imperfections were included in the 3D numerical model by appropriate modeling of individual layers, taking into account their distorted shape, which was obtained on the basis of a priori buckling analysis. This paper analyzes different types of buckling in order to find the most representative one. The proposed procedure is easy to implement and fully scalable. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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15 pages, 4128 KiB

Open AccessArticle

Compression Strength Estimation of Corrugated Board Boxes for a Reduction in Sidewall Surface Cutouts—Experimental and Numerical Approaches

by Lajos Fehér, Renáta Pidl and Péter Böröcz

Materials 2023, 16(2), 597; https://doi.org/10.3390/ma16020597 - 07 Jan 2023

Cited by 3 | Viewed by 3293

Abstract

Corrugated cardboard boxes are generally used in modern supply chains for the handling, storage, and distribution of numerous goods. These packages require suitable strength to maintain adequate protection within the package; however, the presence and configuration of any cutouts on the sidewalls significantly [...] Read more.

Corrugated cardboard boxes are generally used in modern supply chains for the handling, storage, and distribution of numerous goods. These packages require suitable strength to maintain adequate protection within the package; however, the presence and configuration of any cutouts on the sidewalls significantly influence the packaging costs and secondary paperboard waste. This study aims to evaluate the performance of CCBs by considering the influence of different cutout configurations of sidewalls. The compression strength of various B-flute CCB dimensions (200 mm, 300 mm, 400 mm, 500 m, and 600 mm in length, with the same width and height of 300 mm), each for five cutout areas (0%, 4%, 16%, 36%, and 64%) were experimentally observed, and the results were compared with the McKee formula for estimation. The boxes with cutout areas of 0%, 4%, 16%, 36%, and 64% showed a linear decreasing tendency in compression force. A linear relationship was found between compression strength and an increase in cutout sizes. Packages with 0% and 4% cutouts did not show significant differences in compression strength (p < 0.05). Furthermore, this study shows a possible way to modify the McKee estimation for such boxes after obtaining empirical test data since the McKee formula works with a relatively high error rate on corrugated cardboard boxes with sidewall cutouts. Utilizing the numerical and experimental results, a favorable estimation map can be drawn up for packaging engineers to better manage material use and waste. The results of the study showed that the McKee formula does not appropriately estimate the box compression strength for various cutout sizes in itself. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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14 pages, 3667 KiB

Open AccessArticle

Sensitivity Analysis of Open-Top Cartons in Terms of Compressive Strength Capacity

by Damian Mrówczyński, Tomasz Gajewski and Tomasz Garbowski

Materials 2023, 16(1), 412; https://doi.org/10.3390/ma16010412 - 01 Jan 2023

Cited by 6 | Viewed by 1372

Abstract

Trays in which fruit and vegetables are transported over vast distances are not only stored in extreme climatic conditions but are also subjected to long-term loads. Therefore, it is very important to design them correctly and select the optimal raw material for their [...] Read more.

Trays in which fruit and vegetables are transported over vast distances are not only stored in extreme climatic conditions but are also subjected to long-term loads. Therefore, it is very important to design them correctly and select the optimal raw material for their production. Geometric parameters that define the shape of the packaging may also be optimized in the design process. In this work, in order to select the most important parameters that affect the load capacity of a tray, sensitivity analysis was used. A sensitivity analysis is often the first step in the process of building artificial-intelligence-based surrogates. In the present work, using the example of a specific tray’s geometry, the selection of starting parameters was carried out in the first step, based on the Latin hypercube sampling method. In the next step, local sensitivity analyses were performed at twenty selected starting points of the seventeen-dimensional space of the selected parameters. Based on the obtained results, it was possible to select the parameters that have a significant impact on the load capacity of the tray in the box compression test and whose influence is negligible or insignificant. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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16 pages, 3494 KiB

Open AccessArticle

Developments on Constitutive Material Model for Architectural Soda-Lime Silicate (SLS) Glass and Evaluation of Key Modelling Parameters

by Andrzej Malewski, Marcin Kozłowski, Jacek Podwórny, Marcin Środa and Wojciech Sumelka

Materials 2023, 16(1), 397; https://doi.org/10.3390/ma16010397 - 01 Jan 2023

Cited by 2 | Viewed by 1551

Abstract

Architectural soda-lime silicate glass (SLS) is increasingly taking on complex shapes that require more detailed numerical analysis. Glass modeling is a thoroughly described topic with validated constitutive models. However, these models require a number of precise material parameters for SLS glass, and these [...] Read more.

