Krishna Kannan

A rigorous, comprehensive, and thermodynamically consistent theory has been developed for the fused deposition modelling (FDM) of semi-crystalline polymers. It is sufficiently general in that it can accommodate multiple phase transition mechanisms (crystallization, glass transition, and melting) during the heating and cooling cycles of the process encountered during FDM. The theory predicts the residual stresses and the resulting warpage in the polymer part due to the temperature-dependent, spatially varying specific volumes of each phase, precipitated by the inhomogeneous distribution of temperature. The theory treats the semi-crystalline polymer as a constrained mixture of multiple phases, where glass is assumed to be a new phase of the polymer. The statistically based Avrami kinetics for crystallization, modified for non-isothermal processes, is recovered as a particular case of our non-equilibrium thermodynamic analysis. Moreover, the theory predicts the temperature corresponding to the local free energy minima as the ideal glass transition temperature analogous to that of Franz and Parisi's mean field theory with a statistical basis.

A thermodynamic framework has been developed for a class of amorphous polymers used in fused deposition modeling (FDM), in order to predict the residual stresses and the accompanying distortion of the geometry of the printed part (warping). When a polymeric melt is cooled, the inhomogeneous distribution of temperature causes spatially varying volumetric shrinkage resulting in the generation of residual stresses. Shrinkage is incorporated into the framework by introducing an isotropic volumetric expansion/contraction in the kinematics of the body. We show that the parameter for shrinkage also appears in the systematically derived rate-type constitutive relation for the stress. The solidification of the melt around the glass transition temperature is emulated by drastically increasing the viscosity of the melt. In order to illustrate the usefulness and efficacy of the constitutive relation that has been developed, we consider four ribbons of polymeric melt stacked on top of each other such as those extruded using a flat nozzle: each layer laid instantaneously and allowed to cool for one second before another layer is laid on it. Each layer cools, shrinks and warps until a new layer is laid, at which time the heat from the newly laid layer flows into the previous laid layer and heats up the bottom layers. The residual stresses of the existing and newly laid layers readjust to satisfy equilibrium. Such mechanical and thermal interactions amongst layers result in a complex distribution of residual stresses. The plane strain approximation predicts nearly equibiaxial tensile stress conditions in the core region of the solidified part, implying that a preexisting crack in that region is likely to propagate and cause failure of the part during service. The free-end of the interface between the first and the second layer is subjected to the largest magnitude of combined shear and tension in the plane with a propensity for delamination.

We develop a 3D nonlinear viscoelastic model for filled elastomeric solids that exhibit good predictive capabilities across multiple deformation modes and strain rates using at most 11 parameters. Through the analysis-driven construction of the rate of dissipation within the rate-type thermodynamic framework of Rajagopal and Srinivasa (2000), we reduce the number of parameters and also introduce the mode-of-deformation-rate dependent viscosity (ηm(K3)) into the constitutive relations. The special form of ηm(K3) accounts for higher values of viscosity in tension as compared to that of other modes of deformation. The broad spectrum of relaxation times exhibited by the elastomers are characterized by categorizing it into short, medium, and long relaxations, each assumed to be associated with one of the three natural configurations. The strong mode-dependent response exhibited by HNBR50, where the compression–relaxation is faster than tension–relaxation, is predicted accurately only when all the natural configurations are active. In contrast, the response of NR is predicted by using just two natural configurations because the polymer molecules are restricted to two extremes of the relaxation spectrum as a consequence of the high affinity between carbon black and the polymer molecules. The entire model is implemented in Abaqus/Standard through the user subroutine UMAT that interacts with an external solver, DDASPK, which solves for the internal variables. We show that the analytical form for the consistent Jacobian can be derived, and establish the efficacy of the implementation by simulating non-homogeneous shear on a hockey puck geometry made of HNBR50 with a concave lateral surface. The simulation shows good agreement with experimental data.

We use the theory developed by [43] to simulate in Abaqus the printing of a drug-eluting bioresorbable stent (BRS), which is used to treat a stenosed renal artery, by fused deposition modeling (FDM). The stent is assumed to be printed using a semi-crystalline polylactic acid (PLA). We control the process parameters to architect the microstructure of the stent such that the stent has an amorphous glassy phase on a crystalline backbone, which would ensure sufficient strength along with the regulated release of the drug into the bloodstream. Through this simulation, we highlight those regions in the stent geometry that should adhere to strict quality control requirements during the fabrication process. In this regard, it is observed that a preexisting crack at the core of the third layer has a very high tendency to propagate along the ‘r’ or ‘z’ direction, whereas a preexisting crack at the core of the second layer has a very high tendency to propagate along the ‘r’ direction, thus increasing the probability of an intra-layer delamination process during service. Similarly, the stent has a high chance of inter-layer delamination between the second and third layers by the mode-I mechanism for cracking. Moreover, the final cup-like warped geometry of the stent could injure the arterial wall during deployment by balloon expansion and also during service, thus increasing the risk of neointimal hyperplasia.

We develop new rate-type constitutive relations on a set of orthonormal tensor basis and the corresponding set of Lode invariants, which require only 9 material parameters to predict the mechanical response of the human brain tissue. The mode-dependent response of the tissue is captured by invoking the Hill-stable elastic potential of Prasad and Kannan (2020) and constructing a new form for the rate of dissipation, thus introducing the mode-of-deformation dependent modulus terms and the mode-of-deformation-rate dependent viscosities into the rate-type thermodynamic framework of Rajagopal and Srinivasa (2000). Through the analysis-driven construction of the rate of dissipation, we incorporate maximum change in the viscosities with respect to the mode-of-deformation rates and limit the number of material parameters. Our model satisfactorily predicts the complicated load-unload cycles (pre-conditioned and conditioned) and the stress relaxation data under multiple modes of deformation and multiple rates for the Corona Radiata (CR) region of the brain tissue. It also captures the tension–compression asymmetry in the response and the higher relaxation time in compression loading than in shear loading.