Modeling rock specimens through 3D printing: Tentative experiments and prospects

Current developments in 3D printing (3DP) technology provide the opportunity to produce rock-like specimens and geotechnical models through additive manufacturing, that is, from a file viewed with a computer to a real object. This study investigated the serviceability of 3DP products as substitutes for rock specimens and rock-type materials in experimental analysis of deformation and failure in the laboratory. These experiments were performed on two types of materials as follows: (1) compressive experiments on printed sand-powder specimens in different shapes and structures, including intact cylinders, cylinders with small holes, and cuboids with pre-existing cracks, and (2) compressive and shearing experiments on printed polylactic acid cylinders and molded shearing blocks. These tentative tests for 3DP technology have exposed its advantages in producing complicated specimens with special external forms and internal structures, the mechanical similarity of its product to rock-type material in terms of deformation and failure, and its precision in mapping shapes from the original body to the trial sample (such as a natural rock joint). These experiments and analyses also successfully demonstrate the potential and prospects of 3DP technology to assist in the deformation and failure analysis of rock-type materials, as well as in the simulation of similar material modeling experiments.     

A robust hyper-elastic beam model under bi-axial normal-shear loadings

In this paper, a simple and robust constitutive model is proposed to simulate mechanical behaviors of hyper-elastic materials under bi-axial normal-shear loadings in the finite strain regime. The Mooney–Rivlin strain energy function is adopted to develop a two-dimensional (2D) normal-shear constitutive model within the framework of continuum mechanics. A motion field is first proposed for combined normal and shear deformations. The deformation gradient of the proposed field is calculated and then substituted into right Cauchy–Green deformation tensor. Constitutive equations are then derived for normal and shear deformations. They are two explicit coupled equations with high-level polynomial non-linearity. In order to examine capabilities of the developed hyper-elastic model, uniaxial tensile responses and non-linear stability behaviors of moderately thick straight and curved beams undergoing normal axial and transverse shear deformations are simulated and compared with experiments. Fused deposition modeling technique as a 3D printing technology is implemented to fabricate hyper-elastic beam structures from soft poly-lactic acid filaments. The printed specimens are tested under tensile/compressive in-plane and compressive out-of-plane forces. A finite element formulation along with the Newton–Raphson and Riks techniques is also developed to trace non-linear equilibrium path of beam structures in large defamation regimes. It is shown that the model is capable of predicting non-linear equilibrium characteristics of hyper-elastic straight and curved beams. It is found that the modeling of shear deformation and finite strain is essential toward an accurate prediction of the non-linear equilibrium responses of moderately thick hyper-elastic beams. Due to simplicity and accuracy, the model can serve in the future studies dealing with the analysis of hyper-elastic structures in which two normal and shear stress components are dominant.     

Dynamic Subsurface Deformation and Strain of Soft Hydrogel Interfaces Using an Embedded Speckle Pattern With 2D Digital Image Correlation

Background

Subsurface mechanisms can greatly affect the mechanical behavior of biological materials, but observation of these mechanisms has remained elusive primarily due to unfavorable optical characteristics. Researchers attempt to overcome these limitations by performing experiments in biological mimics like hydrogels, but measurements are generally restricted due to the spatio-temporal limitations of current methods.

Objective

Utilization of contemporary 3D printing techniques into soft, transparent, aqueous yield-stress materials have opened new avenues of approach to overcoming these roadblocks. By incorporating digital image correlation with such 3D printing techniques, a method is shown here that can acquire full-field deformation of a hydrogel subsurface in real-time.

Methods

Briefly, the method replaces the solvent of a transparent and low polymer concentration yield-stress material with an aqueous hydrogel precursor solution, then a DIC speckle plane is 3D printed into it. This complex is then polymerized using photoinitiation thereby locking the speckle plane in place.

Results

Full-field deformation measurements are made in real-time as the embedded speckle plane (ESP) responds with the bulk to the applied load. Example results of deformation and strain fields associated with indentation, relaxation, and sliding contact experiments are shown.

