Computational Mechanics

In computational structural dynamics, particularly in the presence of nonsmooth behavior, the choice of the time-step and the time integrator has a critical impact on the feasibility of the simulation. Furthermore, in some cases, as in the case of a bridge crane under seismic loading, multiple time-scales coexist in the same problem. In that case, the use of multi-time scale methods is suitable. Here, we propose a new explicit–implicit heterogeneous asynchronous time integrator (HATI) for nonsmooth transient dynamics with frictionless unilateral contacts and impacts. Furthermore, we present a new explicit time integrator for contact/impact problems where the contact constraints are enforced using a Lagrange multiplier method. In other words, the aim of this paper consists in using an explicit time integrator with a fine time scale in the contact area for reproducing high frequency phenomena, while an implicit time integrator is adopted in the other parts in order to reproduce much low frequency phenomena and to optimize the CPU time. In a first step, the explicit time integrator is tested on a one-dimensional example and compared to Moreau-Jean’s event-capturing schemes. The explicit algorithm is found to be very accurate and the scheme has generally a higher order of convergence than Moreau-Jean’s schemes and provides also an excellent energy behavior. Then, the two time scales explicit–implicit HATI is applied to the numerical example of a bridge crane under seismic loading. The results are validated in comparison to a fine scale full explicit computation. The energy dissipated in the implicit–explicit interface is well controlled and the computational time is lower than a full-explicit simulation.

After a survey the refined numerical treatment and verification is presented for a rate-independent macroscopic unified PT material model (including mass conservation with respect to phase fractions and covexified free energy) by Govindjee and Miehe (Comput Methods Appl Mech Eng 191:215–238, 2001) for describing SME and SE effects within a linear kinematic setting. Special attention is given to temperature dependent PTs. The material model was implemented into ABAQUS via the UMAT material interface in 2004. Validation of this PT model is carried out with experimental data supplied by Xiangyang et al. (J Mech Phys Solids 48:2163–2182, 2000), using 3D finite element computations. Experimentally gained material data from different sources are used and numerical results of energy barriers for PTs are given. Another feature is the simulation of suppressed shape memory effects by quasiplastic temperature induced PT. Furthermore, a plane strain problem is treated with comparisons of butterfly shaped expansions of martensitic PT and plastic deformation, correspondingly.

The demand for shape memory alloy (SMA) actuators in high-technology applications is increasing; however, there exist technical challenges to the commercial application of SMA actuator technologies, especially associated with actuation duration. Excessive activation duration results in actuator damage due to overheating while excessive deactivation duration is not practical for high-frequency applications. Analytical and finite difference equation models were developed in this work to predict the activation and deactivation durations and associated SMA thermomechanical behavior under variable environmental and design conditions. Relevant factors, including latent heat effect, induced stress and material property variability are accommodated. An existing constitutive model was integrated into the proposed models to generate custom SMA stress–strain curves. Strong agreement was achieved between the proposed numerical models and experimental results; confirming their applicability for predicting the behavior of SMA actuators with variable thermomechanical conditions.

A refined non-conforming triangular plate/shell element for linear and geometrically nonlinear analysis of plates and shells is developed in this paper based on the refined non-conforming element method (RNEM). A conforming triangle membrane element with drilling degrees of freedom in Cartesian coordinates and the refined non-conforming triangular plate-bending element RT9, in which Kirchhoff kinematic assumption was adopted, are used to construct the present element. The displacement continuity condition along the interelement boundary is satisfied in an average sense for plate analysis, and the coupled displacement continuity requirement at the interelement is satisfied in an average sense, thereby improving the performance of the element for shell analysis. Selectively reduced integration with stabilization scheme is employed in this paper to avoid membrane locking. Numerical examples demonstrate that the present element behaves quite satisfactorily either for the linear analysis of plate bending problems and plane problems or for the geometrically nonlinear analysis of thin plates and shells with large displacement, moderate rotation but small strain.

Numerical simulations of the particle-vortex interactions for an unforced, incompressible, spatially developing horizontal particle-laden turbulent planar jet are reported. Effects of the initial two-phase velocity slip on the instantaneous concentration distribution of particles with and without the influence of gravity are studied. Continuous phase simulation is performed by the method of large eddy simulation (LES) while the particle phase is solved by a Lagrangian method. Extensive results on the particle-laden jet flow are obtained. Simulation of the gas-phase reproduces the essential features of the coherent structures in the planar jet. Length of the potential core and essential features of the coherent structures in the planar jet are compared with experimental and other theoretical results. The simulation shows that initial two-phase velocity slip plays an important role in enforcing particle transverse dispersion in the jet region and sharply changes the instantaneous particle distribution. Furthermore, results demonstrate the influence of gravity on particle dispersion and sedimentation. Such pronounced effect of gravity on instantaneous concentration of particles with increased Stokes number and initial slip coefficients emphasize the need for the consideration of gravity for horizontal particle-laden jet.

 An efficient meshfree formulation based on the first-order shear deformation theory (FSDT) is presented for the static analysis of laminated composite beams and plates with integrated piezoelectric layers. This meshfree model is constructed based on the element-free Galerkin (EFG) method. The formulation is derived from the variational principle and the piezoelectric stiffness is taken into account in the model. In numerical test problems, bending control of piezoelectric bimorph beams was shown to have the efficiency and accuracy of the present EFG formulation for this class of problems. It is demonstrated that the different boundary conditions and applied actuate voltages affects the shape control of piezolaminated composite beams. The meshfree model is further extended to study the shape control of piezo-laminated composite plates. From the investigation, it is found that actuator patches bonded on high strain regions are significant in deflection control of laminated composite plates.

The surface-to-surface master–master contact treatment is a technique that addresses pointwise contact between bodies with no prior election of slave points, as in master–slave case. For a given configuration of contact-candidate surfaces, one needs to find the material points associated with a pointwise contact interaction. This is the local contact problem (LCP). The methodology can be applied together with numerical models such as geometrically nonlinear finite elements, discrete elements and multibody dynamics. A previous publication has addressed the possibility of degenerating the local contact problem, which yields the derivation of point-surface, curve-surface and other simplifications on the geometric treatment in the same mathematical formulation, sharing a single numerical implementation. This has useful applications for singularities or non-uniqueness scenarios on the LCP. The present work provides a framework for the degenerated master–master contact formulation including friction. An enhanced friction model is proposed, accounting for a combination of elastic and dissipative effects at the interface. Details of derivations and numerical implementation are given as well as examples related to beam-shell interaction.

In this study, a new computational modeling of the gas-surface interaction is proposed to explain the results of the scattering experiments of molecular beams from solid surfaces, especially from industrial surfaces. The characteristic feature of the model is to settle the adsorbed gas layer and the collision layer which involve adsorbed molecules and surface molecules, respectively. Incident molecules experience force due to the gas-solid potential gradient, changing their trajectories which is computed by Molecular Dynamics method. The gas molecules are scattered from the surfaces after collisions with adsorbed or surface molecules. The simulated results are compared with the experimental ones: i.e., flux distributions, TOF spectra and the average energy of scattered molecules.