Macroscopic Mechanical Response Research Articles

Exploring the micro-to-macro response of granular soils with real particle shapes by way of μCT-aided DEM analyses

This contribution provides high-fidelity images of real granular materials with the aid of X-ray micro-computed tomography (μCT), and employs a multi-sphere representation to reconstruct non-spherical particles. Through discrete-element method (DEM) simulations of granular samples composed of these non-spherical clumps, the effect of particle shape on the macroscopic mechanical response and microscopic soil fabric evolution is examined for soil assemblies under triaxial compression. Simulation results indicate that materials with more irregular particles tend to show higher shear resistance in both peak and critical states, while exhibiting higher void ratio under isotropic loading conditions and in the critical state. The proposed critical state parameters for describing the sensitivity of the mean coordination number to confining pressures are larger as particles become more irregular. At a microscopic level of observation, directional and scalar parameters of particle contacts are sensitive to predefined particle shapes. More irregular materials appear to exhibit higher fabric anisotropy with respect to particle orientation in the critical state, while the branch vector is affected by both contact modes and particle shape. The critical stress ratio from the simulation results is validated by comparing with experimental results, and further found to be linearly linked to the shape-weighted fabric anisotropy indices.

In-Situ synchrotron investigation of elastic and tensile properties of oxide dispersion strengthened EUROFER97 steel for advanced fusion reactors

The augmentation of mechanical properties of reduced activation ferritic martensitic steels through the introduction of creep resistant nano-oxide particles produces a class of oxide dispersion strengthened steels, which have attracted significant interest as candidates for first wall supporting structural materials in future nuclear fusion reactors. In the present work, the effect of temperature on the elastic properties and micro-mechanics of 0.3 wt% Y2O3 oxide dispersion strengthened steel EUROFER97 is investigated using synchrotron high energy X-ray diffraction in-situ tensile testing at elevated temperatures, alongside the non-oxide strengthened base steel as a point of comparison. The single crystal elastic constants of both steels are experimentally determined through analysis of the diffraction peaks corresponding to specific grain families in the polycrystalline samples investigated. The effect of temperature on the evolving dislocation density and character in both materials is interrogated, providing insight into deformation mechanisms. Finally, a constitutive flow stress model is used to evaluate the factors affecting yield strength, allowing the strengthening contribution of the oxide particles to be assessed, and correlation between the thermally driven microstructural behaviour and macroscopic mechanical response to be determined.

NEPE Propellant Mesoscopic Modeling and Damage Mechanism Study Based on Inversion Algorithm.

To accurately characterize the mesoscopic properties of NEPE (Nitrate Ester Plasticized Polyether) propellant, the mechanical contraction method was used to construct a representative volume element (RVE) model. Based on this model, the macroscopic mechanical response of NEPE propellant at a strain rate of 0.0047575 s-1 was simulated and calculated, and the parameters of the cohesive zone model (CZM) were inversely optimized using the Hooke-Jeeves algorithm by comparing the simulation results with the results of the uniaxial tensile test of NEPE propellants. Additionally, the macroscopic mechanical behavior of NEPE composite solid propellants at strain rates of 0.00023776 s-1 and 0.023776 s-1 was also predicted. The mesoscopic damage evolution process of NEPE propellants was investigated by the established model. The study results indicate that the predicted curves are relatively consistent with the basic features and change trends of the test curves. Therefore, the established model can effectively simulate the mesoscopic damage process of NEPE composite solid propellants and their macroscopic mechanical properties.

Research on the Influence Mechanism of Moisture Content on Macroscopic Mechanical Response and Microscopic Evolution Characteristic of Limestone

