Youqi Wang

Multi-chain digital element analysis in textile mechanics

Abstract The concept of multi-chain digital element analysis is established. This new approach is a general numerical tool for textile mechanics. It can be used for textile process design and for fabric deformation, strength and failure analyses. In multi-chain digital analysis, fabric is considered as an assembly of yarns; furthermore, a yarn is considered as an assembly of fibers. Each fiber is modeled as a frictionless pin-connected rod element chain, defined as “digital chain”. Once the length of these rod elements approaches zero, the digital chain becomes a fully flexible one-dimensional entity with a circular cross section. It imitates the physicality of the fiber. Since a yarn is composed of many fibers, it is modeled as an assembly of digital chains. Contact between digital chains is modeled by contact elements. A procedure, similar to finite element analysis, is adopted. Displacement of fiber inside a fabric is derived based upon the global stiffness matrix and the boundary conditions. As a result, both detailed yarn paths and cross-section shape can be traced during the textile forming process or fabric deformation. In order to describe the new concept, two numerical examples are presented. The multi-chain digital element approach is used for the simulation of the two-dimensional weaving and three-dimensional braiding processes. One can observe, section-by-section, the yarn cross-section shape inside the woven and braided fabric.

Digital-element simulation of textile processes

Abstract This paper establishes the concept of a digital-element. A digital-element model was developed to simulate textile processes and determine the micro-geometry of textile fabrics. It models yarns by a pin-connected digital-rod-element chain. As the element length approaches zero, the chain becomes fully flexible, imitating the physicality of yarns. Contacts between yarns are modeled by contact elements. If the distance between two nodes on different yarns approaches the yarn diameter, contact occurs between them. Yarn micro-structure inside the preform is determined by process mechanics, such as yarn tension and inter-yarn friction and compression. The textile process is modeled as a non-linear solid mechanics problem with boundary displacement (or motion) conditions. First, a simple twisting process is simulated, validating the digital-element model. Then, the yarn geometry of a 3-D, four-step braided preform is analyzed. These numerical results reveal the details of yarn paths within the preform. Such results can only be arduously and expensively obtained when achieved through experimental observation, but cannot be generalized; or are inadequately detailed when achieved through existing analytical methods. This makes it possible, therefore, to conduct a quantitative analysis on the distribution of yarn orientation and fiber volume fraction inside a preform. Yet the value of this new model reaches far beyond that of the braiding process. As a general tool, it is advantageous for other textile processes, such as twisting, weaving and knitting and for the investigation of textile preform deformation during the consolidation process. The new numerical approach described here is identified as digital-element simulation rather than as finite-element simulation because of a special yarn discretization process. With the conventional finite-element approach, the element preserves the physical properties of the discretized body. In contrast, with this model the element itself does not preserve physical properties: physical properties are imitated by the element link. The concept is similar to digital discretization. Therefore, the term ‘digital element’ is more appropriate. The size of the element must be very small compared to the size normally employed in finite element analysis.

2-D nano-scale finite element analysis of a polymer field

Abstract Two types of 2-D nano-scale finite elements, the chemical bond element and the Lennard–Jones element, are formulated based upon inter-atomic and inter-molecular force fields. A nano-scale finite element method is employed to simulate polymer field deformation. This numerical procedure includes three steps. First, a polymer field is created by an off-lattice random walk, followed by a force relaxation process. Then, a finite element mesh is generated for the polymer field. Chemical bonds are modeled by chemical bond elements. If the distance between two non-bonded atoms or monomers is shorter than the action range of the Lennard–Jones attraction (or repulsion), a Lennard–Jones element is inserted between them. Finally, external load and boundary conditions are applied and polymer chain deformation is simulated step by step. During polymer deformation, failed Lennard–Jones bond elements are removed and newly formed Lennard–Jones elements are inserted into the polymer field during each loading step. The process continues until failure occurs. Two examples are presented to demonstrate the process. Stress–strain curves of polymer fields under unidirectional tensile load are derived. Continuum mechanical properties, such as modulus and polymer strength, are determined based upon the stress strain curve. Further, throughout the deformation process one observes polymer chain migration, nano-scale void generation, void coalescence and crack development.

A modified self-consistent computational model for an electrostrictive graft elastomer

An electrostrictive graft elastomer, as recently developed by NASA, is a type of electro-active polymer. In this paper, a 2D computational model with a self-consistent boundary is developed. Firstly, three-dimensional deformations, induced by both bending angle and dihedral torsional angle changes, are projected onto a two-dimensional plane. Using both theoretical and numerical analyses, the projected 2D equilibrium bending angle is shown to have the same value as the 3D equilibrium bending angle. The 2D equivalent bending stiffness is derived using a series model based upon the fact that both bending and dihedral torsion produce a configurational change. Equivalent stiffness is justified by polymer chain end-to-end distance characteristics. Secondly, a self-consistent scheme is developed to eliminate the boundary effect. Eight images of the unit cell are created peripherally, with the original unit cell in the center. Thus the boundary can only affect the rotation of the eight images, not the central unit cell. A computational model is employed to determine the electromechanical properties of the electrostrictive graft elastomer. Relations between electric field induced strain and electric field strength are calculated. The effect of molecular scale factors, such as free volume fraction, graft weight percentage and graft orientation, are also discussed.

