Mech_004 Biaxial Test on Sand with Adaptive Remeshing
Contents
This example provides an introduction to adaptive remeshing and in particular to mesh refinement to capture localised deformation on a shear band. Specific issues considered are:
1Control of the adaptive remeshing process.
2Error estimation using the rate of plastic strain.
3Control of the maximum element size in highly deformed regions using mesh coarsening data.
The example documentation assumes that the following examples have been undertaken beforehand:
1Mesh_001 2-D Unstructured Mesh Generation
2Mech_001 Mechanical Analysis Introduction
The location of regions that exhibit high strain rates is continually changing during the evolution of a geological structure. Additional complexities not present in the original model may emerge; e.g. due to localisation of the deformation, altering the element density necessary for obtaining accurate solutions. Furthermore, relative deformation in regions of faulting, or large geometrical changes induced by folding, often result in excessive element distortion leading to rapid element quality degradation that eventually results in premature termination of the simulation. Adaptive mesh refinement is used to overcome these problems by: 1Evaluating the distortion of the elements and triggering a remesh once elements become too distorted, or if the element size is too large to capture changes in local deformation patterns; e.g. the onset of a fault. 2Evaluating the target mesh using a combination of: (a) User defined maximum and minimum allowable element sizes, applied to the complete mesh or parts of the mesh (b) Error indicators that identify the spatial distribution of target element size; e.g. based on the plastic strain rate. 3Performing the remesh and then mapping the solution data from the old mesh to the new mesh while addressing: (a) Consistency with the constitutive equations, (b) The requirement of equilibrium (which is fundamental for implicit FE simulation), (c) Compatibility of the history--dependent internal variables transfer with the displacement field on the new mesh, (d) Compatibility with evolving boundary conditions, (e) Minimisation of the numerical diffusion of transferred state fields.
Mesh in Initial Configuration
Mesh in After Extension and Deposition of a Syn-Kinematic Layer Mesh Refinement on Faults and Coarse Mesh in Elastic Fault Blocks Adaptivity is defined using 1 Adaptivity_control_data - which identifies that adaptive remeshing is to be used and defines the key control data 2One or more Adaptivity_set_data iset - which define additional data to control the error estimation and target element size either for the whole domain or specific regions of the domain.
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The problem consists of a 30mm high by 10mm wide sand sample that is analysed in plane strain biaxial conditions. The top and base of the sample are fully prescribed, with the top surface having horizontal displacement dx = -0.5mm and vertical displacement dy = 2mm. The small horizontal displacement provides a non-symmetric load that promotes the formation of a single shear band rather than symmetric failure with conjugate shear bands. The confining pressure is 100 Pa which is applied as an initial condition.
The material corresponds to "sand_1" in the "training.mdb" material database, The model is elastoplastic with linear elasticity. The main properties for this material are:
The shape of the initial yield surface in the p-q plane, hardening evolution of pc vs epv and the shape of the initial yield surface in the deviatoric plane are shown below.
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Simulation Cases
Three Cases are considered with a full description of part-geometry and prescribed boundaries provided in Case 1 Extension via a Prescribed Boundary
Case 1 Basic Set Up for Adaptive Remeshing
Case 2 Refinement using Mesh Coarsening Criteria