The uniaxial compression experiments and acoustic emission (AE) monitoring are conducted to investigate the macroscopic mechanical behavior and microscopic fracture characteristics of limestone samples with varying moisture contents. The findings revealed that as the moisture content increases from 0 to 6.6%, there is a decrease in peak stress and an increase in peak strain. A clear trend towards greater complexity in fracture characteristics is observed with increasing moisture content. In addition, AE activities demonstrate a heightened frequency, accompanied by an elevation in the corresponding multifractal parameter Δα as the moisture content rises. These variations are attributed to the increase in moisture content, which promotes the proliferation of small-scale microcracks and inhibits their evolution into large-scale microcracks. Consequently, the damage and failure process of the limestone samples transitions from being predominantly controlled by a few large-scale microcracks to being collectively influenced by a multitude of small-scale microcracks as the moisture content increases. In conjunction with the Criterion of Microcrack Density, the correctness of the analysis above is substantiated through mathematical derivation. Further, a quantitative model that links the microcrack system to moisture content is established based on the multifractal parameter Δα. Following this, a characterization model that depicts the macroscopic mechanical properties of limestone affected by moisture content is developed. This model effectively encapsulates the quantitative relationship between moisture content and the macroscopic characteristics of limestone and is validated through fitting experimental data. This research contributes to understanding the macroscopic mechanical response and microscopic fracture characteristics of limestone samples with different moisture contents, providing valuable insights and guidance for ensuring safety during engineering construction processes.

Evolution of microstructure and deformation mechanisms in a metastable Fe42Mn28Co10Cr15Si5 high entropy alloy: A combined in-situ synchrotron X-ray diffraction and EBSD analysis

In this work, a combination of in-situ high synchrotron X-ray diffraction and electron backscattered diffraction were used to systematically investigate the activation and evolution of the deformation mechanisms in an as-cast Fe42Mn28Co10Cr15Si5 metastable high entropy alloy deformed until fracture at room temperature. This work unveils the critical role of the dual-phase γ-f.c.c. / ε-h.c.p. microstructure on the deformation response of the alloy. The different deformation modes, i.e., slip, transformation induced plasticity (TRIP) and transformation induced twinning (TWIP), were seen to initiate at different loading stresses and then to overlap. Quantitative microstructural characterization, which included the evolution of the phase fraction, stress partitioning, dislocation density, c/a ratio and lattice strain for different planes, was performed to elucidate the role of each phase on the macroscopic mechanical response of the metastable high entropy alloy. Furthermore, the magnitude of the different strengthening contributions has been quantified for the first time.

The alteration of the structure and macroscopic mechanical response of porcine patellar tendon by elastase digestion.

Background: The treatment of patellar tendon injury has always been an unsolved problem, and mechanical characterization is very important for its repair and reconstruction. Elastin is a contributor to mechanics, but it is not clear how it affects the elasticity, viscoelastic properties, and structure of patellar tendon. Methods: The patellar tendons from six fresh adult experimental pigs were used in this study and they were made into 77 samples. The patellar tendon was specifically degraded by elastase, and the regional mechanical response and structural changes were investigated by: (1) Based on the previous study of elastase treatment conditions, the biochemical quantification of collagen, glycosaminoglycan and total protein was carried out; (2) The patellar tendon was divided into the proximal, central, and distal regions, and then the axial tensile test and stress relaxation test were performed before and after phosphate-buffered saline (PBS) or elastase treatment; (3) The dynamic constitutive model was established by the obtained mechanical data; (4) The structural relationship between elastin and collagen fibers was analyzed by two-photon microscopy and histology. Results: There was no statistical difference in mechanics between patellar tendon regions. Compared with those before elastase treatment, the low tensile modulus decreased by 75%-80%, the high tensile modulus decreased by 38%-47%, and the transition strain was prolonged after treatment. For viscoelastic behavior, the stress relaxation increased, the initial slope increased by 55%, the saturation slope increased by 44%, and the transition time increased by 25% after enzyme treatment. Elastin degradation made the collagen fibers of patellar tendon become disordered and looser, and the fiber wavelength increased significantly. Conclusion: The results of this study show that elastin plays an important role in the mechanical properties and fiber structure stability of patellar tendon, which supplements the structure-function relationship information of patellar tendon. The established constitutive model is of great significance to the prediction, repair and replacement of patellar tendon injury. In addition, human patellar tendon has a higher elastin content, so the results of this study can provide supporting information on the natural properties of tendon elastin degradation and guide the development of artificial patellar tendon biomaterials.