Architectural soda-lime silicate glass (SLS) is increasingly taking on complex shapes that require more detailed numerical analysis. Glass modeling is a thoroughly described topic with validated constitutive models. However, these models require a number of precise material parameters for SLS glass, and these are very sensitive to changes in glass composition. The currently available information is based on SLS glass tested in the late 1990s. As a result, most current publications are based on the above data. The object of this work was to analyze the available sources and update the information on selected key parameters for modeling. Using the currently utilized SLS glass in construction, the coefficient of thermal expansion (CTE), glass transition temperature, and the Young’s modulus have been experimentally investigated. The updated material parameters will allow for more accurate modeling of the SLS glass currently used in construction, and in consequence will make the prototyping process for glass with complex geometries possible to be transferred from the production stage to the design stage, resulting in shorter production times. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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19 pages, 6341 KiB

Open AccessArticle

Numerical Simulation of the Impact of Water Vapour and Moisture Blockers in Energy Diagnostics of Ventilated Partitions

by Barbara Ksit, Anna Szymczak-Graczyk and Roman Pilch

Materials 2022, 15(22), 8257; https://doi.org/10.3390/ma15228257 - 21 Nov 2022

Cited by 2 | Viewed by 1293

Abstract

Current trends towards saving energy and designing sustainable buildings result in most designers focusing on achieving the best thermal parameters, thereby neglecting a careful moisture analysis. Excessive moisture content in building partitions degrades the mechanical properties of materials, reduces thermal insulation properties (which [...] Read more.

Current trends towards saving energy and designing sustainable buildings result in most designers focusing on achieving the best thermal parameters, thereby neglecting a careful moisture analysis. Excessive moisture content in building partitions degrades the mechanical properties of materials, reduces thermal insulation properties (which leads to an increase in the demand for thermal energy) and worsens the microclimate in rooms. Modern digital solutions help create appropriate models of partitions that work for many years in good environmental conditions. According to the analysis of air parameters, 1 m³ of air at 20 °C contains approx. 17.3 g of water. When the temperature of the air reaches the dew point temperature, water vapour condenses. The dew point depends on air temperature and relative air humidity; for instance, at the same air temperature of 20 °C, the dew point temperature at 40% relative air humidity is 6 °C, whereas at 90% relative humidity, it is over 18 °C. This means that the higher the value of relative humidity in the room at a certain temperature, the lower the temperature that will cause condensation. The article presents a numerical analysis of the insulation work of flexible materials within the layers of ventilated partitions in an 8-year simulated period of varying environmental conditions. The aim of the article is to analyze different models and variants of ventilated partition operation with respect to the advisability of using a vapour barrier to avoid the problem of destruction of thermal insulation and finishing layers of a ventilated roof. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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12 pages, 1230 KiB

Open AccessArticle

Influence of Modified Starch Admixtures on Selected Physicochemical Properties of Cement Composites

by Marta Sybis and Emilia Konował

Materials 2022, 15(21), 7604; https://doi.org/10.3390/ma15217604 - 29 Oct 2022

Cited by 1 | Viewed by 1254

Abstract

The conducted research aimed to evaluate the influence of admixtures of various modified starches on the rheological properties of cement composites and their influence on the compressive strength of hardened cement mortars. The study involved 17 different modified starch admixtures. Using a rheometer, [...] Read more.