Conclusions

This method has successfully observed the subsurface mechanical response in the bulk of a hydrogel and has the potential to answer fundamental questions regarding biological material mechanical behaviors.

     

Natural dynamic characteristics of a circular cylindrical Timoshenko tube made of three-directional functionally graded material

The natural dynamic characteristics of a circular cylindrical tube made of three-directional(3 D) functional graded material(FGM) based on the Timoshenko beam theory are investigated. Hamilton’s principle is utilized to derive the novel motion equations of the tube, considering the interactions among the longitudinal, transverse,and rotation deformations. By dint of the differential quadrature method(DQM), the governing equations are discretized to conduct the analysis of natural dynamic charact...     

Comparison of Flow and Transport Experiments on 3D Printed Micromodels with Direct Numerical Simulations

Understanding pore-scale flow and transport processes is important for understanding flow and transport within rocks on a larger scale. Flow experiments on small-scale micromodels can be used to experimentally investigate pore-scale flow. Current manufacturing methods of micromodels are costly and time consuming. 3D printing is an alternative method for the production of micromodels. We have been able to visualise small-scale, single-phase flow and transport processes within a 3D printed micromodel using a custom-built visualisation cell. Results have been compared with the same experiments run on a micromodel with the same geometry made from polymethyl methacrylate (PMMA, also known as Perspex). Numerical simulations of the experiments indicate that differences in experimental results between the 3D printed micromodel and the Perspex micromodel may be due to variability in print geometry and surface properties between the samples. 3D printing technology looks promising as a micromodel manufacturing method; however, further work is needed to improve the accuracy and quality of 3D printed models in terms of geometry and surface roughness.

     

Correction to: Time and Space Fractional Diffusion in Finite Systems

Additive manufacturing technology, or 3D printing, with silica sand has enabled the manufacture of porous rock analogues for the use in experimental studies of geomechanical properties of reservoir rocks. The accurate modelling of the fluid flow phenomena within a reservoir and improving the performance of hydrocarbon recovery require an understanding of physical and chemical interactions of the reservoir fluids and the rock matrix. Therefore, for the 3D printed samples to serve as rock analogues, flow properties have to be equivalent to the petrophysical properties of their natural counterparts, such as Berea sandstone. In this study, sandstones that were 3D printed with silica sand and Poly-Furfuryl alcohol (PFA) binder, were used to investigate interactions between porous media with different fluids. Wettability preference of 3D printed samples was characterized through contact angle measurements, as well as co-current and counter-current spontaneous imbibition experiments. Results indicated that 3D printed sandstones had mixed-wet characteristics due to the high preference of silica grains for polar fluids and the affinity PFA binder to the oleic phase. Printing configurations including binder saturation were found to greatly influence the wettability preference of the 3D printed analogue rocks as higher PFA concentrations resulted in more strongly oil-wet preferences. Efforts to optimize the printing process and challenges to control the wettability preferences of the 3D printed samples are also highlighted.

     

3D打印混凝土各向异性力学性能研究

近年来,混凝土3D打印技术在土木建筑等领域取得了快速的发展和应用。与模板浇筑工艺不同,3D打印在逐行逐层堆叠的建造过程中引入了一定量的层间弱面和空隙,造成了细观非均质性;而且3D打印过程无法自动嵌入钢筋,制备纤维混凝土作为打印材料可有效改善力学性能。本文首先制备了一种适用于挤出型3D打印工艺的玄武岩纤维增强陶砂混凝土,将水平打印层作为XY平面,然后从三个正交方向加载,实验测试了3D打印混凝土的抗压、抗弯等力学性能,提出了各向异性系数及其评估方法。研究结果表明,对于单轴压缩,X方向强度最高,而对于抗弯性能,Y方向强度最高。纤维对挤出型3D打印材料的各向异性影响较大,纤维掺量越大,各向异性越大。     

Finite element formulation for active functionally graded thin-walled structures

For the analysis and design process of smart structures with integrated piezoelectric patches, the finite element method provides an effective simulation approach. In this paper, an attempt on modeling and simulation of the behavior of hybrid active structures is carried out using developed Kirchhoff-type-four-node shell element.The finite element results are compared with reference solutions taking into account the electromechanical responses of smart structures with various geometries, and the results show very high agreement. The main aspect of the application of the proposed element is to predict the behavior of FGM shells containing piezoelectric layers. A set of numerical analyses is performed in order to highlight the applicability and effectiveness of the present finite element model, notably for smart FGM structures. A comprehensive parametric study is conducted to show the influence of material composition, the placement and the thickness of the piezoelectric layers on the deformation of the laminated structure.     