Study on Dynamic Parameters and Energy Dissipation Characteristics of Coal Samples under Dynamic Load and Temperature

Coal and rock dynamic disasters such as rock burst and outburst seriously threaten the sustainable development of the coal mining industry, which are intimately correlated with the nonlinear dynamic response process of the deep coal and rock mass. This study conducts coal dynamic experiments under vibration load from room temperature to 60 °C by using the split Hopkinson bar (SHPB) with a temperature real-time control system and analyzes the variation in stress and strain and the energy dissipation characteristics of coal during the dynamic load process. The expression equation of dissipated energy of coal at different scales is established, and the judgment conditions of the macroscopic mechanical behavior of coal are analyzed theoretically. The stress curves show a multi-stress peak phenomenon when the coal samples are subjected to different temperatures and dynamic loads, and the coal’s dynamic stress and temperature show a polynomial fitting relationship at different stages. When the coal sample is subjected to temperature and dynamic load, the macroscopic changes in incident energy, reflected energy, and dissipated energy are consistent; that is, various energies gradually increase to a fixed value and tend to stabilize with the time of stress wave action. The transmission energy exhibits a rising trend in correlation with the duration of the dynamic load action, but the value is less than 0.1 J. The growth gradients of the different energies, in descending order, are: the growth gradient of incident energy, reflection energy, dissipation energy, and transmission energy. The energy inflection point appears at 60 °C. Based on the linear elastic fracture mechanics and damage mechanics theories, the expression for coal energy dissipation from the nanoscale to the microscale is established, and the relationship between energy dissipation and macroscopic mechanical behavior response of the coal samples is analyzed. The main physical components of the coal sample are calcite and kaolinite. Within the temperature range of 18–60 °C, the macroscopic failure form of the coal is horizontal tensile failure. The study results are introduced into dynamic disaster prevention and control and the surrounding rock system stability evaluation in deep mines.

The anisotropic grain size effect on the mechanical response of polycrystals: The role of columnar grain morphology in additively manufactured metals

Additively manufactured (AM) metals exhibit highly complex microstructures, particularly in terms of grain morphology which typically features heterogeneous grain size distribution, irregular and anisotropic grain shapes, and the so-called columnar grains. The conventional morphological descriptors based on grain shape idealization are generally inadequate for representing complex and anisotropic grain morphology of AM microstructures. The primary aspect of microstructural grain morphology is the state of grain boundary spacing or grain size whose effect on the mechanical response is known to be crucial. In this paper, we formally introduce the notion of axial grain size from which we derive mean axial grain size, effective grain size, and grain size anisotropy as robust morphological descriptors capable of effectively representing highly complex grain morphologies. We instantiated a discrete sample of polycrystalline aggregate as a representative volume element (RVE) featuring random crystallographic orientation and misorientation distributions. However, the instantiated RVE incorporates the typical morphological features of AM microstructures including distinctive grain size heterogeneity and anisotropic grain size owing to its pronounced columnar grain morphology. We ensured that any anisotropy observed in the macroscopic mechanical response of the instantiated sample primarily originates from its underlying anisotropic grain size. The RVE was then employed for mesoscale full-field crystal plasticity simulations corresponding to uniaxial tensile deformation along various axes via a spectral solver and a physics-based crystal plasticity constitutive model which was developed, calibrated, and validated in earlier studies. Through the numerical analyses, we isolated the contribution of anisotropic grain size to the anisotropy in the mechanical response of polycrystalline aggregates, particularly those with the characteristic complex grain morphology of AM metals. This contribution can be described by an inverse square relation.

Influence of microscopic parameters on the macroscopic mechanical response of sand

In order to study the influence of microscopic parameters on the macroscopic mechanical response of sand, the discrete element software PFC3D is used to establish the numerical model of the triaxial test of sand in this paper, the indoor triaxial test of sand is carried out to calibrate the numerical model. The triaxial tests are finished under the conditions of confining pressures of 100 kPa, 200 kPa, 300 kPa, and 400 kPa, respectively. The influence of the microscopic parameters on the macroscopic mechanical response of the sand is analyzed, the orthogonal experimental method is used to study the sensitivity of the numerical model to microscopic parameters such as porosity, flexible boundary stiffness, normal tangential stiffness ratio, and friction coefficient. The results show that the peak strength and residual strength of the stress-strain curve of sand are most affected by the friction coefficient, they are positively correlated with the friction coefficient under different confining pressures. The normal tangential stiffness ratio is negatively correlated, it is less affected by porosity and boundary flexibility stiffness, the sensitivities of different microscopic parameters are analyzed through the orthogonal tests, the results of orthogonal tests and numerical simulations show the consistent patterns in terms of sensitivity to microscopic parameters. The results can provide the reference for the influence of microscopic parameters and the macroscopic mechanical response of sand.

