A microstructure-based hyperelastic model for open-cell solids

Mesoscopic continuum hyperelastic models for open-cell solids subject to large elastic deformations are derived from the architecture of the cellular body and the microscopic responses of the cell walls. These models are valid for general structures, with randomly oriented cell walls, made from an arbitrary isotropic nonlinear hyperelastic material, and subject to finite triaxial stretches. Their analyses provide global descriptors of the cellular structure, such as nonlinear stretch and shear moduli, and Poisson's ratio. Comparisons with numerical simulations show that the mesoscopic models capture well the mechanical responses under large strain deformations of three-dimensional periodic structures and of two-dimensional honeycombs made from a neo-Hookean material

Finite Strain Homogenization Using a Reduced Basis and Efficient Sampling

The computational homogenization of hyperelastic solids in the geometrically nonlinear context has yet to be treated with sufficient efficiency in order to allow for real-world applications in true multiscale settings. This problem is addressed by a problem-specific surrogate model founded on a reduced basis approximation of the deformation gradient on the microscale. The setup phase is based upon a snapshot POD on deformation gradient fluctuations, in contrast to the widespread displacement-based approach. In order to reduce the computational offline costs, the space of relevant macroscopic stretch tensors is sampled efficiently by employing the Hencky strain. Numerical results show speed-up factors in the order of 5-100 and significantly improved robustness while retaining good accuracy. An open-source demonstrator tool with 50 lines of code emphasizes the simplicity and efficiency of the method.Comment: 28 page

Computed tomography-based modeling of structured polymers

Because of their excellent specific strength and energy absorption properties, polymeric foams find their application in a wide range of engineering areas. Their specific mechanical response results from a subtle interplay between the intrinsic material response of the polymer base material and the complex microstructure related to their process history. In order to optimize foam products, the macroscopic mechanical response of foams should be predictable for multiple and mixed loading conditions. In other words the central question concerns the extent to which the structure of a foam and the material constituting the structure contribute to the final properties. To address this topic an understanding of the underlying deformation and failure mechanics is required. In this thesis an approach which combines X-ray Computed Tomography (CT) and Finite Element (FE) simulations is evaluated. X-ray CT is a technique that enables the detailed description of the foam’s microstructure up to a resolution of 1 µm. The first part focuses on the effects of modeling structured polymers, i.e. honeycomb and foam structures, with this technique. A regular honeycomb structure is modeled with a perfect RVE exposed to periodic boundary conditions and compared with a model based on CT-images exposed with symmetry boundary conditions. A nonlinear elasto-viscoplastic constitutive model is used to describe the intrinsic response of the polycarbonate base material. The highly non-linear response of the structure is captured and contact phenomena in the large strain regime, leading to densification, are incorporated. The comparison with a fully hyper elastic description of the base material revealed that the mechanical response can be explained in terms of a rate dependent onset of plasticity, causing a deviation from a non-linear elastic response. A discrepancy between the ideal RVE and CT model is assigned to the absence of imperfections in the ideal RVE compared with the more realistic CT model. To study the influence of the irregular microstructure in case of X-ray CT-based moddeling on the predicted mechanical response, an irregular closed-cell foam structure is characterized and converted into a 2D FE model where the model size (number of cells in the model) and discretization (number of elements over the thickness of a cell wall) are varied. The results show that, in case of an elastic material response, the RVE-model should contain a minimum of 12 cells to correctly represent the bulk mechanical response. On the other hand, the influence of discretization show a stiffening of the response when increasing the element size in the small strain regime. When the element size becomes larger than the size of the smallest details, this results in loss of local connectivity and stiffness reduction. The applicability of the developed micromechanical modeling is demonstrated on a Rapid Prototyped (RP) foam structure. This foam structure, based on the scaled-up microstructure of a real foam, is created using stereo lithography RP. The RP structure is characterized with X-ray CT and converted into a FE model, based on quadratic tetrahedral elements. For proper characterization of the base material, compression samples are made with RP and the intrinsic response is determined just above its glass transition temperature Tg. The mechanical response of the RP structures is experimentally characterized at different temperatures and strain rates. FE simulations are in good qualitative agreement with the experimental observations. Although the mechanical response is over predicted by the FE simulations, it is demonstrated that this is likely to be related to small temperature variations. Also for the RP structures a comparison with between a hyperelastic and viscoplastic description of the base material revealed that due to rate dependent plasticity the response deviates from a non-linear elastic response. Finally, the mechanical response of an open-cell polyurethane foam is determined with the microstructural simulations in five loading conditions: uniaxial compression and tension, simple shear and hydrostatic compression and tension. In uniaxial loading the response corresponds to the experimental results in the elastic regime, where the deviation beyond this regime is due to the viscous response of the foam. Similar to elasto-viscoplastic foams, it is believed that the response to loads at different rates, approaches the hyperelastic response for high strain rates and that the viscous behavior at low strain rates originates from the base material. The typical volumetric response is analyzed using compression and tensile experiments and 3D FE simulations on a microstructural level. In compression, the volume decreases and the apparent Poisson’s ratio decreases gradually from 0.3 to 0. This mechanism is confirmed by in-situ compression experiments and FE simulations. The microstructural origin is bending of cell struts followed by the collapse of the foam’s microstructure through buckling. In tension, however, an increase of the volume is found up to a maximum, after which it decreases as well. The microstructural simulations show that this decrease is related to buckling of the struts oriented pendicular to the loading direction. Based on the experimental observations and the X-ray CT-based FE simulations, three macroscopic hyperelastic constitutive models are tested on their ability to describe the non-linear elastic response as well as the volume response of the foam in the five loading conditions. The main conclusion is that existing macroscopic models are of limited use. Since none of them is able to describe hydrostatic loading situations and, as a consequence, also behave moderately in shear, they all lack predictive power in more complex loading situations. The importance of including all loading conditions for material parameter fitting is clear, when compared to only incorporate the data of uniaxial compression, resulting in a significantly over predicted response in shear

