New bounds on local strain fields inside random heterogeneous materials

A methodology is presented for bounding the higher LpLp norms, 2⩽p⩽∞2⩽p⩽∞, of the local strain inside random media. We present optimal lower bounds that are given in terms of the applied loading and volume fractions for random two phase composites. These bounds provide a means to measure load transfer across length scales relating the excursions of the local fields to applied loads. These results deliver tight upper bounds on the macroscopic strength domains for statistically defined heterogeneous media.

► Introduced a methodology for bounding the local strain inside random media.
► Presented optimal lower bounds on the strain inside random two phase composites.
► These bounds provide a means to measure load transfer across length scales.
► Delivered tight upper bounds on the macroscopic strength domains inside composites.
► The bounds are given in terms of the applied loading and the volume fractions