Investigation into the fracture behavior of ZK60 Mg alloy rolling sheet under different stress triaxiality

In order to investigate the fracture behavior of the ZK60 Mg alloy rolling under different stress triaxiality, the different nominal stress triaxiality samples were well-designed, and the in-situ DIC tensile tests were carried out. The finite element method (FEM) model was validated by experimental results and the stress triaxiality evolution of samples was determined by modeling. The fracture strain of the ZK60 Mg alloy was non-monotonic with the nominal stress triaxiality increase and the best deformation performance of the central hole sample was indicated via the experimental and modeling results. The low stress triaxiality gradient of the central hole sample led to better deformation performance in terms of the macroscopic mechanical response. The transformation of the fracture mechanism from shear transgranular fracture to intergranular fracture and then to transgranular fracture during the stress triaxiality increased from 0 to 2/3 and was revealed via scanning electron microscope (SEM) characterization and FEM modeling. To further confirm the above fracture mechanism, X-ray computed tomography (XCT) was carried out to characterize the micro damage volume fraction and morphology. Due to the transgranular fracture induced by the high stress triaxiality at the initial fracture position of the central hole sample, the micro damage was smaller, delaying the fracture failure and achieving higher strain.

A mesoscopic constitutive model for woven fabrics with large deformation

The meso-structure of woven fabrics plays a pivotal role in enabling significant deformations. To precisely characterize the deformation behavior of woven fabrics, a mesoscale model based on their meso-structure is developed. In this model, the fiber yarn is represented as a Timoshenko beam with fluctuations described by the shape function. A novel approach is proposed to establish the relationship between the macroscopic mechanical response and the infinitesimal strain of the beam, employing the principle of virtual work. The shearing behavior of woven fabrics is characterized by considering friction energy dissipation and transverse compression among fiber yarns. The general applicability of the proposed model is validated through its application to glass fiber woven fabrics and jute fiber woven fabrics. The model parameters are determined through uniaxial tensile and bias-extension experiments. The accuracy of the model is verified using bias-extension and picture frame experiments. The results demonstrate that the proposed model can effectively simulate the large deformation of woven fabrics.

Study on Deformation Mechanism of Saturated Sand Based on Discrete Element Method

Based on the discrete element program (particle flow code PFC3D), the effects of the initial void ratio on the macroscopic and microscopic mechanical responses, phase transition state and critical state characteristics of saturated sand are systematically investigated in drained tests. The phenomenon that saturated sand enters the critical state earlier than the laboratory macroscopic results is revealed from the microscopic point of view. The results show that the phase transition state of the saturated sand can be reflected by the extreme values of void ratio, sliding ratio, suspended particle ratio and mechanical coordination number. Compared to the macroscopic parameters stress ratio and volume strain, the microscopic parameters can earlier reveal the critical state of saturated sand. The saturated sands with different initial void ratios have the same anisotropy component at the critical state. At the phase transition state, only the weight of normal contact force anisotropy is in the peak state. During the development of saturated sand from shrinkage to dilatancy, the velocity of particle motion on the diagonal 45° shear surface of the sample is intense and the particle motion is dominated by rotation. The above conclusions expand the current understanding of the deformation mechanism at the phase transition state and critical state of the soil.

Thermomechanical Coupling in Polydomain Liquid Crystal Elastomers

Abstract Liquid crystal elastomers (LCEs) are made of liquid crystal molecules integrated with rubber-like polymer networks. An LCE exhibits both the thermotropic property of liquid crystals and the large deformation of elastomers. It can be monodomain or polydomain in the nematic phase and transforms to an isotropic phase at elevated temperature. These features have enabled various new applications of LCEs in robotics and other fields. However, despite substantial research and development in recent years, thermomechanical coupling in polydomain LCEs remains poorly studied, such as their temperature-dependent mechanical response and stretch-influenced isotropic-nematic phase transition. This knowledge gap severely limits the fundamental understanding of the structure-property relationship, as well as future developments of LCEs with precisely controlled material behaviors. Here, we construct a theoretical model to investigate the thermomechanical coupling in polydomain LCEs. The model includes a quasi-convex elastic energy of the polymer network and a free energy of mesogens. We study the working conditions where a polydomain LCE is subjected to various prescribed planar stretches and temperatures. The quasi-convex elastic energy enables a “mechanical phase diagram” that describes the macroscopic effective mechanical response of the material, and the free energy of mesogens governs their first-order nematic-isotropic phase transition. The evolution of the mechanical phase diagram and the order parameter with temperature is predicted and discussed. Unique temperature-dependent mechanical behaviors of the polydomain LCE that have never been reported before are shown in their stress-stretch curves. These results are hoped to motivate future fundamental studies and new applications of thermomechanical LCEs.

