Extended syntax

The extended syntax uses the ``metastep'' concept and has the following format:

NonLinearStatic	[nmsteps(in) #]
	nsteps(in) #
	[renumber(in) #]
	[contextOutputStep(in) #]
	[sparselinsolverparams(string) #]
	[nonlinform(in) #]
	$\langle$[nonlocstiff(in) #]$\rangle$
	$\langle$[nonlocalext() #]$\rangle$
	$\langle$[loadbalancing() #]$\rangle$

This record is immediately followed by metastep records with the format described bellow. The analysis parameters have following meaning

• nmsteps - determines the number of ``metasteps'', default is 1.
• nsteps - determines number of solution steps.
• Nonzero value of optional parameter renumber turns on the equation renumbering to optimize the profile of characteristic matrix (uses Sloan algorithm). By default, profile optimization is not performed. It will not work in parallel mode.
• contextOutputStep - causes the context file to be created for every contextOutputStep-th step and when needed. Useful for postprocessing.
• The sparselinsolverparams parameter describes the sparse linear solver attributes and is explained in section 6.17.
• nonlinform - formulation of non-linear problem. If == 1 (default), total Lagrangian formulation in undeformed original shape is used (first-order theory). If == 2, the equlibrated displacements are added to original ones and updated in each time step (second-order theory).
• nonlocstiff - determines whether the tangent stiffness extension for nonlocal models is activated. If == 0 (default) this option is not active. If == 1 the support for nonlocal tangent stiffness is activated.
• The nonlocalext turns on the nonlocal constitutive extension. The extension considers a band of remote elements involved in computation of nonlocal variables (see fig. 7 illustrating this approach for node-cut partitioning).
• The loadbalancing parameter describes the dynamic load balancing attributes and is explained in section 6.19.

The metastep record has following general syntax:

	nsteps(in) #
	[controllmode(in) #]
	[deltat(rn) #]
	rtolv(rn) #
	[stiffmode(in) #]
	[refloadmode(in) #]
	solverParams() #
	[sparselinsolverparams(string) #]
	[donotfixload() #]

where

-

controllmode - determines the type of solution control used for corresponding meta step. if == 0 then indirect control will be used to control solution process (default). if == 1 then direct displacement or load control will be used. In the later mode, one can apply the prescribed load increments as well as control displacements.

-

deltaT - is time step length. If not specified, it is set equal to 1,0. Each solution step has associated the corresponding intrinsic time, at which the loading is generated. The deltaT determines the spacing between solution steps on time scale.

-

rtolv - determines relative convergence norm (both for displacement iterative change vector and for residual unbalanced force vector).

-

stiffMode - If == 0 (default) then tangent stiffness will be used at new step beginning and whenever numerical method will ask for stiffness update. If == 1 the use of secant tangent will be forced. The secant stiffness will be used at new step beginning and whenever numerical method will ask for stiffness update. If == 2 then original elastic stiffness will be used during the whole solution process.

-

The refloadmode parameter determines how the reference force load vector is obtained from given totalLoadVector and initialLoadVector. The initialLoadVector describes the part of loading which does not scale. Works only for force loading, other non-force components (temperature, prescribed displacements should always given in total values). If refLoadInputMode is 0 (rlm_total, default) then the reference incremental load vector is defined as totalLoadVector assembled at given time. If refLoadInputMode is 1 (rlm_inceremental) then the reference load vector is obtained as incremental load vector at given time.

-

solverParams - parameters of solver. The solver type is determined using controllmode.

 $$

The sparselinsolverparams parameter describes the sparse linear solver attributes and is explained in section 6.17.

-

By default, reached load at the end of metastep will be maintained in subsequent steps as fixed, non scaling load and load level will be reset to zero. This can be changed using keyword donotfixload, which if present, causes the loading to continue, not resetting the load level. For the indirect control the reached loading will not be fixed, however, the new reference loading vector will be assembled for the new metastep.

