Shakedown Analysis of Particle-Reinforced Metal Matrix Composites (PRMMCs): A Multiscale and Lower-Bound Approach
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Particle Reinforced Metal Matrix Composites (PRMMCs) are increasingly used in the aerospace and automotive industries because of their high strength-to-weight ratio and superior wear resistance. However, their long-term mechanical performance under cyclic and variable loads remains largely unexplored, particularly in safety-critical applications where failure must be prevented over extended service life. Shakedown analysis, particularly Melan’s static theorem [1938], offers a promising approach to assess the long-term behavior of materials under variable loading conditions, including cyclic and time-independent load histories. Despite its potential, the practical application of this theory to PRMMCs remains limited, as traditional modeling approaches often idealize the micro-structure and overlook the intrinsic heterogeneity of these composites, failing to capture critical local interactions between reinforcement particles and the matrix. Recent studies, such as those of Chen et al. [2018, 2019], have started to address these limitations by incorporating micro-structural characteristics and boundary effects, thus laying the groundwork for a more accurate shakedown assessment of PRMMCs. This research introduces a multiscale computational framework for lower-bound shakedown analysis of PRMMCs by extending the methodology of Simon et al. [2011, 2013], originally based on Melan’s theorem. Synthetic yet realistic 3D micro-structures are generated as proposed by Neumann et al. [2017], accurately capturing particle morphology, size, and spatial distribution. Then, homogenization techniques are applied to extract effective material properties from Representative Volume Elements (RVEs), which are subsequently used in macroscopic shakedown analysis. The methodology enables us to investigate the influence of micro-structural features such as particle size, volume fraction, and boundary conditions on shakedown limits. By bridging realistic micro-structural modeling with lower-bound shakedown theory, this framework provides a reliable and computationally efficient tool for assessing PRMMC performance under variable loading conditions. The results demonstrate the effectiveness of the framework in conducting shakedown analysis to predict shakedown limits and to support the safe, optimized design of next-generation materials for high-performance structural applications.