Internal Elastic Strains of AZ31B Plate during Unloading at Twinning-Active Region

Magnesium alloys, being the lightest structural metals, have garnered significant attention in various fields. The characterization of inelastic behavior has been extensively investigated by researchers due to its impact on structural component performance. However, the occurrence of twinning in the absence of any applied driving force during unloading has lacked reasonable explanations. Moreover, the influence of deformation mechanisms other than twinning on inelastic behavior remains unclear. In this study, uniaxial tension and compression tests were conducted on hot-rolled magnesium alloy plates, and neutron diffraction experiments were employed to characterize the evolution of macroscopic mechanical response and microscopic mechanisms. Additionally, a twinning and detwinning (TDT) model based on the elastic visco-plastic self-consistent (EVPSC) model has been proposed, incorporating back stress to describe the deformation behavior during stress relaxation. This approach provides a comprehensive understanding of the inelastic behavior of magnesium alloys from multiple perspectives and captures the influence of microscale mechanisms. A thorough understanding of the inelastic behavior of magnesium alloys and a reasonable explanation for the occurrence of twinning under zero-stress conditions offer valuable insights for the precise design of magnesium alloy structures.

In situ X-ray tomography study on internal damage evolution of solid propellant for carrier rockets

Nitrate Ester Plasticized Polyether (NEPE) propellant has been widely used for carrier rockets. However, the propellant is usually subjected to complex loads, changing the microstructures, which eventually affects its structural integrity. To elucidate the damage mechanism of the propellant, an in situ tensile testing rig with a maximum strain rate of 0.1 s−1 was developed with high-resolution synchrotron X-ray tomography. The internal microstructure and the resultant damage evolution have been characterized quantitatively. The mechanical behaviour of sampled propellant was extracted from the dynamic mechanical analysis. In addition, numerical simulation in terms of the spatial geometry of filler particles was performed in the framework of the micromechanical approach. To visualize the debonding process, a cohesive-zone model was employed to trace the debonding at the filler/matrix interface and then the damage evolution was characterized according to the cohesive behaviour. The results can assist in correlating the cohesive behaviour due to local heterogeneity with the macroscopic mechanical response for the NEPE propellant.

3D mesoscale investigation on the compressive fracture of concrete with different aggregate shapes and interface transition zones

The purpose of this work is to investigate the effect of aggregate shape parameters and interface transition zone (ITZ) thickness on the mechanical properties and failure behavior of concrete under uniaxial compression. A 3D mesoscopic model including mortar, shape-alterable aggregate and thickness-controllable ITZ was established in ABAQUS software by programming. Based on the concrete damaged plasticity (CDP) method and the cohesive element approach, the simulation analysis was carried out from the aspects of macroscopic mechanical response, macroscopic failure morphology, mesoscale fracture propagation, and energy dissipation. Results indicate that polyhedral aggregate and spherical aggregate have no significant effect on the macroscopic mechanical properties of concrete. Aggregates with sharp edges and corners may cause concrete to be destroyed into more fragments. The ITZ with 0 thickness and medium thickness can predict the compressive strength of concrete, ITZ model with solid thickness is more suitable for meso-crack research. Thinner solid ITZ fits poorly with the experimental value, and the change of ITZ has little influence on polyhedral aggregates. It is proposed to establish a polyhedral aggregate and medium thickness ITZ model for mesoscale concrete numerical simulation.

