三维(3D)打印是一种增材制造工艺。相应地，四维(4D)打印是一个涉及多个研究领域的制造工艺。4D打印保留了3D打印的一般属性(如减少材料浪费、消除注射模具、冲压模具和机械加工过程)，并且随着时间的推移能实现产品第四维度的智能行为。在打印过程中，这种智能行为(通常由逆数学问题)编码进刺激响应多材料中，并在打印后通过刺激该材料来实现。3D和4D打印结构的主要区别是4D打印存在一个附加的维度，这个维度可以随着时间的推移进行智能进化。然而，目前还没有用于建模和预测这个附加维度的一般公式。本文从基本原理开始，导出并验证了一个具有特定格式的一般双指数公式，该公式可以模拟几乎所有4D结构的时间相关性行为(如水、光化学、光热、溶剂、pH、湿度、电化学、电热、超声波等响应)。研究表明，需要利用两种类型的时间常数来捕捉4D多材料的正确的时间相关性行为。本文引入了4D多材料结构中主动材料和被动材料的界面错配压力的概念，从而得到了两个时间常数之一。本文从几乎所有刺激响应材料的时间相关性行为的统一模型中开发和提取另一个时间常数。本文的结果从最基本的概念开始，并以控制方程结束，可以作为未来4D打印领域研究的一般设计原则，其中时间相关性行为应该被正确地理解、建模和预测。

Three-dimensional (3D) printing is an additive manufacturing process. Accordingly, four-dimensional (4D) printing is a manufacturing process that involves multiple research fields. 4D printing conserves the general attributes of 3D printing (such as material waste reduction, and elimination of molds, dies, and machining) and further enables the fourth dimension of products to provide intelligent behavior over time. This intelligent behavior is encoded (usually by an inverse mathematical problem) into stimuliresponsive multi-materials during printing, and is enabled by stimuli after printing. The main difference between 3D- and 4D-printed structures is the presence of one additional dimension, which provides for smart evolution over time. However, currently there is no general formula for modeling and predicting this additional dimension. Herein, by starting from fundamentals, we derive and validate a general biexponential formula with a particular format that can model the time-dependent behavior of nearly all 4D (hydro-, photochemical-, photothermal-, solvent-, pH-, moisture-, electrochemical-, electrothermal-, ultrasound-, etc. responsive) structures. We show that two types of time constants are needed to capture the correct time-dependent behavior of 4D multi-materials. We introduce the concept of mismatch-driven stress at the interface of active and passive materials in 4D multi-material structures, leading to one of the two time constants. We develop and extract the other time constant from our unified model of time-dependent behavior of nearly all stimuli-responsive materials. Our results starting from the most fundamental concepts and ending with governing equations can serve as general design principles for future research in the field of 4D printing, where time-dependent behaviors should be properly understood, modeled, and predicted.