Modeling and experimental investigations of the stress-softening behavior of soft collagenous tissues

This paper deals with the formulation of a micro-mechanically based dam-age model for soft collagenous tissues. The model is motivated by (i) a sliding filament model proposed in the literature [1] and (ii) by experimental observations from electron microscopy (EM) images of human abdominal aorta specimens, see [2]. Specifically, we derive a continuum damage model that takes into account statistically distributed pro- teoglycan (PG) bridges. The damage model is embedded into the constitutive framework proposed by Balzani et al. [3] and adjusted to cyclic uniaxial tension tests of a hu- man carotid artery. Furthermore, the resulting damage distribution of the model after a circumferential overstretch of a simplified arterial section is analyzed in a finite element calculation

Mechanical modeling of incompressible particle-reinforced neo-Hookean composites based on numerical homogenization

In this paper, the mechanical response of incompressible particle-reinforced neo-Hookean composites (IPRNC) under general finite deformations is investigated numerically. Threedimensional Representative Volume Element (RVE) models containing 27 non-overlapping identical randomly distributed spheres are created to represent neo-Hookean composites consisting of incompressible neo-Hookean elastomeric spheres embedded within another incompressible neo-Hookean elastomeric matrix. Four types of finite deformation (i.e., uniaxial tension, uniaxial compression, simple shear and general biaxial deformation) are simulated using the finite element method (FEM) and the RVE models with periodic boundary condition (PBC) enforced. The simulation results show that the overall mechanical response of the IPRNC can be well-predicted by another simple incompressible neo-Hookean model up to the deformation the FEM simulation can reach. It is also shown that the effective shear modulus of the IPRNC can be well-predicted as a function of both particle volume fraction and particle/matrix stiffness ratio, using the classical linear elastic estimation within the limit of current FEM software

Nonlinear analysis of microscopic instabilities in fiber-reinforced composite materials

Abstract Failure induced by fiber microbuckling is a frequent failure mode in continuous fiber-reinforced composite materials subjected to compression along the fibers direction. This failure mechanism may lead to a notable decrease of the compressive strength of composite materials since may also induce the initiation and propagation of cracks at the micro-structural level. A detailed microscopic continuum analysis with an appropriate representation of different sources of nonlinearities is usually required to capture the effects of different microscopic failure modes (instability, fracture damage, for instance), at the expense of a very large computational effort. In order to avoid a direct modeling of all microstructural details of the composite solid, micromechanically based multiscale techniques can be adopted in coupling with first order homogenization schemes. To this end a semiconcurrent two-scale approach is proposed in which the macroscopic constitutive law is evaluated resolving a micromechanical BVP in each macroelement of the homogenized domain; the microscopic model adopts a full finite deformation continuum formulation to study the interaction between local fiber buckling and matrix or fiber/matrix interface microcracks in presence of unilateral self-contact between crack surfaces. Numerical results are obtained to provide accurate predictions of the critical load level associated to microscopic instabilities in 2D fiber-reinforced composite solids

