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Finite element force method for joint and material nonlinearity problems
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DOI：10.1016/j.compgeo.2026.108674.png)
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Abstract
En 中文
For geotechnical structures such as slopes and tunnels, their deformation and strength are characterized by both joint nonlinearity and material nonlinearity. Here, joints refer to various geological and artificial interfaces that obey Coulomb’s friction law. The properties of joint nonlinearity and material nonlinearity differ significantly: the former belongs to state nonlinearity, while the latter to process nonlinearity. Directly coupling these two types of nonlinearities during programming is highly likely to cause iterative entanglement, thereby impeding the convergence of iterations. In this study, the contact stress on the joint surface is taken as the primal unknown quantity. The behaviors of both joints and elastoplastic materials are described using variational inequalities, and the iterations are conducted uniformly by means of process iteration. This approach avoids the introduction of any artificial parameters, including Kn/Ks of joints (normal and shear stiffness coefficients). The convergence of the two types of nonlinearities is theoretically guaranteed, thereby completely resolving the issue of iterative entanglement between state nonlinearity and process nonlinearity. Although the proposed solution is implemented within the framework of the force method, most of the involved matrices are identical to those employed in the traditional displacement method, facilitating its straightforward transplantation into displacement method-based programs. The analysis of highly challenging problems has demonstrated that the numerical performance of the method proposed herein is far superior to that of those popular methods including those mature software products.
Keywords:
Joints
Elastoplasticity
Contact
Force method
Variational inequality
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6.2
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2.9W
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