Mechanics of fish skin: A computational approach for bio-inspired flexible composites

Natural materials and structures are increasingly becoming a source of inspiration for the design novel of engineering systems. In this context, the structure of fish skin, made of an intricate arrangement of flexible plates growing out of the dermis of a majority of fish, can be of particular interest for materials such as protective layers or flexible electronics. To better understand the mechanics of these composite shells, we introduce here a general computational framework that aims at establishing a relationship between their structure and their overall mechanical response. Taking advantage of the periodicity of the scale arrangement, it is shown that a representative periodic cell can be introduced as the basic element to carry out a homogenization procedure based on the Hill-Mendel condition. The proposed procedure is applied to the specific case of the fish skin structure of the Morone saxatilis, using a computational finite element approach. Our numerical study shows that fish skin possesses a highly anisotropic response, with a softer bending stiffness in the longitudinal direction of the fish. This softer response arises from significant scale rotations during bending, which induce a stiffening of the response under large bending curvature. Interestingly, this mechanism can be suppressed or magnified by tuning the rotational stiffness of the scale-dermis attachment but is not activated in the lateral direction. These results are not only valuable to the engineering design of flexible and protective shells, but also have implications on the mechanics of fish swimming.     

On the mechanics of fishscale structures

Biological and manmade structures often share the same specifications and design constraints: structural support, lightweight or protection against specific threats. In this context, the structure of fishscales, consisting of small rigid plates growing out of the skin of a majority of fish species, are characterized by a large variety of shape, size and properties in order to achieve particular functions. The present study introduces a basic two-dimensional micromechanical model that permits to establish a correlation between the flexural response of a scaled skin and the nature of its underlying structure, including both geometric and material aspects. The model is used to predict trends in the structure’s response and illustrates the fact that the scale design, arrangement and properties can be tailored to achieve a wide spectrum of response. In particular, fishscale structure possesses an inherent strain-stiffening response that can be suppressed or magnified by certain structural features. This particularity, shared by most biological materials, ensures that the structure provides both a structural and protective support for the animal.     

Multi-scale micromorphic theory for hierarchical materials

For the design of materials, it is important to faithfully model macroscopic materials response together with mechanisms and interactions occurring at the microstructural scales. While brute-force modeling of all the details of the microstructure is too costly, many of the current homogenized continuum models suffer from their inability to capture the correct underlying deformation mechanisms—especially when localization and failure are concerned. To overcome this limitation, a multi-scale continuum theory is proposed so that kinematic variables representing the deformation at various scales are incorporated. The method of virtual power is then used to derive a system of coupled governing equations, each representing a particular scale and its interactions with the macro-scale. A constitutive relation is then introduced to preserve the underlying physics associated with each scale. The inelastic behavior is represented by multiple yield functions, each representing a particular scale of microstructure, but collectively coupled through the same set of internal variables. The theory is illustrated by two applications. First, a one-dimensional example of a three-scale material is presented. After the onset of softening, the model shows that the localization zone is distributed according to two distinct length scale determined by the model. Second, a two-scale continuum model is introduced for the failure of porous metals. By comparing the theory to a direct numerical simulation (DNS) of the microstructure for a specimen in tension, we show that the model capture the main physics, and at the same time, remains computationally affordable.     

The Effective Permeability of Cracks and Interfaces in Porous Media

The presence of interfaces in fluid/solid biphasic media is known to strongly influence their behavior both in terms of solid deformation and fluids flow. Mathematical models have traditionally represented these interfaces as lines of no-thickness and whose behavior is given in terms of effective permeabilities whose physical meaning is often disconnected to the microscopic nature of the interface. This article aims to reconcile macroscopic and microscopic interface representations by investigating how the nature of microscopic flows and pressures in the interface can be used to explain its macroscopic behavior. By invoking a proper thickness average operation, we derive an closed form expression that relates the effective interfaces permeabilities to its microscopic properties. In particular, we find that the effective interface permeabilities are strongly influenced by three factors: the ratio of bulk and interface permeabilities, the fluid viscosity, and the physical thickness of the interface.

     

A micromorphic model for the multiple scale failure of heterogeneous materials

The multi-scale micromorphic theory developed in our previous paper [Vernerey, F.J., Liu, W.K., Moran, B., 2007. Multi-scale micromorphic theory for hierarchical materials. J. Mech. Phys. Solids, doi:10.1016/j.jmps.2007.04.008] is used to predict the failure of heterogeneous materials illustrated by a high strength steel alloy possessing two populations of hard particles distributed at two distinct length scales in an alloy matrix. To account for the effect and size of microstructural features during fracture, additional kinematic variables are added, giving rise to the couple stresses associated with each population of particles. The various stress and strain measures must satisfy a set of coupled multi-scale governing equations derived from the principle of virtual power. A three-scale constitutive model is then developed to represent the failure of the alloy from nucleation, growth and coalescence of voids from each population of particles. For this, three distinct yield functions, each corresponding to a different scale, are introduced. Cell model simulations using finite elements are performed to determine the constitutive relations based on the key microstructural features. Two-dimensional failure analyses are then presented in tension and in shear, and show good agreement with direct numerical simulation of the microstructure.