Research on two-dimensional (2D) materials, such as graphene and molybdenum disulfide (MoS 2 ), 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 (MoS 2 ). 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.

In this work, the kinematics and basic laws of microcontinuum field theories, including micromorphic theory and micropolar theory, are introduced. Then, constitutive equations for micromorphic thermo-visco-elastic solids, heat conducting fluids, and thermal plasticity are rigorously derived. The concept of material force, which may also be named as Eshelby mechanics, is briefly introduced. The balance law of pseudo-momentum, including the detailed expression of the material forces, for the mathematical theory of micromorphic plasticity is rigorously derived. Finally, a set of finite element equations for the coupling of finite displacement, micromotion, and temperature fields is rigorously formulated.

This presentation focuses on the new and upcoming concept of 4D printing and its vast scope and importance in the research and development in industry. The 3D printing object is considered as a layered structure. Each layer may have different orientation. Therefore each layer may behave differently under the change of its environment. We formulate the theoretical shape changing process of 4D printing resulted from (I) the biological growth or swelling, (II) the change of temperature, and (III) the effect of electric field on piezoelectric material of the 3D printing product. Then we illustrate this theory visually through finite element analysis by solving several typical problems. Large strain is incorporated in the finite element formulation. We verify the finite element code through the conservation of the axis-symmetry or the mirror symmetry of the sample problems. This presentation demonstrates the capabilities and applicability of 4D printing.

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.