Recovery Behavior of Artificial Skin Materials After Object Contact

Abstract

As social robots and lifelike prosthetics get into closer contact with humans, understanding the mechanical behavior of the embedding skin materials for prosthetic and social robotic fingertips is of great importance. The time-dependent behavior can alter the performance of the embedded sensors. This paper investigates two types of embedding materials (i.e. silicone and polyurethane) for their recovery after contact with a surface. A visco-hyperelastic finite element model of a fingertip is described. This model allows the visualization of the materials’ responses after a creep test. This analysis was performed to investigate the recovery time of the materials after contact was made. Simulation results show the differences between the two materials. The results are useful for materials selection and to further investigate other design alternatives and to minimize the effects of the time delay.

1 Introduction

Our hands have important communicative, emotional, and functional purpose. For example, we can greet others and we are able to communicate directions and sizes with the human hand [1–4]. Through touch, we are able to console someone else’s emotional pain or make someone feel appreciated [5–8]. For those who may have lost their hands through disease, accident or war, the use of one’s hand for independent living, for hygiene or for feeding oneself may be the most important function that have been lost. Likewise, for the robotic hands of social robots (i.e. robots that socially interact and collaborate with humans), transporting an object from one position to another is equally important [9, 10]. That function requires contact between the artificial hand and a tool or another object.

Before an artificial hand can grasp and manipulate an object, contact has to be first established through the synthetic skin and then through the embedded tactile sensors. The tactile sensing system has to detect the following: contact between the finger and the object [11, 12]; contact between the object and the environment [10, 13]; slippage [11, 14]; local shape [15, 16]; and global shape [17, 18]. To make sense of that information, the time-dependent mechanical behavior of the synthetic skin has to be understood because it can alter the response of the embedded tactile sensors.

A highly viscoelastic skin could make the signals from an embedded contact sensor to have a long decay until the skin material stabilizes. In a creep test, an applied constant stress will result to an increased strain in a viscoelastic material. After the stress is released, the material will gradually return to its initial state. If the selected material has a long recovery time, the embedded sensor will continue to be on its active state even after the load on the skin surface is removed. This work investigates the behavior of two typically used artficial skin materials and determine their behavior after its contact with an object.

This paper is structured as follows. Section 2 describes the skin samples and the finite element model used. Section 3 presents the results on the recovery of the artificial skin. The last section concludes this paper and provides the future directions.

Fig. 1.

The two-dimensional finite element axisymmetric model of the synthetic fingertip. The shape was made to approximate a cross-section of the human fingertip. The fixed region serves as a stiff support similar to the function of the bone. The flat plate indenter was oriented as shown. They were modeled as rigid, analytical surfaces.

2 Materials and Methods

2.1 Artificial Skin Samples

For these simulations, we used silicone (GLS 40, Prochima, s.n.c., Italy) and polyurethane (Poly 74-45, Polytek Devt Corp, USA) as representative materials of those used in earlier works as artificial skins for prosthetics and robotics [19, 20]. These materials were previously characterized in [21, 22] for their viscoelastic and hyperelastic behaviors.

2.2 Finite Element Modeling

A two-dimensional finite element (FE) model of a fingertip (Fig. 1) was created in the commercial finite element software Abaqus (Dassault Systemes). The model adopted the geometry of the fingertip presented in [23, 24]. The plain strain 8-node biquadratic element type was used to model the fingertip skin. The indenter was modeled as a rigid, analytical flat surface. The visco [25] computation mode was used in this work. The skin layer was assumed to have hyperelastic and viscoelastic behaviors. The contact between the fingertip and the plate was assumed to be frictionless. The constitutive equations are shown at the Appendix.

Fig. 2.

The contours for the vertical logarithmic strain for the 3 mm skin thickness model. A and B. For the silicone sample taken at 7 s and 17 s, respectively. C and D. For polyurethane sample taken at 7 s and 17 s, respectively.

2.3 Simulation Procedure

A creep test requires that a constant force is applied to the material in order to demonstrate the creeping process through displacement or strain measures. Full fingertip models with 1, 3, and 5 mm thickness were used to investigate the skin recovery. Additional simulation conditions represented on the 3 mm skin are shown on Fig. 2. A concentrated vertical force of 10 N was applied through the reference point, denoted as RP in Fig. 1.

The loading profile was specified such that the time to reach the peak force was set to 1 s. The force was maintained constant for 5 s. The duration of unloading was set to 1 s. Data on the nodal vertical displacement (U2) and vertical logarithmic strain (LE22) were collected from two nodes on the fingertip model. The first was the node directly below the plate where the concentrated force was applied. The second was the node from an element just above the “bone” surface as shown on Fig. 1. The recovery time was obtained from the instant that the load was released at T = 7 s until T = 17 s. For each fingertip thickness, the cut-off criteria were set to be at 10 % of the strains at the instant when the load was released. This criterion is similar to the cutoff used in [26].

Fig. 3.

