Traditional efforts in the design of damage-tolerant structural materials were largely exercises in optimizing the combination of strength and ductility. However, the simultaneous consideration of these two conflicting mechanical indices, improving one inevitably sacrifices the other, makes the design extremely complex and difficult, due to the dilemma of choosing between them. Here, physically guided by the energy variational expression in trans-scale continuum mechanics theory, we propose a general mechanics principle for material design that involving only one index: towards strong and tough material the strain energy density limit (w) should be maximized, i.e., strain energy density maximization principle, referred to as wmax principle. It aims to guide the attainment of exceptional comprehensive mechanical properties, while circumventing the dual-index dilemma by employing a singular index w. Extensive experimental data analyses prove that (i) the maximum wmax always exists, at a critical dimension of characteristic microstructure dc,micro, and (ii) w can effectively index strength-ductility synergy and the wmax is conjugated with both high strength and high ductility, verifying the validity of wmax principle. The universality, practicality and downward compatibility are also examined. The dc,micro approaches twice the span of strain gradient region around internal boundary, suggesting that the microstructure state with wmax is the critical state with strongest strain gradient. Importantly, the w improvement as a function of the characteristic size of either microstructure or deformation field can be well captured by strain gradient theory, confirming the consistence between the wmax principle, experimental results and trans-scale continuum theories. This principle opens up a new design concept for advanced structural materials from the perspective of microstructure-w-mechanical properties relationship.

中文翻译：

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材料设计的应变能密度最大化原理和跨尺度连续体理论中的反射


设计耐损伤结构材料的传统工作主要是优化强度和延展性的组合。然而，同时考虑这两个相互冲突的机械指标，改进一个不可避免地牺牲了另一个，由于在它们之间做出选择的困境，使设计变得极其复杂和困难。在这里，以跨尺度连续介质力学理论中的能量变分表达式的物理指导，我们提出了一个只涉及一个指标的材料设计通用力学原理：对于坚固和坚韧的材料，应变能密度极限 （w） 应最大化，即应变能密度最大化原理，称为 wmax 原理。它旨在指导实现卓越的综合机械性能，同时通过采用单一指数 w 来规避双指数困境。大量的实验数据分析证明，（i） 最大 wmax 始终存在，位于特征微观结构 dc、micro 的临界维度上，（ii） w 可以有效地指标强度-延展性协同作用，并且 wmax 同时具有高强度和高延展性，验证了 wmax 原理的有效性。还检查了通用性、实用性和向下兼容性。dc，micro 接近内部边界周围应变梯度区域跨度的两倍，表明具有 wmax 的微观结构状态是应变梯度最强的临界状态。重要的是，应变梯度理论可以很好地捕捉到作为微观结构或变形场特征大小的函数的 w 改进，证实了 wmax 原理、实验结果和跨尺度连续体理论之间的一致性。 该原理从微观结构-w-机械性能关系的角度为先进结构材料开辟了新的设计思路。