Abstract

In this paper we propose a mortar algorithm for the study of contact mechanics in three dimensional elasticity problems. The projection surface used for integrating the equations is selected through a local cartesiana base defined in each contact element. In this way, some difficulties in the algorithm implementation as well as in the linearization of the equations are avoided. The proposed examples show that the algorithm satisfies the patch tests. Finally, we use the algorithm in an industrial application, the contact of an internal combustion engine valve with its seat.

Abstract

The extended system is known as a reliable algorithm for the direct computation of instability points on the equilibrium path of mechanical structures. This article describes the application of the extended system as critical point computation method to mechanical contact problems. In this type of problems inequality constraints have to be considered. Moreover a prediction method based on the extended system algorithm is presented which allows the detection of favorable starting values for a critical point computation on the equilibrium path.

Abstract

Underground construction involves all sort of challenges in analysis, design, project and execution phases. The dimension of tunnels and their structural requirements are growing, and so safety and security demands do. New engineering tools are needed to perform a safer planning and design. This work presents the advances in the particle finite element method (PFEM) for the modelling and the analysis of tunneling processes including the wear of the cutting tools. The PFEM has its foundation on the Lagrangian description of the motion of a continuum built from a set of particles with known physical properties. The method uses a remeshing process combined with the alpha-shape technique to detect the contacting surfaces and a finite element method for the mechanical computations. A contact procedure has been developed for the PFEM which is combined with a constitutive model for predicting the excavation front and the wear of cutting tools. The material parameters govern the coupling of frictional contact and wear between the interacting domains at the excavation front. The PFEM allows predicting several parameters which are relevant for estimating the performance of a tunnelling boring machine such as wear in the cutting tools, the pressure distribution on the face of the boring machine and the vibrations produced in the machinery and the adjacent soil/rock. The final aim is to help in the design of the excavating tools and in the planning of the tunnelling operations. The applications presented show that the PFEM is a promising technique for the analysis of tunnelling problems.

Abstract

A modular discrete element framework is presented for large-scale simulations of industrial grain-handling systems. Our framework enables us to simulate a markedly larger number of particles than previous studies, thereby allowing for efficient and more realistic process simulations. This is achieved by partitioning the particle dynamics into distinct regimes based on their contact interactions, and integrating them using different time-steps, while exchanging phase-space data between them. The framework is illustrated using numerical experiments based on fertilizer spreader applications. The model predictions show very good qualitative and quantitative agreement with available experimental data. Valuable insights are developed regarding the role of lift vs drag forces on the particle trajectories in-flight, and on the role of geometric discretization errors for surface meshing in governing the emergent behavior of a system of particles.

Abstract

Comparative studies of different discrete element models of a rock-type material are presented. The discrete element formulation employs spherical particles with the cohesive interaction model combining linear elastic behaviour with brittle failure. Numerical studies consisted in simulation of the uniaxial compression test. Two cylindrical specimens with particle size distributions yielding different degree of heterogeneity have been used. Macroscopic response produced by different discrete element models has been compared. The main difference between the compared models consists in the evaluation of micromechanical constitutive parameters. Two approaches are compared. In the first approach, the contact stiffness and strength parameters depend on the local particle size, while in the second approach, global uniform contact parameters are assumed for all the contacting pairs in function of average geometric measures characterizing the particle assembly. The size dependent contact parameters are calculated as functions of geometric parameters characterizing each contacting particle pair. As geometric scaling parameters, the arithmetic and harmonic means, as well as the minimum of the radii of two contacting particles are considered. Two different models with size dependent contact parameters are formulated. The performance of these models is compared with that of the discrete element model with global uniform contact parameters. Equivalence between the models with size dependent and uniform contact parameters has been checked. In search of this equivalence, different methods of evaluation of global uniform parameters have been studied. The contact stiffness has been evaluated in terms of the average radius of the particle assembly or in terms of the averages of the arithmetic and harmonic means of the contact pair radii, the geometric parameters used in the evaluation of the contact stiffness in the size-dependent models. The uniform contact strengths have been determined as functions of the averages of radii squares, squares of arithmetic radii means or squares of minimum radii of the contacting pairs.

For the more homogenous specimen, the models with local size dependent parameters and models with global uniform parameters give similar response. The models with uniform parameters evaluated according to the averages of the geometric parameters used in the evaluation of local parameters ensure better agreement with the respective models with size-dependent parameters than the models with uniform parameters evaluated according to the particle radii. Simulations using the more heterogenous specimen reveal differences between the considered models. There are significant differences in stress–strain curves as well as in the failure pattern. The models with local size-dependent parameters are more sensitive to the change of heterogeneity than the model with global uniform parameters.

Abstract

Abstract

Software development for high-performance scientific computing continues to evolve in response to increased parallelism and the advent of on-node accelerators, in particular GPUs. While these hardware advancements have the potential to significantly reduce turnaround times, they also present implementation and design challenges for engineering codes. We investigate the use of two strategies to mitigate these challenges: the Kokkos library for performance portability across disparate architectures, and the DARMA/vt library for asynchronous many-task scheduling. We investigate the application of Kokkos within the NimbleSM finite element code and the LAME constitutive model library. We explore the performance of DARMA/vt applied to NimbleSM contact mechanics algorithms. Software engineering strategies are discussed, followed by performance analyses of relevant solid mechanics simulations which demonstrate the promise of Kokkos and DARMA/vt for accelerated engineering simulators.

Abstract

In this paper a robust topology optimization algorithm for linear elastic structures in unilateral contact is presented. The deformation of the linear elastic structure is constrained by support structures that are modeled with the help of Signorini's contact conditions. The contact conditions in turn are enforced with the augmented Lagrangian approach. Doing so, the robust optimization considers uncertainties at the support such as manufacturing tolerances and its local friction behavior. Due to high numerical costs in robust optimization, the firstorder second-moment approach is used to approximate the mean and variance of the objective. This approximation results in minimal additional costs to approximate the mean, the variance and their gradients. Consequentially, a gradient-based optimization algorithm can be used to minimize a weighted sum of both. The results show that the presented approach indeed improves the robustness with respect to uncertain contact conditions compared to a deterministic optimization.

Abstract