Multiscale analysis of materials with anisotropic microstructure as micropolar continua

Multiscale procedures are often adopted for the continuum modeling of materials composed of a specific micro-structure. Generally, in mechanics of materials only two-scales are linked. In this work the original (fine) micro-scale description, thought as a composite material made of matrix and fibers/particles/crystals which can interact among them, and a scale-dependent continuum (coarse) macro-scale are linked via an energy equivalence criterion. In particular the multiscale strategy is proposed for deriving the constitutive relations of anisotropic composites with periodic microstructure and allows us to reduce the typically high computational cost of fully microscopic numerical analyses. At the microscopic level the material is described as a lattice system while at the macroscopic level the continuum is a micropolar continuum, whose material particles are endowed with orientation besides position. The derived constitutive relations account for shape, texture and orientation of inclusions as well as internal scale parameters, which account for size effects even in the elastic regime in the presence of geometrical and/or load singularities. Applications of this procedure concern polycrystals, wherein an important descriptor of the underlying microstructure gives the orientation of the crystal lattice of each grain, fiber reinforced composites, as well as masonry-like materials. In order to investigate the effects of micropolar constants in the presence of material non central symmetries, some numerical finite element simulations, with elements specifically formulated for micropolar media, are presented. The performed simulations, which extend several parametric analyses earlier performed [1], involve two-dimensional media, in the linear framework, subjected to compression loads distributed in a small portion of the medium

Mechanical Metamaterials with Negative Compressibility Transitions

When tensioned, ordinary materials expand along the direction of the applied force. Here, we explore network concepts to design metamaterials exhibiting negative compressibility transitions, during which a material undergoes contraction when tensioned (or expansion when pressured). Continuous contraction of a material in the same direction of an applied tension, and in response to this tension, is inherently unstable. The conceptually similar effect we demonstrate can be achieved, however, through destabilisations of (meta)stable equilibria of the constituents. These destabilisations give rise to a stress-induced solid-solid phase transition associated with a twisted hysteresis curve for the stress-strain relationship. The strain-driven counterpart of negative compressibility transitions is a force amplification phenomenon, where an increase in deformation induces a discontinuous increase in response force. We suggest that the proposed materials could be useful for the design of actuators, force amplifiers, micro-mechanical controls, and protective devices.Comment: Supplementary information available at http://www.nature.com/nmat/journal/v11/n7/abs/nmat3331.htm

Auxetic regions in large deformations of periodic frameworks

In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic mechanisms constructed from quadrilaterals with diagonals as periods and other frameworks with two vertex orbits. We relate several geometric and kinematic descriptions.Comment: Presented at the International Conference on "Interdisciplinary Applications of Kinematics" (IAK18), Lima, Peru, March 201

Escaping the Ashby limit for mechanical damping/stiffness trade-off using a constrained high internal friction interfacial layer.

The development of new materials with reduced noise and vibration levels is an active area of research due to concerns in various aspects of environmental noise pollution and its effects on health. Excessive vibrations also reduce the service live of the structures and limit the fields of their utilization. In oscillations, the viscoelastic moduli of a material are complex and it is their loss part - the product of the stiffness part and loss tangent - that is commonly viewed as a figure of merit in noise and vibration damping applications. The stiffness modulus and loss tangent are usually mutually exclusive properties so it is a technological challenge to develop materials that simultaneously combine high stiffness and high loss. Here we achieve this rare balance of properties by filling a solid polymer matrix with rigid inorganic spheres coated by a sub-micron layer of a viscoelastic material with a high level of internal friction. We demonstrate that this combination can be experimentally realised and that the analytically predicted behaviour is closely reproduced, thereby escaping the often termed 'Ashby' limit for mechanical stiffness/damping trade-off and offering a new route for manufacturing advanced composite structures with markedly reduced noise and vibration levels

