Computational Mechanics

This study presents a numerical solution to convective heat transfer in laminar flow in the thermal entrance region of a rectangular duct with two indented sides. The flow is considered to be hydrodynamically fully developed and thermally developing laminar flow of incompressible, Newtonian fluids with constant thermal properties. The ducts are subjected to a constant wall temperature. An algebraic technique is used to discretize the solution domain and a boundary-fitted coordinate system is numerically developed. The governing equations in the boundary-fitted coordinates are solved by the control volume-based finite difference method. Distribution of the bulk temperature and the Nusselt number along the direction of flow is calculated and presented graphically. Also calculated is the thermal entrance length of the rectangular ducts with two indented sides. The parameters, such as the friction factor times the Reynolds number, and the Nusselt number for the fully developed flow and thermally developing flow are obtained.

We generalize the multiscale overlapped domain framework to couple multiple rate-independent standard dissipative material models in the finite deformation regime across different length scales. We show that a fully coupled multiscale incremental boundary-value problem can be recast as the stationary point that optimizes the partitioned incremental work of a three-field energy functional. We also establish inf-sup tests to examine the numerical stability issues that arise from enforcing weak compatibility in the three-field formulation. We also devise a new block solver for the domain coupling problem and demonstrate the performance of the formulation with one-dimensional numerical examples. These simulations indicate that it is sufficient to introduce a localization limiter in a confined region of interest to regularize the partial differential equation if loss of ellipticity occurs.

 This paper presents a numerical model for three-dimensional transversely isotropic bimaterials based on the boundary element formulation. The point force solutions expressed in a united-form for distinct eigenvalues are studied for transversely isotropic piezoelectricity and pure elasticity. A boundary integral formulation is implemented for the modeling of two-phase materials. In this study, the stress distributions are computed for a near interface flaw. The influences of the shape and location of the flaw on the the stress concentration are examined. The accuracy of the numerical procedures is validated through selected example problems and comparison studies.

The paper reports on the prediction of the flow field around smooth cylinders in cross flow at high Reynolds number. Both circular and square-sectioned cylinders are considered. The principal feature of these flows, and the primary cause for the difficulty in their prediction, is the development of a von Karman vortex street leading to significant fluctuations in surface pressures. It has already been established from several previous studies that eddy-viscosity closures fail to capture the correct magnitude of these fluctuations though there is no consensus as to the underlying causes. In this work, it is argued that the organized fluctuations in the mean-flow field introduce energy into the random turbulence motions at a frequency that corresponds exactly to the shedding frequency and that, as a consequence, it becomes necessary to explicitly account in the turbulence closure for the resulting modification of the spectral transfer process. A proposal to account for this direct energy transfer in the context of two-equation eddy-viscosity closures is put forward and is checked by comparisons with experimental data from both square and circular cylinders at high Reynolds number. Uncertainties in the predictions due to numerical discretization errors are systematically minimized. The outcome of comparisons with experimental data and with results from alternative closures, including Large-Eddy Simulations, validate the proposal.

We study the analytical and numerical behaviour of the adiabatic shearing flow of an incompressible Newtonian liquid with temperature-dependent viscosity, under a time-periodic boundary velocity. We give sufficient stability conditions for the solution of the governing balance and constitutive equations and we present numerical results for the asymptotic convergence of the flow. Essentially, we verify that the stress decays to a time oscillatory function while the temperature exhibits a strongly non-uniform distribution with its maximum value tending to infinity with time.

In this paper, a nonlocal energy-informed neural network is proposed to deal with elastic solids containing discontinuities by considering the long-range interactions of material points. First, the solution to peridynamic equilibrium equation is converted to an variational energy minimization problem based on principle of virtual work, which automatically satisfies the zero-traction boundary conditions and avoids the introduction of artificial damping. Furthermore, the energetic representation of behavior of physical system can be tractable as the loss function for deep learning neural network. This allows to approximate the solution of the system by the active machine learning community. As the basic technique in deep learning, automatic differentiation is capable to evaluate derivatives for smooth functions, but it is prone to singularity due to the presence of discontinuities. To address this limitation, spatial integration is employed in the proposed neural network to evaluate the strain energy of the system rather than the spatial derivatives of displacement fields calculated by automatic differentiation. Moreover, the initial cracks can be directly introduced in the constitutive model without the explicit definition of crack surfaces. The accuracy and efficiency of the proposed neural network is validated by conducting several mechanical problems with or without discontinuities. More importantly, the proposed neural network is capable to capture the jump discontinuities at the crack surfaces, where the neural network with automatic differentiation is hard to address. Additionally, the convergence of the proposed neural network and the comparison of two widely used activation functions are investigated.