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Symplectic Analysis of Wrinkles in Elastic Layers with Graded Stiffnesses

Wrinkles in layered neo-Hookean structures were recently formulated as a Hamiltonian system by taking the thickness direction as a pseudo-time variable. This enabled an efficient and accurate numerical method to solve the eigenvalue problem for onset wrinkles. Here, we show that wrinkles in graded elastic layers can also be described as a time-varying Hamiltonian system. The connection between wrinkles and the Hamiltonian system is established through an energy method.

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Deriving a lattice model for neo-Hookean solids from finite element methods

Lattice models are popular methods for simulating deformation of solids by discretizing continuum structures into spring networks. Despite the simplicity and efficiency, most lattice models only rigorously converge to continuum models for lattices with regular shapes. Here, we derive a lattice model for neo-Hookean solids directly from finite element methods (FEM). The proposed lattice model can handle complicated geometries and tune the material compressibility without significantly increasing the complexity of the model.

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EMI 2018 Mini-Symposium MS20 “Nonlinear mechanics of highly deformable solids and structures”

Dear Colleague,

The next Engineering Mechanics Institute Conference (EMI) will take place from May 29th to June 1st, 2018, at MIT.

As organizers of the Mini-Symposium MS20 “Nonlinear mechanics of highly deformable solids and structures”, it is our pleasure to invite you and your students to participate in our mini symposium.
The deadline for abstract submission is January 31st, 2018.

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Predicting fracture energies and crack-tip fields of soft tough materials

Soft materials including elastomers and gels are pervasive in biological systems and technological applications. Whereas it is known that intrinsic fracture energies of soft materials are relatively low, how the intrinsic fracture energy cooperates with mechanical dissipation in process zone to give high fracture toughness of soft materials is not well understood. In addition, it is still challenging to predict fracture energies and crack-tip strain fields of soft tough materials.

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Stroh formalism and hamilton system for 2D anisotropic elastic

 

We have read some papers of stroh formalism and the textbook of Tom Ting, and found that the stroh formalism and the hamilton system proposed by prof.zhong wanxie had some relation. We want to know whether the stroh formalism is enough for the analysis of the anisotropic elastic? Thus's to say, for some problems could not  give the satisfied answer which we may try the hamilton framework. I briefly compare the two methods as follows:

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wave propagation in Hamilton Systems

I am a junior graduate student now, and very interesting in wave motion. My advisor Prof. Zhong wanxie and his PHD student qiang Gao have developed a precise numerical technique to solve the Rayleigh wave frequency equation, which can avoid the missing root. They did a systematic work involving surface wave propagation in a transversely isotropic stratified solid resting on an elastic semi-infinte space, wave propagation in the anisotropic layered media and the propagation of stationary and non-stationary random waves in a viscoelastic, transversely isotropic and stratified half space.

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Questions about symplectic conservation of MD

MD method is widely employed in different areas. However, as we all known that the limitation in timescales and length scales and the stiffness problem due to high frequency molecular vibrations are still important and difficult issues to be solved. While, characteristics of symplectic conservation is important for numerical methods. I found that only a few leteratures discussed this issue, and seldom new symplectic methods were widely adopted expect for the classical leap-frog Verlet  algorithm whose characteristics of symplectic conservation was proofed later.

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