The recovery behavior of the artificial skin materials. The resulting displacements for silicone: A. On a node on the skin surface directly below the plate. B. On a node from an element just above the “bone” surface. The resulting displacements for polyurethane: C. On a node on the skin surface directly below the plate. D. On a node from an element just above the “bone” surface.

Fig. 4.

The nodal logarithmic strains plotted over time for silicone, A, and polyurethane, B. The insets shows the magnified strains immediately after the release of the load T = 7 s and 10 s after, T = 17 s.

3 Results

Plotted on Fig. 3A for silicone and Fig. 3C for polyurethane are the displacements of a node located on the skin surface. Plotted on Fig. 3B for silicone and Fig. 3D for polyurethane are the displacements of a node near the bone surface. The displacement profile of the subsurface node resembles the profile at the skin surface albeit with smaller magnitude.

The logarithmic strain results of silicone in Fig. 4A and inset, for the 3 mm thick skin show negligible residual strains, 10 s after the load was released. For the three skin thicknesses that were investigated, the plot suggests that silicone can achieve full recovery within 1 s after the release of load from the plate.

For the polyurethane material, the typical behavior of creep in viscoelastic materials is evident from the continued increase of displacement, even as the force is kept constant from T = 1 s to T = 6 s (Fig. 4B). Residual strains can be observed from the logarithmic strain contours, 10 s after contact was removed (Fig. 4B inset). For the three models with polyurethane material, the plot suggests that the residual strains from a 10 N load and applied for 5 s will be about 0.5 % after 10 s of load removal.

4 Conclusion

Upon the artificial finger’s contact with an object, the stresses and strains that occur at the contact interface are detected by the embedded tactile sensors. However, due the viscoelastic and hyper elastic properties of synthetic skins, these can cause delay in the signals that are detected by the tactile sensors. Consequently, the lag in the sensor’s response can make the difference between having an object slip from the fingers or having sufficient time to grasp an object firmly.

In this paper, a finite element model of a fingertip was presented. This model had visco-hyperelastic behavior where the recovery behavior of the artificial skin was investigated. Results show that as compared to the silicone samples, the polyurethane material samples had longer delays in the response of a node. This node can represent what an embedded sensor can detect. Future work involves validating the model with micro sensors that can be embedded to be about 1 to 5 mm beneath the skin surface or using digital image correlation techniques to visualize the strains. In addition, more studies are needed to develop hardware or software-based approaches to compensate or eliminate the effects of the long delay in recovery of the artificial skin that will be selected.

Appendix

Viscoelastic and hyperelastic constitutive equations were used to represent the behavior of the synthetic materials. The total stress is equal to the sum of the hyperelastic (HE) stress and the viscoelastic (VE) stress such that:

$$\begin{aligned} \sigma (t)=\sigma _{HE}(t) + \sigma _{VE}(t) \end{aligned}$$

(1)

The hyperelastic behavior was derived from a function of strain energy density per unit volume, U.

$$\begin{aligned} \textit{U}=\sum \limits _{i=1}^N\frac{2\mu _i}{\alpha _i^2}\Big [\lambda _1^{\alpha _i}+\lambda _2^{\alpha _i}+\lambda _3^{\alpha _i}-3+\frac{1}{\beta }(J ^{-\alpha _i\beta })\Big ] \end{aligned}$$

(2)

$$\begin{aligned} \sigma _{HE}=\frac{2}{J}F\frac{du}{dC}F^T \end{aligned}$$

(3)

where $J=\lambda _1\lambda _2\lambda _3$ is the volume ratio, $\alpha _i$ and $\mu _i$ where $\nu$ is the Poisson’s ratio, N, is the number of terms used in the strain energy function, and F and C are the deformation gradient and the right Cauchy-Green deformation tensors, respectively.

It was assumed that the candidate materials were incompressible, and therefore the volume ratio was set to unity. In the current case of uniaxial compression, the following relationships were used: $\lambda _1=\lambda , \lambda _2=\lambda _3= \sqrt{\lambda }$.

The viscoelastic behavior was defined as follows, with a relaxation function g(t) applied to the hyperelastic stress:

$$\begin{aligned} \sigma _{VE}=\int _0^t\dot{g}(\tau )\sigma _{HE}(t-\tau )d\tau \end{aligned}$$

In order to describe several time constants for the relaxation, the stress relaxation function g(t) was defined using the Prony series of order $N_G$, where $g_i$ and $\tau _i$ are the viscoelastic parameters:

$$\begin{aligned} g(t)=\Biggl [1-\sum \limits _{i=1}^{N_G}g_i(1-e^{-t/\tau _i})\Biggl ] \end{aligned}$$

(4)

The coefficients for hyperelastic ( N ), stress relaxation ($N_G$) and Poisson’s numbers ($\nu$) are given in Tables 1 and 2.

Table 1. Coefficients for silicone sample ($\nu =0.49$)

Table 2. Coefficients for the polyurethane sample ($\nu =0.47$)