Interfacial failure in plastic bonded explosives

Plastic bonded explosives (PBXs) materials are a form of particulate composite materials consisting of stiff energetic crystals with different particle sizes. These crystals are randomly distributed inside a soft polymer binder material with volume fraction greater than 85%. The binder material holds the crystal particles together, provides means of dissipating energy in cases of accidental load, increases the material’s storage life and enables safe handling without deterioration of the explosive performance. The mechanical properties of PBX materials profoundly depend on the mixture ratio formulation, the constituents’ material properties, environmental conditions (temperature, pressure, humidity), and loading rate. Mechanical characterisation of the polymer bonded explosives (PBXs), though very costly, is therefore crucial for their safe handling during storage and transportation while preserving the optimal explosive performance. The modulus of the PBX binder is five orders of magnitude lower than the modulus of the explosive crystals. Despite the low volume fraction (5% - 15%), the binder material influences the PBX material properties significantly, hence characterisation of the binder material is vital. A rheological constitutive law model can capture the pronounced time-dependent and temperature-dependent behaviour of the binder over a large deformation range. In this project, the material properties of the binder were determined using constant shear strain rate, shear stress relaxation and monotonic tensile test results obtained over a wide range of temperature and strain rates. A visco-hyperelastic model was parameterised using the derived test data. In addition, a methodology is proposed for extracting valid test data from rheological testing of soft solid materials where the storage modulus is higher than the loss modulus. The PBX materials fracture predominantly by interface debonding between the binder and explosive crystals, at temperatures above the glass transition temperature of the binder. Crystal to crystal friction, even with an insignificant external load, can lead to an accidental detonation of the PBX material. This interfacial debonding can be described by cohesive zone laws. In this project, the cohesive zone material properties, namely the linear stiffness (1), the interface cohesive stress ( ) and the interface cohesive energy () were determined using fracture testing coupled with Digital Image Correlation (DIC) to capture the deformation and strain fields around the crack tip. According to the experimental results, the cohesive zone parameters for the particle-binder interface are strain rate-independent, whereas as temperature rises, the cohesive zone properties drop significantly, especially the interface cohesive stress and the interface cohesive energy. The mechanical properties of the PBX composite were also determined experimentally; the test results showed that PBX-1 (the material under this study, filler is crystalline cyclotetramethylene tetranitramine (HMX) and the matrix is nitrocellulose-based polymer, volume fraction 88%) has better mechanical properties, i.e. higher Young’s modulus, failure stress and failure strain, under compressive and flexural loading, as compared to tensile loading at the same temperature and load rate.In addition, PBX microstructure models were constructed using SolidWorks and MacroPac software. Simulations based on regularly packed microstructures, i.e. body-centred cubic, face-centred cubic, hexagonal-closed packed and simple cubic, with volume fractions of 10%, 20%, 30%, 40% and 50%, were conducted in order to determine the effect of the microstructure on the bulk properties. The lower volume fractions for arbitrary representative volume elements were chosen for the parametric study, as it enabled the microstructure meshing easier and simulation results could be validated. The effects of spatial distribution and number and size of particles were also studied while keeping a constant 30% volume fraction. Two types of virtual PBXs materials were analysed, a PBX material (PBX-A) with an elastic-plastic binder, and a PBX material (PBX-B) with a visco-hyperelastic binder. For the elastic-plastic binder PBX-A, the correlation between the crystals dispersion within the binder (nearest-neighbour distance, mode distance, volume disorder) and the PBX properties (Young’s modulus, failure stress, yield stress and plateau stress) were investigated. The bulk Young’s modulus, yield stress and plateau stress increased as the volume fraction increased, whereas the micro-yield stress decreased as the volume fraction increased. Plateau stress, macro-yield stress and Young’s modulus were a function of the particle mode distance, whereas micro-yield stress and tress triaxiality were a function of minimum nearest neighbour distance. For PBX-B, the instantaneous shear modulus and failure stress increased as the volume fraction increased, whereas the failure strain decreased as the volume fraction increases. The instantaneous initial shear modulus was a function of mode and minimum nearest-neighbour distance. The study showed that the mechanical properties of PBX materials could be tailored by controlling the particles’ spatial distribution, morphology, the volume fraction, and the binder system.Open Acces