New Mechanics of Traumatic Brain Injury

The prediction and prevention of traumatic brain injury is a very important aspect of preventive medical science. This paper proposes a new coupled loading-rate hypothesis for the traumatic brain injury (TBI), which states that the main cause of the TBI is an external Euclidean jolt, or SE(3)-jolt, an impulsive loading that strikes the head in several coupled degrees-of-freedom simultaneously. To show this, based on the previously defined covariant force law, we formulate the coupled Newton-Euler dynamics of brain's micro-motions within the cerebrospinal fluid and derive from it the coupled SE(3)-jolt dynamics. The SE(3)-jolt is a cause of the TBI in two forms of brain's rapid discontinuous deformations: translational dislocations and rotational disclinations. Brain's dislocations and disclinations, caused by the SE(3)-jolt, are described using the Cosserat multipolar viscoelastic continuum brain model. Keywords: Traumatic brain injuries, coupled loading-rate hypothesis, Euclidean jolt, coupled Newton-Euler dynamics, brain's dislocations and disclinationsComment: 18 pages, 1 figure, Late

Linear viscoelasticity - bone volume fraction relationships of bovine trabecular bone

Trabecular bone has been previously recognized as time-dependent (viscoelastic) material, but the relationships of its viscoelastic behaviour with bone volume fraction (BV/TV) have not been investigated so far. Therefore, the aim of the present study was to quantify the time-dependent viscoelastic behaviour of trabecular bone and relate it to BV/TV. Uniaxial compressive creep experiments were performed on cylindrical bovine trabecular bone samples ([Formula: see text] ) at loads corresponding to physiological strain level of 2000 [Formula: see text] . We assumed that the bone behaves in a linear viscoelastic manner at this low strain level and the corresponding linear viscoelastic parameters were estimated by fitting a generalized Kelvin–Voigt rheological model to the experimental creep strain response. Strong and significant power law relationships ([Formula: see text] ) were found between time-dependent creep compliance function and BV/TV of the bone. These BV/TV-based material properties can be used in finite element models involving trabecular bone to predict time-dependent response. For users’ convenience, the creep compliance functions were also converted to relaxation functions by using numerical interconversion methods and similar power law relationships were reported between time-dependent relaxation modulus function and BV/TV

A model for the compressible, viscoelastic behavior of human amnion addressing tissue variability through a single parameter

A viscoelastic, compressible model is proposed to rationalize the recently reported response of human amnion in multiaxial relaxation and creep experiments. The theory includes two viscoelastic contributions responsible for the short- and long-term time- dependent response of the material. These two contributions can be related to physical processes: water flow through the tissue and dissipative characteristics of the collagen fibers, respectively. An accurate agreement of the model with the mean tension and kinematic response of amnion in uniaxial relaxation tests was achieved. By variation of a single linear factor that accounts for the variability among tissue samples, the model provides very sound predictions not only of the uniaxial relaxation but also of the uniaxial creep and strip-biaxial relaxation behavior of individual samples. This suggests that a wide range of viscoelastic behaviors due to patient-specific variations in tissue composition

A population-specific material model for sagittal craniosynostosis to predict surgical shape outcomes

Sagittal craniosynostosis consists of premature fusion (ossification) of the sagittal suture during infancy, resulting in head deformity and brain growth restriction. Spring-assisted cranioplasty (SAC) entails skull incisions to free the fused suture and insertion of two springs (metallic distractors) to promote cranial reshaping. Although safe and effective, SAC outcomes remain uncertain. We aimed hereby to obtain and validate a skull material model for SAC outcome prediction. Computed tomography data relative to 18 patients were processed to simulate surgical cuts and spring location. A rescaling model for age matching was created using retrospective data and validated. Design of experiments was used to assess the effect of different material property parameters on the model output. Subsequent material optimization—using retrospective clinical spring measurements—was performed for nine patients. A population-derived material model was obtained and applied to the whole population. Results showed that bone Young’s modulus and relaxation modulus had the largest effect on the model predictions: the use of the population-derived material model had a negligible effect on improving the prediction of on-table opening while significantly improved the prediction of spring kinematics at follow-up. The model was validated using on-table 3D scans for nine patients: the predicted head shape approximated within 2 mm the 3D scan model in 80% of the surface points, in 8 out of 9 patients. The accuracy and reliability of the developed computational model of SAC were increased using population data: this tool is now ready for prospective clinical application