Theoretical and Computational Analysis on the Melt Flow Behavior of Polylactic Acid in Material Extrusion Additive Manufacturing under Vibration Field

Material extrusion (ME), an extrusion-based rapid prototyping technique, has been extensively studied to manufacture final functional products, whose forming quality is significantly influenced by the melt flow behavior (MFB) inside the extrusion liquefier. Applied vibration has a great potential to improve the MFB, and thereby promote the forming quality of the built product. To reveal the mechanism, a dynamic model of the melt flow behavior (DMMFB) is established based on fluid dynamics, Tanner nonlinear constitutive equation and Newton’s power law equation. The MFB, i.e., pressure drop, shear stress and apparent viscosity, is investigated without and with different vibration applied. The corresponding finite element analysis (FEA) is then carried out. From the comparison between DMMFB and FEA results, it is concluded that the proposed model is reliable. When vibration is applied onto the extrusion liquefier, the time-domain MFB will change periodically. Its effective value decreases significantly, and further decreases with the increase of vibration frequency or amplitude. This paper provides the theoretical basis to improve the MFB by applied vibration, and thereby to enhance the forming quality of ME products.

A nonlinear creep damage model for salt rock

In the creep tests, stress is no longer a constant and increases gradually under the influence of damage occurring during accelerating creep, which is a slow-loading process rather than a conventional creep. With the accumulation of the damage over time, the actual stress increases greatly. The increased actual stress not only generates loading strain but also causes the steady creep rate to rise. This coupling possibly explains why salt rock presents nonlinear accelerating characteristics at the accelerating creep stage. In this work, the constraint of the present creep concept was overcome by assuming that the acceleration creep phase is a coupling process of loading and creeping. Furthermore, we demonstrate that the total strain in this phase is equal to the sum of loading strain and creeping strain. A new nonlinear constitutive equation for creep was then derived, and the mechanisms underlying the nonlinear accelerating characteristics emerging at the stage of accelerating creep are further explained. A step-loading experiment on salt rock was performed for a period of six months. The characteristics of accelerating creep appeared in the last step of loading. This new nonlinear creep damage constitutive model was used to fit and analyze the test data. Obtained results show that this model fits well to these test data and also favorably represents the nonlinear characteristics of accelerating creep, thus supporting the model’s validity.

MODELING THE EFFECT OF VAN DER WAALS ATTRACTION ON THE INSTABILITY OF ELECTROSTATIC CANTILEVER AND DOUBLY-SUPPORTED NANO-BEAMS USING MODIFIED ADOMIAN METHOD

A nano-scale continuum model is applied to investigating the effect of van der Waals (vdW) attraction on pull-in instability of nano-beams in the presence of electrostatic forces. Two cases including the cantilever and doubly-supported beams are considered. The modified Adomian decomposition (MAD) method is employed to solve the nonlinear constitutive equation of nano-beams in the presence of vdW and electrostatic forces for the first time. The results show that the effect of vdW attraction on the instability of the doubly-supported nano-beam is weak when compared to that of the cantilever due to the higher elastic stiffness of the former. Basic design parameters such as the critical deflection and pull-in voltage of the nano-beam are computed. The minimum initial gap and the detachment length of an actuator that does not stick to the substrate due to intermolecular attractions are determined. As a special case, the instability of freestanding nano-electromechanical systems (NEMS) due to vdW attraction is investigated. The MAD solutions are compared with the numerical ones and a proposed lumped model, as well as models available from the literature.

Nonlinear Constitutive Equation and Elastic Constant of Rubber Material

In-depth study of compressible material constitutive equation, using incompressible condition, the nonlinear incompressible elastic solid’s complete irreducible constitutive equation and strain energy function expressed in invariants are derived in this essay. The elastic constants of rubber material are given by fitting the experiment data that was carried out by Treloar with the equation. Then we got evelen exact value of the elastic constants.

SIMULATING DEFLECTION AND DETERMINING STABLE LENGTH OF FREESTANDING CARBON NANOTUBE PROBE/SENSOR IN THE VICINITY OF GRAPHENE LAYERS USING A NANOSCALE CONTINUUM MODEL

Herein, the deflection and instability of a freestanding carbon nanotube (CNT) probe/sensor in the vicinity of the graphene layers are investigated. A nanoscale continuum model is employed to obtain nonlinear constitutive equation of freestanding CNT. The van der Waals attraction is computed from the simplified Lennard-Jones potential for two common engineering cases including large and small number of graphene layers. Four approaches, i.e., approximated function, homotopy perturbation method, lumped parameter model and numerical analysis, are employed to solve the governing equation of CNT. The intermolecular force-induced deflection, minimum initial gap and stable length of freestanding CNT are determined. The analytical results agree well with the numerical solutions.