If controllmode corresponds to direct control, the Newton-Raphson solver is used. Under direct control, the total load vector assembled for specific solution step represents the load level, where equilibrium is searched. The implementation supports also displacement control - it is possible to prescribe one or more displacements by applying ``quasi prescribed'' boundary condition(s)¹ The load level then represents the time, where the equilibrium has been found. The solver parameters (solverParams for load-control are:

	maxiter(in) #
	[minsteplength(in) #]
	[manrmsteps(in) #]
	[ddm(ia) #] [ddv(ra) #] [ddltf(in) #]
	[linesearch(in) #] [lsearchamp(rn) #]
	[lsearchmaxeta(rn) #] [lsearchtol(rn) #]

where

• maxiter determines the maximum number of iterations allowed to reach equilibrium. If equilibrium is not reached, the step length (corresponding to time) is reduced.
• minsteplength parameter is the minimum step length allowed.
• If manrmsteps parameter is nonzero, then the modified N-R scheme is used, with the stiffness updated after manrmsteps steps.
• ddm is array specifying the degrees of freedom, which displacements are controlled. Let the number of these DOFs is N. The format of ddm array is 2*N dofman1 idof1 dofman2 idof2 ... dofmanN idofN, where the dofmani is the number of i-th dof manager and idofi is the corresponding DOF number.
• ddv is array of relative weights of controlled displacements, the size should be equal to N. The actual value of prescribed dofs is defined as a product of its weight and the value of load time function specified using ddltf parameter (see below).
• ddltf number of load time function, which is used to evaluate the actual displacements of controlled dofs.
• linesearch nonzero value turns on line search algorithm. The lsearchtol defines tolerance (default value is 0.8), amplification factor can be specified using lsearchamp parameter (should be in interval $(1,10)$), and parameter lsearchmaxeta defines maximum limit on the length of iterative step (allowed range is $(1.5,15)$).

if controllmode corresponds to indirect control, then CALM solver is used. The value of reference load vector is determined by refloadmode parameter mentioned above at the first step of each metastep. However, the user must ensure, that the same value of reference load vector could be obtained for all solution steps of particular metastep (this is necessary for restart and adaptivity to work). The corresponding meta step solver parameters (solverParams are:

	Psi(rn) #
	MaxIter(in) #
	[minStepLength(in) #]
	stepLength(rn) #
	reqIterations(in) #
	[manrmsteps(in) #]
	[hpcmode(in) #] [hpc(ia) #] [hpcw(ia) #]
	[linesearch(in) #] [lsearchamp(rn) #]
	[lsearchmaxeta(rn) #] [lsearchtol(rn) #]

where

• Psi - CALM $\Psi$ control parameter. For $\Psi$ = 0 displacement control is applied. For nonzero values the load control applies together with displacement control (ALM). For large $\Psi$ load control apply.
• MaxIter - determines the maximum number of iteration allowed to reach equilibrium state. If this limit is reached, restart follows with smaller step length.
• minStepLength - minimum step length. The step length will never be smaller. If convergence problems are encountered and step length cannot be decreased, computation terminates.
• stepLength - initial step length (the arc-length).
• reqIterations - number of required iteration during iterative solution.
• manrmsteps - Forces the use of accelerated Newton Raphson method, where stiffness is updated after manrmsteps steps. By default, the modified NR method is used (no stiffness update).
• hpcmode Parameter determining the alm mode. Possible values are: 0 - (default) full ALM with quadratic constrain and all dofs, 1 - (default, if hpc parameter used) full ALM with quadratic constrain, taking into account only selected dofs (see hpc param), 2 - linearized constrain in displacements only, taking into account only selected dofs with given weight (see hpc and hpcw parameters).
• hpc - Special parameter for Hyper-plane control, when only selected DOFS are taken account in ALM step length condition. Important mainly for material nonlinear problems with strong localization. This array selects the degrees of freedom, which displacements are controlled. Let the number of these DOFs is N. The format of ddm array is 2*N dofman1 idof1 dofman2 idof2 ... dofmanN idofN, where the dofmani is the number of i-th dof manager and idofi is the corresponding DOF number.
• hpcw - Array of dof weights in linear constraint. The dof ordering is determined by hpc param, size of array should be N.
• linesearch nonzero value turns on line search algorithm. The lsearchtol defines tolerance, amplification factor can be specified using lsearchamp parameter (should be in interval $(1,10)$), and parameter lsearchmaxeta defines maximum limit on the length of iterative step (allowed range is $(1.5,15)$).