A computer-implemented method for the automated design of a mechanical actuator 1 by using metamaterials is described. Such a method firstly comprises the step of defining an initial lattice model 2 of the metamaterial, constituted by the repetition of basic geometric elements 3, either two- dimensional or three-dimensional, formed by a plurality of nodes 4 connected by a plurality of beams 5. Then, the method provides defining, between the nodes of the aforesaid regular lattice, the following groups of nodes: a first group of input nodes 41, which constitute an input region R1 intended to receive at least one input mechanical stimulus Mi; a second group of output nodes 42, which constitute an output region R2 intended to provide a desired output mechanical movement, as a result of the action of the actuator; and a third group of removable nodes 43, distinct from the aforesaid nodes of the first group and of the second group. The method then comprises iterating a series of steps which will be described below. In the iteration, the step of modifying a current test lattice is performed, on the basis of a pseudo-random decision determined by means of a computational algorithm, by removing or adding a removable node, or by removing or adding a beam afferent to a removable node, to obtain a modified test lattice. The step is then provided of simulating, by means of computational simulation, the mechanical response of the modified test lattice, when an input mechanical stimulus is applied to the input nodes of the first group, to determine the consequent output mechanical movement of the output nodes of the second group, and to establish the position of the input and output nodes of the modified test lattice in presence of the aforesaid input mechanical stimulus. A figure of merit of the modified test lattice is then calculated, on the basis of the positions of the input and output nodes, established by the aforesaid simulation, in presence of an input mechanical stimulus. Then, the step is performed of either accepting or rejecting the modified test lattice, or establishing a probability of acceptance of the modified test lattice, on the basis of a comparison between the figure of merit of the current test lattice and the parameter of merit of the modified test lattice. In conclusion of the whole of the steps which are iterated, the current test lattice for the subsequent iteration is defined as the initial lattice at the first iteration, or, in subsequent iterations, as the present current test lattice if the modified test lattice was rejected, or as the modified test lattice if it was accepted. The aforesaid iteration comprises at least one step in which a previously removed node is added again. Furthermore, the aforesaid iteration is repeated until a predetermined optimization criterion of the figure of merit is met. At the end of the iteration, the method provides considering the current test lattice determined by the last iteration as the final design model of the mechanical actuator 1 and providing digital data corresponding to the aforesaid final design model for manufacturing the mechanical actuator by metamaterial. A method for making a mechanical actuator 1 and a method for making a metamaterial machine, based on the aforesaid design method, are also described.

METHOD FOR AUTOMATED DESIGN AND FOR MANUFACTURE OF MECHANICAL ACTUATORS BY USING TOPOLOGICAL TRUSS-BASED METAMATERIALS / S. Bonfanti, R. Guerra, S. Zapperi.

### METHOD FOR AUTOMATED DESIGN AND FOR MANUFACTURE OF MECHANICAL ACTUATORS BY USING TOPOLOGICAL TRUSS-BASED METAMATERIALS

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*S. Bonfanti;R. Guerra;S. Zapperi*

##### 2021

#### Abstract

A computer-implemented method for the automated design of a mechanical actuator 1 by using metamaterials is described. Such a method firstly comprises the step of defining an initial lattice model 2 of the metamaterial, constituted by the repetition of basic geometric elements 3, either two- dimensional or three-dimensional, formed by a plurality of nodes 4 connected by a plurality of beams 5. Then, the method provides defining, between the nodes of the aforesaid regular lattice, the following groups of nodes: a first group of input nodes 41, which constitute an input region R1 intended to receive at least one input mechanical stimulus Mi; a second group of output nodes 42, which constitute an output region R2 intended to provide a desired output mechanical movement, as a result of the action of the actuator; and a third group of removable nodes 43, distinct from the aforesaid nodes of the first group and of the second group. The method then comprises iterating a series of steps which will be described below. In the iteration, the step of modifying a current test lattice is performed, on the basis of a pseudo-random decision determined by means of a computational algorithm, by removing or adding a removable node, or by removing or adding a beam afferent to a removable node, to obtain a modified test lattice. The step is then provided of simulating, by means of computational simulation, the mechanical response of the modified test lattice, when an input mechanical stimulus is applied to the input nodes of the first group, to determine the consequent output mechanical movement of the output nodes of the second group, and to establish the position of the input and output nodes of the modified test lattice in presence of the aforesaid input mechanical stimulus. A figure of merit of the modified test lattice is then calculated, on the basis of the positions of the input and output nodes, established by the aforesaid simulation, in presence of an input mechanical stimulus. Then, the step is performed of either accepting or rejecting the modified test lattice, or establishing a probability of acceptance of the modified test lattice, on the basis of a comparison between the figure of merit of the current test lattice and the parameter of merit of the modified test lattice. In conclusion of the whole of the steps which are iterated, the current test lattice for the subsequent iteration is defined as the initial lattice at the first iteration, or, in subsequent iterations, as the present current test lattice if the modified test lattice was rejected, or as the modified test lattice if it was accepted. The aforesaid iteration comprises at least one step in which a previously removed node is added again. Furthermore, the aforesaid iteration is repeated until a predetermined optimization criterion of the figure of merit is met. At the end of the iteration, the method provides considering the current test lattice determined by the last iteration as the final design model of the mechanical actuator 1 and providing digital data corresponding to the aforesaid final design model for manufacturing the mechanical actuator by metamaterial. A method for making a mechanical actuator 1 and a method for making a metamaterial machine, based on the aforesaid design method, are also described.##### Pubblicazioni consigliate

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