Field Tests to Determine Static and Dynamic Response to Traffic Loads of Fiber-Reinforced Polyester No-Name Creek Bridge

No-Name Creek Bridge, built in Russell, Kansas, in 1996, is the first all-composite highway bridge in the United States. Its structural panels are built of glass fiber-reinforced polyester sandwich panels with honeycomb cores. The bridge surface is made of polymer concrete. Two static field tests were conducted, one shortly after its completion in 1996, the other in 1997. In September 2004, after 8 years of service, field tests were repeated to examine the environmental effect on the composite materials. Test results were compared with previous results. No significant change of the bridge rigidity was found after 8 years. In addition, dynamic response to moving traffic loads was investigated. An AASHTO Type 3 truck, with a gross weight of 70,340 lb, was used to apply the traffic load to the bridge. Four types of tests were conducted: static loading, crawl speed loading, moving traffic loading, and impact traffic loading. Dynamic factors and natural frequency were measured.

Two-dimensional computational model for electrostrictive graft elastomer

The electrostrictive graft elastomer is a new type of electromechanically active polymer. Recently developed by NASA, it consists of flexible backbone chains, each with side chains, called grafts. Grafts from neighboring backbones physically cross-link and form crystal units. The flexible backbone chains and the crystal graft units are composed of polarized monomers, which contain atoms with electric partial charges, generating dipole moments. Polarized domains are created by dipole moments in the crystal units. When the elastomer is placed into an electric field, external rotating moments are applied to polarized domains. It stimulates the rotation of the polarized crystal graft units, which further induces deformation of the elastomer. In this paper, two-dimensional computational models are established to analyze the deformation mechanism of the graft elastomer.

Modified two-dimensional computational model for electrostrictive graft elastomer

A modified two-dimensional computational model is developed to calculate the electromechanical properties of the electrostrictive graft elastomer. The electrostrictive graft elastomer, recently developed by NASA, is a type of electro-active polymer. In a previous paper, the authors calculated electrostrictive graft elastomer electromechanical properties using a 2-D atomic force field. For this 2-D polymer structure, a much higher electric field was required to produce strain compared with that required in experiments. Two reasons could explain the higher electric field strength: (1) Polymer chain movement is restricted to a 2-D plane rather than to a 3-D plane. Out-plane dihedral torsional angle change would thus not be modeled. For this reason, 2-D polymer chains are less flexible than actual 3-D polymer chains. (2) Boundary effect of the computational model. In the original model, a unit cell consisting of a single graft unit was developed to simulate the deformation of the electrostrictive graft elastomer. The boundary of the unit cell would restrict the rotation of the graft unit. In this paper, a modified 2-D computational model is established to overcome the above problems. Firstly, three-dimensional deformations, induced by both bending angle and dihedral torsional angle changes, are projected onto a two-dimensional plane. Using both theoretical and numerical analyses, the projected 2-D equilibrium bending angle is shown to have the same value as the 3-D equilibrium bending angle. The 2-D equivalent bending stiffness is derived using a series model based upon the fact that both bending and dihedral torsion produce configuration change. The equivalent stiffness is justified by the characteristics of the polymer chain and end-to-end distance. Secondly, a self-consistent scheme is developed to eliminate the boundary effect. Eight images of the unit cell are created peripherally, with the original unit cell in the center. Thus the boundary can only affect the rotation of the eight images, not the central unit cell. The modified 2-D computational model is employed to determine the electromechanical properties of the electrostrictive graft elastomer. Relations between electric field induced strain and electric field strength is calculated. The effect of molecular scale factors, such as free volume fraction, graft weight percentage, and graft orientation are also discussed. The results should enable molecular scale design of the electrostrictive graft elastomer.

Real Scale Simulation of Ballistic Tests for Multi-Layer Fabric Body Armors

The bottle-neck issues to resolve for numerical simulation of real scale ballistic tests of fabric body armors are computer capacity limitation and prohibitive computational cost. It is not realistic to use micro-level computer simulations for an open end design process. Most numerical simulations are only applicable for small scale parametric analyses, which could facilitate apprehension of fabric failure mechanisms during ballistic impact, but not applicable for the design process.In this paper, a sub-yarn model, the digital element approach, is applied to simulate real scale ballistic tests for soft body armors. In this approach, a yarn is discretized into multiple digital fibers and each fiber is discretized into many digital elements. In order to improve efficiency, two hybrid element mesh concepts are investigated: area based hybrid mesh and yarn based hybrid mesh.The area based hybrid mesh procedure is similar to one utilized in the conventional finite element approach. A fine element mesh is adopted in the area near the impact center; a course element mesh in the area far away. However, numerical simulation results show that the stress wave travels along the principal yarns at the speed of sound immediately after ballistic impact. High yarn stress develops quickly from the impact center to a distance along the principal yarn. As such, the area based hybrid mesh approach fails to obtain improved computer efficiency without loss of accuracy.Because the high stress only develops within principal yarns after a ballistic impact, a yarn based hybrid element mesh procedure is adopted. In this procedure, only principal yarns and yarns near principal yarns are discretized into fine digital fibers; other yarns are discretized into coarse digital fibers. Because only a few principal yarns resist load in a typical ballistic impact, the yarn based hybrid technique could improve simulation efficiency up to 90–95% without sacrificing accuracy.A numerical tool is then developed to generate fabric with a yarn based hybrid mesh. Accuracy of the approach is analyzed. The hybrid mesh technique is applied to simulate real scale ballistic tests of ballistic armors made of 4 to 20 piles of 2-D plain woven fabrics. Numerical results are compared to real scale standard ballistic results.Copyright