## 1 Introduction  
Four-dimensional printing is an innovative technology that leverages the synergy between structural design and smart materials to create complex geometries capable of dynamically responding to external stimuli [1]. Four-dimensional printing is an evolution of 3D printing, an additive manufacturing technique that enables high-precision fabrication of final products through a layer-by-layer deposition process used to build three-dimensional objects [2, 3]. In particular, 4D printing represents an advancement of this technology, allowing the printed objects to change their properties, functionality, or shape over time, which represents the fourth dimension. The direct applications of 4D printing are related to smart packaging [4], the biomedical field [5], soft robotics [6], and the aerospace and automotive industries [7, 8]. In this context, the development of shape memory materials (SMMs) has been very important. Shape memory materials (SMMs) are responsive to external stimuli, with the unique ability to alter their shape when exposed to specific triggers. When a shape change is prompted by temperature variation, this is known as the thermally induced shape memory effect [9]. The most common shape memory materials (SMMs) include shape memory polymers (SMPs) [10]. Among the SMMs, shape memory polymers (SMPs) are particularly popular and studied, with numerous examples in the literature, including polylacticacid (PLA) [11; 12]. In the case of PLA, thermal stimulation is the most common recovery mechanism [13]. The glass transition temperature (Tg) plays a key role in activating shape memory behavior. By heating the material above Tg and subsequently cooling it below this threshold, a reversible transition between the glassy and rubbery states occurs in the polymer's reversible phase, enabling the fixation or release of a temporary shape [14]. For PLA, the Tg ranges between 55 \({}^{\circ}\)C [15] and 65 \({}^{\circ}\)C [16], a range influenced by factors such as crystallinity [17], purity, and the presence of additives [18]. This approach gives rise to the so-called \"metamaterial\"--a term derived from the Greek prefix \"meta-\", meaning \"beyond\", evoking the idea of materials that go beyond conventional boundaries [19]. Metamaterials, through the design of cell geometries on a microscopic scale, can exhibit properties absent in natural materials [20], such as controlled and reversible deformation [21]. The integration of lattice structures in metamaterials also allows for modulating physical characteristics such as stiffness and energy absorption, making them particularly suitable for advanced engineering applications [22; 23]. The geometry of the lattice cell plays a pivotal role in determining the mechanical performance and functional behavior SMP structures fabricated through 4D printing. Several studies have shown that specific geometries--such as honeycomb, auxetic, and body-centered cubic (BCC) arrangements--can drastically influence stiffness, energy absorption, and recovery behavior under cyclic loading. For instance, ref. [24] reported that honeycomb and combined hexagonal structures exhibited superior energy absorption at low temperatures, while configurations with higher density were more effective near the glass transition temperature. Study [25] found that circular cell-based BCC variants offered improved structural integrity and compressive performance compared to standard BCC lattices. In auxetic geometries, the introduction of concave nodes and superelastic elements can enhance impact resistance and energy dissipation [26]. These studies underline the importance of careful geometric selection when designing 4D-printed SMP metamaterials, particularly in applications requiring repeated activation and recovery. In this context, the present work investigates different families of lattice cells--chiral, wavy, and honeycomb--focusing on their flexural behavior and shape memory response over multiple deformation cycles.