AI 中文总结
提出固体变形累积变分框架，递归组合Cosserat、不相容与缺陷源分量，经累积能量耦合，可描述结构分岔、残余变形与迟滞等行为。
AI 中文摘要
提出了一个用于固体变形的累积变分框架。其核心组织原则是递归组合一个材料体的三个结构组成部分：一个相容的Cosserat分量、一个分布不相容分量和一个缺陷源分量。在任意给定的外部条件下，这些分量构成一个组合材料状态。它们在共同的物理边界和初始条件下受控，并通过一个累积能量及相应的场方程耦合。它们不是独立的边值问题，也不必按预定的时间顺序出现。该框架的累积特性涉及组合状态对外部给定条件变化的响应。对于初始完美体的特殊情况，失稳可能产生连续的支路，先有缺陷参与，然后有源参与。这样的序列是所选初始状态和本构能量的分岔性质，而非框架的定义性层级。一个一维特例说明了结构分岔、由保留结构产生的残余变形和残余应力、对初始组合状态的依赖性、反向加载下的方向记忆、参数累积迟滞，以及与结构稳定化相关的可观测切线刚度的变化。一个空间扩展引入了缺陷和源梯度项，并产生一个依赖于尺寸的结构稳定性算子。对于所考虑的稳定的四次能量，梯度项正则化非均匀扰动，但本身不会在已经稳定的三分量支路上产生有限波长局域化不稳定性。这些例子因此区分了累积结构和能量的后果与需要额外本构演化定律的现象。
英文摘要
A cumulative variational framework for solid deformation is proposed. Its central organizing principle is the recursive combination of three structural components of one material body: a compatible Cosserat component, a distributed-incompatibility component, and a defect-source component. At any prescribed external condition these components constitute a combined material state. They are governed under common physical boundary and initial conditions and are coupled through one cumulative energy and the associated field equations. They are not separate boundary-value problems and need not appear in a prescribed temporal sequence. The cumulative character of the framework concerns the response of the combined state to variation of externally prescribed conditions. For the special case of an initially perfect body, loss of stability may produce successive branches with defect and then source participation. Such a sequence is a bifurcation property of the selected initial state and constitutive energy, rather than a defining hierarchy of the framework. A one-dimensional specialization illustrates structural bifurcation, residual deformation and residual stress produced by retained structure, dependence on the initial combined state, directional memory under reverse loading, parametric cumulative hysteresis, and changes of observable tangent stiffness associated with structural stabilization. A spatial extension introduces defect and source gradient terms and yields a size-dependent structural stability operator. For the stable quartic energy considered, the gradient terms regularize nonuniform perturbations but do not by themselves generate a finite-wavelength localization instability on an already stable three-component branch. The examples thereby distinguish consequences of the cumulative structure and energy from phenomena requiring additional constitutive evolution laws.
CommentsSubmitted to the International Journal of Engineering Science