Damage in edge cracking of rolled metal slabs

Materials get damaged under shear deformations. Edge cracking is one of the most serious damage to the metal rolling industry, which is caused by the shear damage process and the evolution of anisotropy. To investigate the physics of the edge cracking process, simulations of a shear deformation for an orthotropic plastic material are performed. To perform the simulation, this paper proposes an elasto-aniso-plastic constitutive model that takes into account the evolution of the orthotropic axes by using a bases rotation formula, which is based upon the slip process in the plastic deformation. It is found through the shear simulation that the void can grow in shear deformations due to the evolution of anisotropy and that stress triaxiality in shear deformations of (induced) anisotropic metals can develop as high as in the uniaxial tension deformation of isotropic materials, which increases void volume. This echoes the same physics found through a crystal plasticity based damage model that porosity evolves due to the grain-to-grain interaction. The evolution of stress components, stress triaxiality and the direction of the orthotropic axes in shear deformations are discussed.     

金属体积成形三维数值仿真的研究进展

金属体积成形是一个具有几何非线性和物理非线性的复杂的塑性大变形问题,采用基于刚塑性／刚粘塑性有限元法的ＣＡＥ仿真技术对其分析,则可掌握其详细的变形规律．本文对体积成形三维有限元仿真技术的发展作了全面的回顾,并详细总结了其中的关键技术、存在的技术难点和发展趋势．     

孔洞缺陷对3D打印Ti-6Al-4V合金疲劳试样应力分布的影响

3D打印金属技术因其个性化及可用于加工复杂零件等显著优点,在医用骨植入体领域得到了快速发展,但3D打印金属材料的孔洞缺陷所引起的应力集中现象严重降低了其疲劳强度,限制了3D打印生物金属材料的运用。本文针对3D打印Ti-6Al-4V合金超声疲劳试样,分析了Micro CT扫描试样得到的三维图像,获得了试样内孔洞缺陷的数量与体积;选择体积分数占比最大的孔洞,采用有限元方法分析了三种不同孔洞分布形式下的局部应力集中现象。研究发现,因空间位置的不同,独立的孔洞、接近自由表面的孔洞、相邻的孔洞三种不同孔洞的分布情况的应力集中系数差异显著。研究结果在一定程度上解释了目前EBM技术打印Ti-6Al-4V合金的孔洞缺陷如何对材料受力后的局部应力情况产生影响。     

三浦折纸超材料结构数字化设计与模型验证

折纸结构在航空航天、柔性电子、汽车船舶和建筑结构等领域具有较好的应用前景. 三浦折纸单元沿三向拓展可构建出三浦折纸超材料结构, 具有高孔隙、可自锁、平面折展、负泊松比、形态可控等特性. 为了便于生成折纸超材料结构的复杂三维模型、推广应用于缓冲吸能结构及可展结构, 本文利用Matlab和Grasshopper软件, 发展了三浦折纸超材料结构的数字化设计方法, 利用数字化建模及3D打印技术, 实现了零厚度及非零厚度三维折纸模型的统一建模, 并开展了物理模型验证分析, 探讨了3D打印制作折纸超材料结构模型的优缺点; 推导了三浦折纸超材料的折痕长度、相对密度、折叠率等特性与几何参数的关系, 利用Abaqus/Explicit软件开展了结构准静态压缩过程分析与验证, 揭示相对密度对结构吸能指标的影响规律. 研究结果表明, 折纸超材料结构数字化设计方法高效、准确, 便于结构选型及优化分析, 所得三维模型结果与理论值吻合较好. 当胞元面板构型、面板厚度及结构折痕总长不变时, 相对密度较小的三浦折纸超材料结构具备更为优异的吸能效率.      

