James K. Knowles Lectures & Caltech Solid Mechanics Symposium - www.caltech.edu

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Monday, February 13, 2017

9:00am to 5:30pm

Gates-Thomas 135

Basile Audoly, Plenary Speaker
The Non-Linear Mechanics of Slender Deformable Bodies

We discuss some challenges arising in the mechanics of
slender (quasi-1D) deformable bodies, such as a thin
thread of polymer, curly hair, or a carpenter's tape for
example. Slender bodies can exhibit a number of
complex and intriguing behaviors that are accessible
through simple experiments. The analysis of slender
bodies exposes one to many of the fundamental concepts
of 3D non-linear mechanics, albeit in a simpler setting where explicit analytical
solutions and fast numerical methods can be proposed. Based on examples, we
review some problems arising in the analysis of deformable bodies, including the
derivation of accurate 1D mechanical models by dimensional reduction, the solution
of non-linear 1D models by analytical or numerical methods, and the analysis of
material or geometrical instabilities.

Sarah A. Bentil, Plenary Speaker
Characterizing the Mechanical Behavior of Soft Materials

The ability to determine the mechanical behavior of soft
materials is invaluable to biomedical applications, such as
the design of biocompatible implants and tissue
simulants. This seminar will highlight two projects where
the mechanical behavior of soft materials was obtained
following quasi-static or dynamic experiments for use in
biomedical applications. In the first project, finite element
(FE) simulations were performed to investigate the benefit of coating siliconsubstrate
microelectrode arrays with hydrogel material. The brain and hydrogel
coating were described using coefficients of the fractional Zener (FZ) constitutive
model that were optimized using quasi-static experimental data from pig brains.
The second project focuses on the development of an eye simulant for assessing the
effectiveness of ocular protective systems. The silicone elastomer, polydimethylsiloxane
(PDMS), was considered as a candidate material for this synthetic eye. PDMS
samples were subjected to shock tube inflation experiments to determine the
dynamic elastic properties. Dynamic pressure history was recorded and digital image
correlation (DIC) was applied to capture the displacement field. The dynamic Young's
modulus of PDMS was extracted using the phase velocity of a traveling wave on the
sample surface and the sample's out-of-plane displacement frequency.

David L. Henann, Plenary Speaker
A Continuum Model for Steady Flows of Dense Granular Materials

Dense, dry granular flows display many manifestations
of grain-size dependence in which cooperative effects
at the microscopic level have an observable impact on
the macroscopic flow phenomenology. In one class of
phenomenology, the characteristic length-scales
associated with flow velocity fields are strongly
dependent on the grain-size. In a second class of
phenomenology, dense granular materials display size-dependence of the flow
threshold. For example, flows of grains down an inclined surface exhibit a size
effect whereby thinner layers require more tilt to flow. Neither of these classes of
behaviors may be captured by scale-independent constitutive theories, and
hence, the formulation of a predictive model for dense granular flow has proven
to be particularly difficult. In this talk, we present a nonlocal continuum-level
constitutive model for steady flow – called the nonlocal granular fluidity model –
aimed at filling this need. We demonstrate that the model quantitatively captures
the size-dependence of both steady flow fields and the flow threshold – i.e., the
conditions under which steady flow is possible – by comparing model predictions
to measurements from experiments and discrete element method calculations.
Throughout, we emphasize the geometric generality of the model by considering
flows in a wide variety of configurations.

Christian Linder, Plenary Speaker
Beyond Inf-Sup: Stability Estimates for Multi-Field Variational Principles by
Means of Energetic Conditions in Incremental Form

It is well known that mixed finite element methods
have to satisfy certain criteria to provide solvability
and stability. The latter criterion is, in the classical
context of two-field saddle-point problems such as
Stokes flow or quasi-incompressible elasticity, ensured by finite element types
that satisfy the well-known inf-sup condition to ensure mesh-independent
stability estimates. A number of finite element methods for novel multi-physics
applications such as coupled Cahn-Hilliard-type flow in elastic media, extended
phase-field models for fracture, poroelasticity or topology optimization as well as
gradient-extended plasticity models have a similar saddle-point structure.
However, they correspond to a multi-field variational principle and only some of
them suffer from similar instabilities. The question as to whether stability
estimates are satisfied in these cases for standard discretizations and, if not, how
conditions can be obtained that satisfy these estimates, will be discussed in this
presentation. Several multi-physics problems developed in our group, that
possess a similar saddle-point structure, are investigated with respect to this
proposed method. For these examples, the satisfaction of the corresponding
conditions is shown by means of numerical tests and novel element types for
poroelasticity, recently proposed by our group, that are based on incompatible
modes and subdivision methods.

For more information, please contact Lynn Seymour by phone at (626) 395-4107 or by email at [email protected] or visit Knowles Lecture.

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