The conducted research aimed to evaluate the influence of admixtures of various modified starches on the rheological properties of cement composites and their influence on the compressive strength of hardened cement mortars. The study involved 17 different modified starch admixtures. Using a rheometer, the values of viscosity and tangential stresses were determined depending on the shear rate, and were subsequently used to determine the yield point and plastic viscosity of cement slurries. The next parameters tested were the flow of fresh cement slurry and the compressive strength of hardened cement composite. The highest fluidisation was recorded for retentate LU-1420-0.5%Ac-R, an increase of 82%. The conducted tests led to the conclusion that admixing cement composites with modified starches changes the rheological parameters and the compressive strength of cement composites. The highest strength gains occurred for the admixtures of retentate LU-1412-R (increase of 25%). Declines in compressive strength were noticed in the retentate LU-1422-R (decrease by 13%) and the retentate OSA-2.5%-R (decrease of 17%). The admixture of starch hydrolysate significantly decreases the yield point of slurries, which in turn may contribute to the fluidisation of concrete mixes and the reduction of mixing water. The lowest values were obtained for retentates LU-1420-0.5%Ac-R (decrease of 94%), and LU-1412-R (decrease of 93%). It was found that the consistency and compressive strength of cement mortars are affected by both the type of modification and the length of the chemical chain of starch. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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13 pages, 5491 KiB

Open AccessArticle

Experimental Investigation of the Failure Scenario of Various Connection Types between Thin-Walled Beam and Sandwich Panel

by Katarzyna Ciesielczyk and Robert Studziński

Materials 2022, 15(18), 6277; https://doi.org/10.3390/ma15186277 - 09 Sep 2022

Cited by 3 | Viewed by 1322

Abstract

The paper presents failure scenarios for various types of connections between a thin-walled beam and a sandwich panel. In addition to standard connections used in civil engineering applications, that is, self-drilling fasteners for sandwich panels, the study examined the use of bolts, blind [...] Read more.

The paper presents failure scenarios for various types of connections between a thin-walled beam and a sandwich panel. In addition to standard connections used in civil engineering applications, that is, self-drilling fasteners for sandwich panels, the study examined the use of bolts, blind rivets, and double-sided acrylic tape applied linearly and pointwise. The connections were subjected to the horizontal load applied with constant eccentricity with respect to the plane of the connection surface. This load arrangement simulates the behaviour of a free flange of the thin-walled beam in bending while lateral-torsional buckling occurs. In this way, the research covers the determination of the lateral stiffness of the thin-walled beam-free flange, while the other flange is connected to the sandwich panel using various connection systems. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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26 pages, 8069 KiB

Open AccessArticle

Experimental Study of Aluminium-Timber Composite Bolted Connections Strengthened with Toothed Plates

by Marcin Chybiński and Łukasz Polus

Materials 2022, 15(15), 5271; https://doi.org/10.3390/ma15155271 - 30 Jul 2022

Cited by 10 | Viewed by 1868

Abstract

This paper presents the first experimental study of the load-slip behaviour of aluminium-timber composite bolted connections reinforced with toothed plates. The effectiveness of the strengthening was evaluated in laboratory push-out tests. The push-out test samples consisted of laminated veneer lumber panels, aluminium alloy [...] Read more.