3D打印多孔热固性聚酰亚胺含油复合材料

以氯化钠(NaCl)作为致孔剂与流变性能调节剂,碳纤维(CF)作为增强填料与流变性能调节剂,苯乙炔基封端聚酰胺酸溶液(PAA)作为基体树脂,配制适用于直书写3D打印的复合墨水,室温下打印成形后经热固化处理和NaCl刻蚀去除后制备了多孔热固性聚酰亚胺/碳纤维(TSPI/CF)复合材料. 研究表明:NaCl与CF对复合墨水的流变学性能具有好的调节作用;打印制备的TSPI/CF复合材料具有低的各向同性尺寸收缩和优异的耐热性能,且耐热性能随着CF含量的增加而提高;CF含量升高,TSPI/CF复合材料的孔隙率提高,平均孔径降低,力学性能增强;多孔TSPI/CF复合材料表现出优异的储油、出油性能以及浸油摩擦学性能.      

Coupling Self-Adaptive Meshing-Based Regularization and Global Image Correlation for Spatially Heterogeneous Deformation Characterization

Background

Image-based global correlation involves a class of ill-posed inverse problems associated with speckle quality and deformation gradients on specimen surfaces. However, the method used to simultaneously integrate the prior information related to images and deformations and effectively regularize these inverse problems still faces severe challenges, especially when complex heterogeneous deformation gradients exist over sample surfaces with locally degraded speckle patterns.

Objective

We propose a novel self-adaptive meshing-based regularization for global image correlation to determine spatially complex heterogeneous deformations.

Methods

A virtual truss system with a linearly elastic constitutive relationship is employed to self-adaptively implement surface meshing by numerically balancing the exerted virtual forces under the constraints of the local speckle image quality and deformation gradients. The 2-norm-based condition number of the local stiffness matrix is introduced to ensure numerical stability during meshing.

Results

The algorithms can behave as a smart regularization procedure integrating all the prior information during numerical calculations, consequently achieving an accurate, precise and robust characterization of heterogeneous deformations, as demonstrated by virtual simulations and actual experiments.

Conclusions

The regularization strategy coupled to image-based correlation is also promising for automatic quantification of complex heterogeneous deformations, particularly from images with locally degraded speckle patterns.

     

3D Strain Field Evolution and Failure Mechanisms in Anisotropic Paperboard

Background

Experimental analyses of the 3D strain field evolution during loading allows for better understanding of deformation and failure mechanisms at the meso- and microscale in different materials. In order to understand the auxetic behaviour and delamination process in paperboard materials during tensile deformation, it is essential to study the out-of-plane component of the strain tensor that is, in contrast to previous 2D studies, only achievable in 3D.

Objective

The main objective of this study is to obtain a better understanding of the influence of different out-of-plane structures and in-plane material directions on the deformation and failure mechanisms at the meso- and microscale in paperboard samples.

Methods

X-ray tomography imaging during in-situ uniaxial tensile testing and Digital Volume Correlation analysis was performed to investigate the 3D strain field evolution and microscale mechanical behaviour in two different types of commercial paperboards and in two material directions. The evolution of sample properties such as the spatial variation in sample thickness, solid fraction and fibre orientation distribution were also obtained from the images. A comprehensive analysis of the full strain tensor in paperboards is lacking in previous research, and the influence of material directions and out-of-plane structures on 3D strain field patterns as well as the spatial and temporal quantification of the auxetic behaviour in paperboard are novel contributions.

Results

The results show that volumetric and deviatoric strain, dominated by the out-of-plane normal strain component of the strain tensor, localize in the out-of-plane centre already in the initial linear stress-strain regime. In-plane strain field patterns differ between samples loaded in the Machine Direction (MD) and Cross Direction (CD); in MD, strain localizes in a more well-defined zone close to the notches and the failure occurs abruptly at peak load, resulting in angular fracture paths extending through the stiffer surface planes of the samples. In CD, strain localizes in more horizontal and continuous bands between the notches and at peak load, fractures are not clearly visible at the surfaces of CD-tested samples that appear to fail internally through more well-distributed delamination.

