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Research on two-dimensional (2D) materials, such as graphene and molybdenum disulfide (MoS2), now involves researchers worldwide, implementing cutting edge technology to study them. However, when considering using 2D materials in such promising applications, one of the major concerns is the mechanical failure, which remains heavily underexplored. In this work, we demonstrate the use of sequential and concurrent multiscale modeling to study the effect of various fracture modes on graphene and molybdenum disulfide (MoS2). Some of the fracture modes explored are pure tensile loading, shear loading, and a combination of tensile and shear loading and cyclic loading to investigate fatigue.

In this work, the kinematics and basic laws of micromorphic theory are briefly introduced. Then, constitutive equations for micromorphic thermo-visco-elastoplastic solids are rigorously derived. Finite element equations for the displacement, micromotion and temperature fields are formulated based on the principle of virtual work. As examples, three-dimensional, dynamic, finite strain, mixed mode fracture mechanics problems have been solved by a general purpose in-house developed code. Numerical results, including temperature, [Formula: see text] norms of stresses, plastic strains and micromotions, are presented and the physical meanings are discussed. This paper provides theoretical fundamentals to study the thermo-visco-elastic-plastic behaviors of micromorphic solids and constructs a numerical framework to study fracture mechanics of edge-crack problems.

The irreversibility, temperature, and entropy are identified for an atomic system of solid material. Thermodynamics second law is automatically satisfied in the time evolution of molecular dynamics (MD). The irreversibility caused by an atom spontaneously moves from a non-stable equilibrium position to a stable equilibrium position. The process is dynamic in nature associated with the conversion of potential energy to kinetic energy and the dissipation of kinetic energy to the entire system. The forward process is less sensitive to small variation of boundary condition than reverse process, causing the time symmetry to break. Different methods to define temperature in molecular system are revisited with paradox examples. It is seen that the temperature can only be rigorously defined on an atom knowing its time history of velocity vector. The velocity vector of an atom is the summation of the mechanical part and the thermal part, the mechanical velocity is related to the global motion (translation, rotation, acceleration, vibration, etc.), the thermal velocity is related to temperature and is assumed to follow the identical random Gaussian distribution for all of its [Formula: see text], [Formula: see text] and [Formula: see text] component. The [Formula: see text]-velocity (same for [Formula: see text] or [Formula: see text]) versus time obtained from MD simulation is treated as a signal (mechanical motion) corrupted with random Gaussian distribution noise (thermal motion). The noise is separated from signal with wavelet filter and used as the randomness measurement. The temperature is thus defined as the variance of the thermal velocity multiply the atom mass and divided by Boltzmann constant. The new definition is equivalent to the Nose–Hover thermostat for a stationary system. For system with macroscopic acceleration, rotation, vibration, etc., the new definition can predict the same temperature as the stationary system, while Nose–Hover thermostat predicts a much higher temperature. It is seen that the new definition of temperature is not influenced by the global motion, i.e., translation, rotation, acceleration, vibration, etc., of the system. The Gibbs entropy is calculated for each atom by knowing normal distribution as the probability density function. The relationship between entropy and temperature is established for solid material.

This work developed the optimal and active control algorithms applicable to structural control for earthquake resistance. [Lewis, F. L., Vrabie, D. and Syrmos, V. L. [2012] Optimal Control (John Wiley & Sons)] developed a rigorous and comprehensive procedure for the derivation of an optimal control strategy based on the calculus of variation. This work is an application of Lewis’ formulation to the control of a structure for earthquake resistance. We developed a computer software which can be used to generate a dynamic model to simulate a planar structure and to construct the control law. This model also includes the tendon driven actuators, sensors and true history of earthquake excitation. The control law has two parts: (I) the feedback control which depends on the estimate state variables (Kalman filter) and (II) the record of the realistic earthquake excitation. The optimal control problem eventually leads to a two-point boundary value problem whose solution hinges on the knowledge of the entire history of the earthquake excitation. We employ true records of earthquake excitation as input. This approach enables one to solve the Riccati equations rigorously. Then, from the simulation results, one may study the relations between the control algorithm design and the characteristics (frequency, amplitude and duration) of earthquake excitation.

Most mechanobiology phenomena commonly involve biological growth and deformation. In this work, we propose an innovative model of cancerous growth which posits that an expandable tumor can be described as a poroelastic medium consisting of solid and fluid components. In our biologically informed mechanical description of tumor growth dynamics, we derive the governing equations of the tumor’s growth and incorporate them with large deformation and materially nonlinear constitutive equations to improve the accuracy and efficiency of our simulation. Meanwhile, the dynamic finite element equations (DFE) for coupled displacement field and pressure field are formulated and solved. The 3-dimensional porous model is introduced. Numerical results are presented and discussed.

Most biological phenomena commonly involve growth and expansion mechanics. In this work, we propose an innovative model of cancerous growth which posits that an expandable tumor can be described as a poroelastic medium consisting of solid and fluid components. To verify the feasibility of the model, we utilized an established epithelial human breast cancer cell line (MDA-MB-231) to generate an in vitro tumorsphere system to observe tumor growth patterns in both constrained and unconstrained growth environments. The tumorspheres in both growth environments were grown with and without the FDA-approved anti-breast cancer anthracycline, Doxorubicin (Dox), in order to observe the influence small molecule drugs have on tumor-growth mechanics. In our biologically informed mechanical description of tumor growth dynamics, we derive the governing equations of the tumor’s growth and incorporate them with large deformation to improve the accuracy and efficiency of our simulation. Meanwhile, the dynamic finite element equations (DFE) for coupled displacement field and pressure field are formulated. Moreover, the porosity and growth tensor are generalized to be functions of displacement and pressure fields. We also introduce a specific porosity and growth tensor. In both cases, the formalism of continuum mechanics and DFE are accompanied by accurate numerical simulations.

It is an established fact that multiscale modeling is an effective way of studying materials over a realistic length scale. In this work, we demonstrate the use of sequential and concurrent multiscale modeling to study the effect of cyclic loading on both the atomic and continuum regions, of graphene, a material which comes with its own set of unique properties. Moreover, to further strengthen this work, we have studied the temperature effects during the cyclic loading, by analyzing the effect of loading and varying temperature gradients.