Hierarchical micro-adaptation of biological structures by mechanical stimuli

Remodeling and other evolving processes such as growth or morphogenesis are key factors in the evolution of biological tissue in response to both external and internal epigenetic stimuli. Based on the description of these processes provided by Taber, 1995 and Humphrey et al., 2002 for three important adaptation processes, remodeling, morphogenesis and growth (positive and negative), we shall consider the latter as the increase/decrease of mass via the increase/decrease of the number or size of cells, leading to a change in the volume of the organ. The work of Rodriguez et al. (1994) used the concept of natural configuration previously introduced by Skalak et al. (1982) to formulate volumetric growth. Later, Humphrey et al. (2002) proposed a constrained-mixture theory where changes in the density and mass of different constituents were taken into account. Many other works about biological growth have been presented in recent years, see e.g. Imatani and Maugin, 2002, Garikipati et al., 2004, Gleason and Humphrey, 2004, Menzel, 2004, Amar et al., 2005, Ganghoffer et al., 2005, Ateshian, 2007, Goriely et al., 2007, Kuhl et al., 2007, Ganghoffer, 2010a, Ganghoffer, 2010b and Goktepe et al., 2010. Morphogenesis is associated to changes in the structure shape (Taber, 1995 and Taber, 2009) while remodeling denotes changes in the tissue microstructure via the reorganization of the existing constituents or the synthesis of new ones with negligible volume change. All these processes involve changes in material properties. Although remodeling and growth can, and usually do, occur simultaneously, there are some cases where these processes develop in a decoupled way. For example, Stopak and Harris (1982) reported some experimental results showing remodeling driven by fibroblasts, with no volume growth. We will assume this scenario in this contribution, focusing exclusively on remodeling processes and on the reorientation of fibered biological structures. It is well known that biological tissue remodels itself when driven by a given stimulus, e.g. mechanical loads such as an increase in blood pressure, or changes in the chemical environment that control the signaling processes and the overall evolution of the tissue. Biological remodeling can occur in any kind of biological tissue. In particular, the study of collagen as the most important substance to be remodeled, in all its types (preferentiallyPeer ReviewedPostprint (author's final draft

Thermo-mechanical and micro-structural characterization of shape memory polymer foams

Shape memory polymer (SMP) materials have the ability to remain in a deformed state and then recover their initial/cast shape. This property has significant potential in many different fields, including aerospace and bio-medical, in which a shape change is desirable and actuation may not be required. SMP materials have been made into nano-reinforced composites and also foamed to improve desired properties for specific applications. SMP foams offer two clear advantages over non-foam SMP materials in applications for the biomedical and aerospace fields. The key advantages are lower density and significant compressibility. The significance of this is that components made out of SMP foam are lighter than traditional SMP materials, more compressible and exhibit minimal transverse change during deformation and shape recovery. This increases the performance and efficiency of devices using SMP foam material. The need for a set of design criteria, models, and limits for the use of shape memory polymer foams was proposed. The effect of temperature and strain on the mechanical behavior, compression, tensile, cyclic compression, constrained recovery and free strain recovery of the material was used to determine the operational limits of the material. Next, the damage mechanism and viscoelastic effects in compressive cycling were determined through further mechanical testing and with the incorporation of three dimensional structure mapping via micro-CT scanning. The influence of microstructure was determined by testing the basic thermomechanical, viscoelastic and shape recovery behavior of foams with relative densities of 20, 30 and 40 percent. A similar suite of tests was then performed on the base epoxy material to generate the material properties necessary to fit constitutive equations to enable computational modeling. This data was then combined with three dimensional microstructures generated from micro-CT scans to develop material models for shape memory foams. These models were then validated by comparing model results to the experimental results under similar conditions.Ph.D.Committee Chair: Gall, Ken; Committee Co-Chair: McDowell, David; Committee Member: Guldberg, Robert; Committee Member: Sanderson, Terry; Committee Member: Shofner, Meisha; Committee Member: Tannenbaum, Rin