Learning from plant movements triggered by bulliform cells: the biomimetic cellular actuator

Abstract

Within the framework of a biomimetic top-down approach, our study started with the technical question of the development of a hinge-free and compliant actuator inspired by plant movements. One meaningful biological concept generator was the opening and closing movements of the leaf halves of grasses. Functional morphological investigations were carried out on the selected model plant Sesleria nitida. The results formed the basis for further clarifying the functional movement principle with a particular focus on the role of turgor changes in bulliform cells on kinetic amplification. All findings gained from the investigations of the biological model were incorporated into a finite-element analysis, as a prerequisite for the development of a pneumatic cellular actuator. The first prototype consisted of a row of single cells positioned on a plate. The cells were designed in such a way that the entire structure bent when the pneumatic pressure applied to each individual cell was increased. The pneumatic cellular actuator thus has the potential for applications on an architectural scale. It has subsequently been integrated into the midrib of the facade shading system Flectofold in which the bending of its midrib controls the hoisting of its wings.

Keywords: Sesleria nitida; bulliform cells; finite-element analysis; hinge-free actuator; motor cells; turgor.

Figure 1.

Role of bulliform cells in leaf movement. (a–c) Bulliform cells are distributed along the entire leaf. (b) The leaf rolls in, when the turgor pressure in the bulliform cells is low. (c) It unrolls again, when the bulliform cells are turgescent. (d–f) Bulliform cells are concentrated near the midrib. (e) The leaf halves fold, when the turgor pressure in the bulliform cells is low. (f) They unfold again, when the bulliform cells are turgescent. ab-ep, abaxial epidermis (= lower epidermis); ad-ep, adaxial epidermis (= upper epidermis); bc, bulliform cells; mr, midrib; sc, sclerenchyma; vb, vascular bundle.

Figure 2.

The top-down approach (technology pull process) of the biomimetic cellular actuator. (1) Which functional principle of hinge-less plant movement can be transferred to an actuator for compliant architectural structures? (2) Grass leaves with opening and closing movements were investigated with respect to their functional morphology. (3) The kinetic amplification of the leaf halves is based on the interaction of turgor-dependent bulliform cells and strengthening tissues. (4) Finite-element models of the entire pressurized cellular actuator and its individual cells were developed. (5) A prototype of the plant-inspired cellular actuator was built and tested. (6) As a precursor model for the market launch, the actuator was integrated into the facade shading device Flectofold [20]. Shading is generated by a continuous motion of the two shading elements initiated by bending of the midrib in between.

Figure 3.

Leaves of S. nitida. (a) Transverse section of an entire leaf stained with ACO. (b) Detail of the midrib stained with PHO. Unstained leaf segments with (c) intact bulliform cells and (d) mechanically damaged bulliform cells on the right side (arrow). The right half of the leaf lamina can be clearly seen to be tilted inwards after damage to the bulliform cells. ab-ep, abaxial epidermis (= lower epidermis); ad-ep, adaxial epidermis (= upper epidermis); bc, bulliform cells; ch, chlorenchyma; mr, midrib; sc, sclerenchyma; sc-mr, midrib sclerenchyma; vb, vascular bundle; vb-mr, midrib vascular bundle (= midvein).

Figure 4.

Process of finite-element (FE) simulation. (a) The outline of the leaf section and the bulliform cells were directly transferred from a microscopic image. (b) Pre-stresses in the leaf tissues are responsible for the folding of the leaf in the event of a drought-stress-induced volume reduction in the bulliform cells. To reproduce this effect in the numerical model, an external horizontal force is applied to the outer edge of the leaf segment considered here. (c) The geometry in a closed position serves as the starting point for the subsequent FE simulation. (d) An increase in pressure, exclusively in the bulliform cells, causes an increase in the opening angle of the leaf lamina.

Figure 5.

Simulation results for the total opening angle between the two leaf halves depend on the respective increase in turgor pressure inside the bulliform cells. The regression line and the coefficient of determination are presented.

Figure 6.

Abstraction process. (a) FE model of a leaf segment of S. nitida with two fan-shaped groups of bulliform cells right and left of the midrib of the biological model. The leaf halves open or close dependent upon the turgor pressure in the bulliform cells. (b) FE model of an individual technical cell. As the air pressure inside the cell increases, the vertical cell walls tilt outwards. (c) If several cells are aligned in a cell row, a bending motion occurs.

Figure 7.

Cell geometry and wall thicknesses for the physical prototype of the biomimetic cellular actuator. All measurements are given in millimetres.

Figure 8.

Angular deflection α of the side wall of the technical cell upon increasing internal cell pressure P.

Figure 9.

Stresses that occur in the cell wall of an individual technical cell at an internal air pressure of 0.02 MPa. The cell width is 40 mm.

Figure 10.

Physical prototype of the cellular actuator inspired by the bulliform cells of S. nitida. The structure lifts an external mass of 0.5 kg.

Figure 11.

Physical prototype of the single cell row actuator bending the midrib of the compliant shading system Flectofold.