Transformation toughening has been used in commercial products for several decades in order to increase the toughness of brittle materials. Composites made from an elastic matrix and elastic-plastic inclusions similarly exhibit increased toughness and R-curve behavior due to the residual stress induced in the wake of the crack tip by the unloaded, plastically deforming fillers. These two mechanisms, in which the eigenstrains in the wake of a major crack lead to toughening, belong to the same class. In this study, we investigate the effect of the elastic heterogeneity of the matrix on such toughening mechanisms and observe that increasing the elastic heterogeneity amplifies the effect. The analysis is relevant for bone, which is a highly heterogeneous hierarchical material, in which localized plastic deformation has been recently shown to occur at dilatational bands. Understanding toughening in bone is a subject of current interest in the context of age-related fragility. The heterogeneity-enhanced eigenstrain toughening effect is of interest for a broad range of engineering applications.

中文翻译：

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存在弹性异质性时的特征应变增韧并应用于骨骼

几十年来，相变增韧已在商业产品中使用，以增加脆性材料的韧性。由弹性基体和弹塑性夹杂物制成的复合材料同样表现出更高的韧性和 R 曲线行为，这是由于卸载的塑性变形填料在裂纹尖端后引起的残余应力。这两种机制，其中主要裂纹后的本征应变导致增韧，属于同一类。在这项研究中，我们研究了基体的弹性异质性对这种增韧机制的影响，并观察到增加弹性异质性会放大这种影响。该分析与骨骼相关，骨骼是一种高度异质的分层材料，其中局部塑性变形最近已被证明发生在膨胀带。在与年龄相关的脆弱性的背景下，了解骨骼中的韧化是当前感兴趣的主题。非均质性增强的本征应变增韧效应在广泛的工程应用中受到关注。