This paper presents the first experimental study of the load-slip behaviour of aluminium-timber composite bolted connections reinforced with toothed plates. The effectiveness of the strengthening was evaluated in laboratory push-out tests. The push-out test samples consisted of laminated veneer lumber panels, aluminium alloy I-beams, and bolts (grade 8.8 10 mm × 125 mm and 12 mm × 135 mm bolts, grade 5.8 10 mm × 125 mm and 12 mm × 135 mm bolts). A group of 16 specimens had toothed plates as additional reinforcement, while 16 specimens had no reinforcement. The impact of the bolt diameter (10 and 12 mm) and bolt grade (5.8 and 8.8) on the behaviour of the connections was also analysed. The values of the ultimate load and the slip modulus for the bolted connections with grade 8.8 10 mm and 12 mm bolts and with grade 5.8 12 mm bolts reinforced by toothed-plate connectors were comparable to the values for the non-reinforced connections. This was because, in the case of grade 8.8 10 mm × 125 mm and 12 mm × 135 mm bolts and grade 5.8 12 mm × 135 mm bolts, the laminated veneer lumber (LVL) slabs split both in the reinforced and non-reinforced connections. The toothed-plate connectors reduced timber destruction in the bearing zones in the LVL slabs. However, they did not protect the LVL slabs against splitting. Therefore, the impact of the toothed plate connectors on the stiffness and strength of the bolted connections with grade 8.8 10 mm and 12 mm bolts and with grade 5.8 12 mm bolts analysed in this paper was found to be negligible. In the case of grade 5.8 10 mm bolts, the LVL slabs did not split. The mean slip modulus k_0.6 of the connections with grade 5.8 10 mm bolts reinforced with toothed plate connectors was 2.9 times higher than that of the non-reinforced connections. However, the strength of the connections with grade 5.8 10 mm bolts was 1.2 times lower after reinforcing. This was because the shanks of the bolts were sheared faster in the reinforced connections than in the non-reinforced connections as a result of the bolt shanks being under the bearing pressure of the aluminium flange, the LVL slab, and the toothed-plate flange. This situation did not occur for the remaining connections because they had a higher strength (grade 8.8 bolts) or a larger diameter (12 mm), and their bolts were less prone to cutting off. The investigated load–slip curves of the reinforced bolted connections can be used for designing and numerical modelling of aluminium-timber composite beams with this type of connection. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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22 pages, 11735 KiB

Open AccessArticle

Study on the Seismic Performance of Stiffened Corrugated Steel Plate Shear Walls with Atmospheric Corrosion

by Xiaoming Ma, Yi Hu, Liqiang Jiang, Lizhong Jiang, Guibo Nie and Hong Zheng

Materials 2022, 15(14), 4920; https://doi.org/10.3390/ma15144920 - 14 Jul 2022

Cited by 4 | Viewed by 1620

Abstract

Corrugated steel plate shear walls (CSPWs) with three different stiffening methods are proposed in this paper, including unstiffened CSPWs (USWs), cross stiffened CSPWs (CSWs) and asymmetric diagonal-stiffened CSPWs (ASWs). A numerical model was established by ABAQUS 6.13 based on the validation of an [...] Read more.

Corrugated steel plate shear walls (CSPWs) with three different stiffening methods are proposed in this paper, including unstiffened CSPWs (USWs), cross stiffened CSPWs (CSWs) and asymmetric diagonal-stiffened CSPWs (ASWs). A numerical model was established by ABAQUS 6.13 based on the validation of an existing cyclic test on a CSPW. This paper presents an investigation of the lateral performance under monotonic loading, seismic performance under cyclic loading and seismic performance under atmospheric corrosion of USW, CSW and ASW. The results show that (1) Stiffeners can improve the elastic critical buckling load, the initial stiffness and the ultimate shear resistance of CSPWs, and the effect of asymmetric diagonal stiffeners is more significant than that of cross stiffeners; (2) Stiffeners can improve the energy dissipation capacity and ductility, delay stiffness degradation and reduce the out-of-plane deformation of CSPWs, and the hysteretic performance of ASWs is obviously better than that of CSWs; and (3) Under atmospheric corrosion, stiffeners are conducive to inhibiting buckling and improving the seismic performance of CSPWs, while the seismic performance of CSWs is significantly affected by corrosion, so asymmetric diagonal stiffeners are better than cross stiffeners in improving the seismic performance of CSPWs. Meanwhile, the formula of ultimate shear resistance of corroded specimens is also fitted in this paper, which can provide design suggestions for practical engineering. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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27 pages, 67201 KiB

Open AccessArticle

Experimental Validation of Deflections of Temporary Excavation Support Plates with the Use of 3D Modelling

by Marek Kopras, Wiesław Buczkowski, Anna Szymczak-Graczyk, Zbigniew Walczak and Sławomir Gogolik

Materials 2022, 15(14), 4856; https://doi.org/10.3390/ma15144856 - 12 Jul 2022

Cited by 1 | Viewed by 1454

Abstract

Almost every project is accompanied by earthworks, very often involving various types of excavation, and the work of people in the excavations. One of the most important tasks in earthworks is to ensure that the walls of the excavation are protected against sliding [...] Read more.