Conclusions

In-plane strain localization preceded a local increase of sample thickness, i.e. the initiation of the delamination process, and at peak load, a dramatic increase in average sample thickening occurred. Different in-plane material directions affected the angles and continuity of the in-plane strain patterns as well as the sample and fracture properties at failure, while the out-of-plane structure affected how the strain fields distributed within the samples.

     

Measurement of deformations on concrete subjected to compression using image correlation

Because the nature of failure in concrete is complicated due to the material heterogeneity, a robust measuring method is essential to obtain reliable deformation data. A nondestructive displacement evaluation system using a digital image cross-correlation scheme, often called computer vision, is developed to make microscopic examinations of the fracture processes in concrete. This is a full-field measuring method that gives an accuracy within the micron range for a 100 mm × 75 mm viewing area. A feedback signal that combines the lateral and axial deformations provides a well-balanced imaging rate both before and after the peak load. Displacement vector diagrams or displacement contour maps of concrete reveal highly nonuniform deformations even in the elastic range. The processes of fracture in concrete are well defined at different deformation levels.     

一种用于层状结构模型的先进计算方法

提出一种针对层状结构模型的先进计算方法。研究的层状结构通常为水平层状板或者层状半空间,结构由横观各向同性（TI）材料组成,材料对称轴指向分层方向。本文方法可以考虑材料的多场耦合特性,即热弹性、多孔弹性和磁电弹性耦合。基于最近提出的傅立叶-贝塞尔级数（FBS）向量函数系和双变量/位置（DVP）方法,建立了本文的先进计算方法。DVP能够无条件稳定地将层矩阵从一层传播到下一层。FBS向量函数系具有以下特点,（1）反映了具有明确类型的广义变形/波,（2）将展开系数预先计算为Love数,然后将其用于涉及问题的模拟。层状地球中的断层（或位错）作用、土-结构相互作用以及近地表地球剖面中的瞬态波等三个典型算例,证明了提出方法的准确性和有效性。     

泡沫铝夹层结构抗冲击性能的近场动力学模拟分析

针对某光学舱所采用的泡沫铝夹层防护结构在破片冲击下的抗冲击性能问题,采用Monte-Carlo方法创建了泡沫铝结构的二维细观模型,在常规态型近场动力学理论中引入了Mises屈服准则和线性各向同性强化模型,建立了近场动力学塑性本构的数值计算框架。基于近场动力学计算程序模拟了低速冲击作用下泡沫铝夹层结构的塑性变形以及有机玻璃背板的裂纹扩展形态,分析了泡沫铝芯材孔隙率对该夹层结构抗冲击性能和损伤模式的影响规律。结果表明：泡沫铝夹层结构良好的塑性变形能力是其发挥缓冲与防护作用的主要因素,并且在一定范围内,泡沫铝芯材孔隙率越高,则夹层结构具有更好的抗冲击性能;当泡沫铝孔隙率从0.4提升到0.7时,泡沫铝对冲击物的动能吸收率从90%提高到99%;模拟结果与实验结果具有较好的一致性,验证了模拟结果的准确性和分析结论的有效性。通过数值模拟,预测了有机玻璃背板的裂纹扩展形态,发现提高泡沫铝的孔隙率能获得更好的防护效果。     

Low frequency acoustic properties of bilayer membrane acoustic metamaterial with magnetic oscillator

A bilayer membrane acoustic metamaterial was proposed to overcome the influence of the mass law on traditional acoustic materials and obtain a lightweight thin-layer structure that can effectively isolate low frequency noise. The finite element analysis(FEA) results agree well with the experimental results.It is proved that the sound transmission losses(STLs) of the proposed structures are higher than those of same surface density acoustic materials. The introduction of the magnetic mass block is different from the traditional design method, in which only a passive mass block is fixed on the membrane. The magnetic force will cause tension in the membrane, increase membrane prestress, and improve overall structural stiffness. The effects of the geometry size on the STLs are discussed in detail. The kind of method presented in this paper can provide a new means for engineering noise control.