Introducing a level-set based shape and topology optimization method for the wear of composite materials with geometric constraints

Abstract

The wear of materials continues to be a limiting factor in the lifetime and performance of mechanical systems with sliding surfaces. As the demand for low wear materials grows so does the need for models and methods to systematically optimize tribological systems. Elastic foundation models offer a simplified framework to study the wear of multimaterial composites subject to abrasive sliding. Previously, the evolving wear profile has been shown to converge to a steady-state that is characterized by a time-independent elliptic equation. In this article, the steady-state formulation is generalized and integrated with shape optimization to improve the wear performance of bi-material composites. Both macroscopic structures and periodic material microstructures are considered. Several common tribological objectives for systems undergoing wear are identified and mathematically formalized with shape derivatives. These include (i) achieving a planar wear surface from multimaterial composites and (ii) minimizing the run-in volume of material lost before steady-state F. Feppon wear is achieved. A level-set based topology optimization algorithm that incorporates a novel constraint on the levelset function is presented. In particular, a new scheme is developed to update material interfaces; the scheme (i) conveniently enforces volume constraints at each iteration, (ii) controls the complexity of design features using perimeter penalization, and (iii) nucleates holes or inclusions with the topological gradient. The broad applicability of the proposed formulation for problems beyond wear is discussed, especially for problems where convenient control of the complexity of geometric features is desired.

Topology Optimization of Composite Materials for Wear: A Route to Multifunctional Materials for Sliding Interfaces

“…[19][20][21][22] A significant improvement in wear modeling has been achieved via incorporating Winkler and Pasternak foundation models into wear modeling. [23][24][25][26][27][28][29][30][31][32][33][34] In recent studies, a Pasternak foundation model coupled with Archard's wear law showed a good agreement with experimental results, Figure 1. [25,26,28] This model has been further improved in Jia et al [27] , where a Pasternak foundation wear model is shown to accurately simulate an asymmetric worn surface caused by unidirectional sliding effects.…”

“…Wear models that combine Archard's wear law and Pasternak foundation models, Figure 1, have been previously established to predict material removal and the topographical evolution of composite material surfaces subjected to wear. [25][26][27][28][29][30][32][33][34] It has a great potential in different engineering applications such as chemical mechanical polishing (CMP), the rotary wear of A u t h o r M a n u s c r i p t A u t h o r M a n u s c r i p t thrust-washers or the evolution of grinding dental tissues. [25,27,30,31,33] .…”

“…The location, shape, and number of inclusions have historically been defined based on experience and parametric optimization. Recently, topology optimization has been extended to include tribological problems; Feppon et al [34] introduced a topology A u t h o r M a n u s c r i p t A u t h o r M a n u s c r i p t optimization method for the wear of composite materials based on a level-set method. In Feppon's work, a bi-material surface with an arbitrary material distribution is optimized to minimize a run-in wear volume via nucleating holes with a topological gradient, using a penalization parameter to control the complexity of the design, and applying volume constraints.…”

“…In this article, for the first time, experimental measurements including wear volume, wear rate and topographical evolution are made to validate topology optimized composite systems from Feppon et al [34] In this way, the tested bi-material systems are pioneering advances in surface design for composite wear. First, the physics-based model employed in the optimization framework is recalled along with a summary of the optimization protocol.…”

Contact Geometry Adaptation in Fretting Wear: A Constructive Review

“…A range of wear contact profiles with variable wear resistance of a sliding punch was considered by Goryacheva (1998) in the case of the Archard-Kragelsky wear model (2) with a particular focus on the steady-state solutions. The transient wear contact problems for composite materials were considered recently using different approaches, including the method of dimensionality reduction with application to an axisymmetric heterogeneous annular cylindrical punch (Li et al, 2018) and a level-set based shape and topology optimization method with application to a Pasternak elastic foundation model (Feppon et al, 2017). By using an appropriate symmetrization of the integral equation kernel, Argatov and Chai (2019b) extended the Galin method for analyzing the transient contact pressure distribution and derived an upper estimate for the wearing-in period.…”