Almost every project is accompanied by earthworks, very often involving various types of excavation, and the work of people in the excavations. One of the most important tasks in earthworks is to ensure that the walls of the excavation are protected against sliding and that people working in and around the excavation are safe. Very often, in addition to criteria relating to safety and stability of the excavation, economic considerations are also an important criterion. This issue arises as early as the design stage and is related to the choice of construction and materials of which the shoring is to be made in such a way as to be able to withstand the pressure of the soil, ground loads resulting from stored excavated material and the operation of working machinery. Ongoing monitoring of the excavations and their reinforcement is also very important. The paper describes the unique results of experimental field tests, the purpose of which was to analyse the values of deflections of steel support plates of temporary excavation carried out on the object in 1:1 scale. The course of the experiment is presented for excavation support plates with a total depth of 6 m. Direct tests of the deflection arrow were carried out using two techniques, traditionally with a patch, and with laser scanning. Field tests were carried out for the designed situation without backfill load as well as for backfill load of 3.84, 15.36, 26.88 and 38.4 kN·m⁻², respectively, for two measurement stages. Stage-I of the study consisted in collecting the results for soil in intact condition, whereas Stage-II collected results for loosened soil. The research experiment was supported by numerical calculations performed using the finite difference method in variational approach. The measured maximum deflections ranged from 14.40 to 16 mm, and the calculated values were 14.95 and 14.99 mm. The comparison of calculation results and tests proved to be very consistent. The analysis of the values of deflections showed that backfill load does not have a significant effect on the deflection of the lower plate, but it does affect the deflection of the first plate up to a depth of 1.2 m. Based on the obtained results, it is recommended to assume the limit (maximum) deflection arrow for support plates of temporary excavations at least as w_gr = L/130, where L is the span of the plate. The calculation of deflection values was based on deflection values obtained experimentally and numerically for two steel variants: S235JR and S355JR. The w_gr indicator of the maximum deflection arrow proposed by the authors is not stipulated by the industry standards, but it can be very helpful for the designing of excavation reinforcement. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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Review

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18 pages, 2035 KiB

Open AccessReview

Review on Stress-Fractional Plasticity Models

by Pengfei Qu, Yifei Sun and Wojciech Sumelka

Materials 2022, 15(21), 7802; https://doi.org/10.3390/ma15217802 - 04 Nov 2022

Cited by 2 | Viewed by 1410

Abstract

Fractional calculus plays an increasingly important role in mechanics research. This review investigates the progress of an interdisciplinary approach, fractional plasticity (FP), based on fractional derivative and classic plasticity since FP was proposed as an efficient alternative to modelling state-dependent nonassociativity without an [...] Read more.

Fractional calculus plays an increasingly important role in mechanics research. This review investigates the progress of an interdisciplinary approach, fractional plasticity (FP), based on fractional derivative and classic plasticity since FP was proposed as an efficient alternative to modelling state-dependent nonassociativity without an additional plastic potential function. Firstly, the stress length scale (SLS) is defined to conduct fractional differential, which influences the direction and intensity of the nonassociated flow of geomaterials owing to the integral definition of the fractional operator. Based on the role of SLS, two branches of FP, respectively considering the past stress and future reference critical state can be developed. Merits and demerits of these approaches are then discussed, which leads to the definition of the third branch of FP, by considering the influences of both past and future stress states. In addition, some specific cases and potential applications of the third branch can be realised when specific SLS are adopted. Full article

(This article belongs to the Special Issue Experimental Research and Computational Analysis of Eco- and Bio-Materials)

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