A Comprehensive Experimental Study on Mechanical Anisotropy and Failure Mode of 3D Printed Gypsum Rocks: From Composition and Microstructure to Macroscopic Mechanical Properties Response

A Comprehensive Experimental Study on Mechanical Anisotropy and Failure Mode of 3D Printed Gypsum Rocks: From Composition and Microstructure to Macroscopic Mechanical Properties Response

Study on the mechanism of water-induced degradation of slip zone soils and FDEM coupled simulation of slopes based on multi-scale characteristic

The evolution of the mechanical properties of slip zone soils had a greater impact on the structure of soil slopes with large upper porosity and excellent infiltration conditions. Especially under the rainfall effect, it was easy to be affected by the infiltration effect of internal injury, which will lay a ‘hidden danger’ for the slope body to trigger sliding in the secondary transformation process. In this paper, based on Haijiao ping landslide in Guizhou, SEM image recognition techniques were used to reveal the water-induced degradation mechanism of the sliding zone soil from multiple scales and the damage parameters were obtained. Meanwhile, the FDEM numerical model was established to simulate the stability of the slope coupled with indoor TCT test results. The results proved that the angle of internal friction decreased linearly with the increase of water content on the macroscopic scale, but the cohesive force showed an increase and then a significant decrease. The effect of matrix suction in the microscopic scale was significant at lower water content, the internal cohesion formed a large number of agglomerate structures to resist external deformation, but the microstructure was loose and porous after sufficient water immersion. The pore space spreads directionally and the area increases by 2.66 times. The cross-scale discrete-finite element coupled simulation method based on image recognition can visually respond to the macroscopic mechanical properties and stability change response of the slope body caused by microscopic damage. The water-induced degradation effect of rainfall on slip zone soils was the inherent factors for the initiation deformation of landslide. The artificial excavation was the external factor that triggered the slope to slide. This type of landslide was more concealed in its natural state and prone to deformation when excavated after long-term rainfall.

Biomechanical modeling of rice seedling stalk based on multi-scale structure and heterogeneous materials

Rice seedling stalks are biologically characterized by multilayer porous structure and multiphase inhomogeneous material properties. This biological properties make it challenging to reveal the biomechanical behavior and damage mechanism of rice seedling stalks under mechanical load. In this research, the mechanical properties of the cell wall in each leaf sheath of rice seedling stalk were measured by nanoindentation, and a three-dimensional (3D) structure model of rice seedling stalk was established using micro-computed tomography (Micro-CT). According to the gray value difference in the CT images, rice seedling stalk was defined as three types of materials: protoplasts, parenchyma cell wall and collenchyma cell wall. A 3D finite element model of rice seedling stalk with heterogeneous material distribution was established based on the mapping relationship of gray value-density-elastic modulus. The accuracy of the model was verified by radial compression and axial tensile tests from three aspects: macroscopic mechanical response, microscopic mechanical behavior, and actual load effect. The results show that the modeling method is fast and reliable, and effectively improves the analytical accuracy of biomechanical properties for living plant materials with multi-layer porous structure characteristics, heterogeneous anisotropic material properties, and high moisture content. It also provides a useful tool for revealing the damage mechanism and quantitative damage evaluation of living plants under mechanical loading. This will be of great help to the optimization of the structure and working parameters of transplanting mechanism.

A physically-based constitutive model for amorphous glassy polymers in large deformations

A physically-based constitutive model for predicting the mechanical response of amorphous glassy polymers at room temperature and low strain rates was established within the frame of thermodynamics and kinematics. In our previous work (Lan et al., 2022b), the concepts of permanent entanglement (PE) and dynamic entanglement (DE) were utilized to reproduce the complicated behavior of amorphous glassy polymers from quasi-static to dynamic loading at temperatures from below to near the glass transition temperature. PE formed by the coiling of macromolecular chains is relatively stable and contributes to the yield and unloading behavior. DE formed by the weak interaction between monomers of adjacent segments is unstable and contributes to the macroscopic yield peak and strain hardening. However, due to including many parameters, the model is not easy to apply in practice. In this work, by ignoring the influence of temperature, the previous model (Lan et al., 2022b) was simplified. Taking polycarbonate (PC) and polystyrene (PS) as examples, the simplified model focused on the macroscopic mechanical behavior under simple compression and cyclic simple compression, analyzed the effects of mesh and specimen size on the evolution of shear bands under plane strain compression, and compared the obvious differences in localized deformation of these two types of amorphous polymers under plane strain compression. In addition, the forging process of PC at room temperature was simulated. By comparing the predictions with the experiments, it is demonstrated that the simplified model can reproduce the macroscopic mechanical response of amorphous polymers under simple compression, cyclic simple compression, plane strain compression and forging.