A Review on Mechanical Models for Cellular Media: Investigation on Material Characterization and Numerical Simulation

Abstract

Cellular media materials are used for automobiles, aircrafts, energy-efficient buildings, transportation, and other fields due to their light weight, designability, and good impact resistance. To devise a buffer structure reasonably and avoid resource and economic loss, it is necessary to completely comprehend the constitutive relationship of the buffer structure. This paper introduces the progress on research of the mechanical properties characterization, constitutive equations, and numerical simulation of porous structures. Currently, various methods can be used to construct cellular media mechanical models including simplified phenomenological constitutive models, homogenization algorithm models, single cell models, and multi-cell models. This paper reviews current key mechanical models for cellular media, attempting to track their evolution from their inception to their latest development. These models are categorized in terms of their mechanical modeling methods. This paper focuses on the importance of constitutive relationships and microstructure models in studying mechanical properties and optimizing structural design. The key issues concerning this topic and future directions for research are also discussed.

A Low‐Cost, User‐Friendly Rheo‐Optical Compression Assay to Measure Mechanical Properties of Cell Spheroids in Standard Cell Culture Plates

“…Among the rheological models available in literature, [ 49 ] we have used, as an example, a phenomenological model originally developed to describe the mechanical behavior of foams. [ 50 ] The model, schematized in Figure a, consists of three elements in a parallel combination: a linear spring with an elastic constant k p , a linear spring with elastic constant k in series with a dashpot with viscosity c, and a nonlinear spring with deformation‐dependent coefficient k D .…”

Quasi-Static Mechanical Response of Density-Graded Polyurea Elastomeric Foams

“…The individual regions within a typical stress–strain response of a foam sample, namely, elastic, plateau, and densification regions, can be readily captured by scaling laws as a function of the relative foam density . However, the homogenized stress–strain curve can also be represented by several empirical or phenomenological models, e.g., refs , , . The Avalle model was used herein to represent the average stress–strain curves of all investigated sample configurations σ = A ( 1 − e false( prefix− E A false) ε ( 1 − ε ) m ) + B true( ε 1 − ε true) n where the first term signifies the elastic and plateau regions, while the second term embodies the densification .…”

Properties, Applications and Recent Developments of Cellular Solid Materials: A Review

“…In many real-world applications, cellular materials operate as a cushion and are loaded dynamically. This loading process is frequently accompanied by a high loading strain rate [40]. When a side accident occurs at a speed of 90 km/h, the protective foam in the car-side door panels can be stretched up to 1500 s −1 .…”

“…At 40 km/h, the strain rate of the car's foam energy-absorbing box approaches 200 s −1 . The mechanical characteristics of the cellular medium cannot be precisely assessed by the static test result and model when the cellular medium is subjected to greater strain and a higher strain rate during dynamic loading [40]. Therefore, it is crucial to look at their mechanical behavior under dynamic loads in high strain rate loading circumstances.…”