A three-dimensional finite strain micromorphic materially linear isotropic elastic model is formulated in two ways for finite element implementation: (i) direct finite strain elasticity; and (ii) rate form with semi-implicit time integration. The model is based upon the finite strain isotropic micromorphic elasticity model proposed by Eringen and Suhubi in 1964. For (i), the direct formulation, the constitutive equations are calculated in the reference configuration, and the resulting stresses are mapped to the current configuration. For (ii), the rate formulation, the constitutive equations are integrated in time in the current configuration using the Truesdell objective stress rates. After formulating the coupled weak form, the balance of linear momentum and the balance of first moment of momentum are linearized to construct the consistent tangent for solution by the Newton-Raphson method. Three-dimensional numerical examples are analysed to compare the two formulations (i) and (ii) for standard finite strain isotropic elasticity, and the formulation (i) is used to demonstrate the elastic length scale effects that come through the higher-order couple stress in the micromorphic theory.
This study proposes a new method to obtain the lateral response of pile groups by incorporating the pile group effect in layered soils. When a pile is loaded laterally, it creates a zone of influence in the direction of loading. In a pile group, each pile placed in the influence zone of prior piles is exposed to extra loads due to the load transfers from other piles. This mechanism results in a group effect which causes each pile in the group to have a different deflection curve compared to that of an identical isolated single pile under the same load. This study starts with a mathematical approach to model the interaction of two piles and then extends it to pile groups. The governing differential equation of a pile deflection problem is modified to take the pile-soil-pile interaction into account and solved analytically for each pile while the soil parameters and displacement fields around each pile are obtained numerically using the finite difference method written in Fortran language. The model captures the additional pile deflections induced by the group effects in pile groups and the results match well with the results of the existing methods, especially the finite element method.
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