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We compare the structural and mechanical properties of static packings composed of frictionless convex (ellipses) and concave (rigid dimers) particles in two dimensions. We employ numerical simulations to generate static packings and measure the shear stress in response to applied simple shear strain as a function of the aspect ratio and amount of compression. We find that the behavior near jamming is significantly different for ellipses and dimers even though both shapes are roughlydoi:10.1039/c001085e fatcat:hq5xwlg2srbrxkbkw7oa3lzevi