## 1 Introduction  
Current commercially available prostheses are mostly energy-storing -and -releasing (ESR) feet and they are the most prescribed prosthetic feet for individuals with K3 and K4 levels of ambulation. ESR feet are passive prosthetic devices made of elastic elements, which ensure the ESR feet work as springs that store energy during the mid-stance of the gait cycle and release it for the propulsion during late stance [1, 2]. The elastic elements are generally leaf springs, also called blades, of composite materials (carbon fiber-reinforced plastic--CFRP); or glass fiber-reinforced plastic--GFRP). The stiffness of the elastic elements is a crucial characteristic of foot prostheses. Stiffness depends on the geometries and the material properties, especially for ESR feet [3, 4], and the choice of the global stiffness category of foot prostheses depends on the weight and the users' activity levels [5]. Moreover, the few active ankle prosthetic devices on the market are joined to feet by a system of composite leaf springs (see Table 1 for remarkable examples). The contribution of the elastic elements is always significant. The present work aims to propose and apply a systematic methodology that includes elastic elements in the design process of prosthetic feet. The methodology combinesnumerical and experimental techniques for the design and the functional verification of foot prostheses. The proposed methodology consists of three main phases: (i) the _design phase_, which includes the stiffness and safety optimization; (ii) the _mechanical test phase_ on a physical prototype; and (iii) the _functionality verification phase_. The stiffness optimization, carried out during the _design phase_, is performed using static structural finite element (FE) analyses (FEA). Optimizing a passive foot prosthesis means optimizing its stiffness in such a way that it gives rotations in both dorsiflexion and plantarflexion similar to the rotations of a healthy foot. In the ankle-foot system of a human who has not suffered any amputation to the lower limbs, there are muscles that control every movement giving the desired or necessary rotation. With transtibial amputation, most of the muscles are eliminated or reduced and a passive device such as the ESR foot cannot guarantee active control as muscles do. However, by studying the literature, it is possible to determine the loads to which a healthy foot is subjected while walking and its corresponding rotations. Therefore, an ESR foot can be optimized in terms of stiffness considering the loads it is subjected to and the rotations it must make while walking. In previous publications, FEA was used with different aims in the design/study of prosthetic feet. [PERSON] et al. and [PERSON] et al. used FEA to analyze the stress-strain behavior of load-bearing components [6; 7]. [PERSON] et al. also used FEA to analyze the energy stored by an ESR foot [7]. FEAs were also applied to the design of foot prostheses that comply with standards such as ISO 22675 (www.iso.org, accessed on 1 January 2021) [8] or _American Orthotic and Prosthetic Guidelines_ (AOPA, www.aopanet.org, accessed on 1 January 2021) [9]. FEA was used by [PERSON] et al. to carry out the stiffness optimization of the elastic elements of passive [10] prosthetic feet, while [PERSON] et al. used it for the same aim but to optimize a quasi-passive [11] foot prosthesis. The profile shapes of prosthetic feet were to obtain an optimal roll-over by carrying structural FEAs [12; 13]. [PERSON] et al. designed an ESR foot with elastic elements in the composite materials (glass fiber) [14]. [PERSON] et al. included FEA in a methodology that concerned ESR prosthetic foot characterization; however, they did not propose it as a tool to design a new energy-storing and -releasing foot [15]. [PERSON] et al.