import { MatN, VecN } from '@holotope/core';
import type { SimplexConstitutiveEvaluationN } from './simplex-constitutive.js';
/**
 * Matrix-free directional curvature evidence for one simplex energy.
 *
 * `products[i]` is the derivative of the current-position gradient at vertex
 * `i`, hence the mathematical potential `Hessian(U) * direction`.
 */
export interface SimplexConstitutiveHessianVectorEvaluationN<TEvaluation extends SimplexConstitutiveEvaluationN<unknown>> {
    /** Constitutive energy and gradient at the unperturbed positions. */
    readonly base: TEvaluation;
    /** Defensive direction copies in simplex-vertex order. */
    readonly directions: readonly VecN[];
    /** Directional derivative of the intrinsic right Cauchy–Green tensor. */
    readonly directionalRightCauchyGreen: MatN;
    /** Directional derivative of the law's second Piola stress. */
    readonly directionalSecondPiolaStress: MatN;
    /** Potential Hessian-vector products in simplex-vertex order. */
    readonly products: readonly VecN[];
    /** Norm of the summed products; translation invariance makes it zero. */
    readonly netProductResidual: number;
}
interface PreparedSimplexConstitutiveHessianVectorN<TEvaluation extends SimplexConstitutiveEvaluationN<unknown>> {
    readonly caller: string;
    readonly base: TEvaluation;
    readonly currentPositions: readonly VecN[];
    readonly directions: readonly VecN[];
    readonly inverseRestFactor: MatN;
    readonly directionalRightCauchyGreen: MatN;
}
/** Internal directional kinematics shared by every simplex constitutive law. */
export declare function prepareSimplexConstitutiveHessianVectorN<TEvaluation extends SimplexConstitutiveEvaluationN<unknown>>(caller: string, currentPositions: readonly VecN[], directions: readonly VecN[], base: TEvaluation): PreparedSimplexConstitutiveHessianVectorN<TEvaluation>;
/** Internal gradient-product completion from a directional second Piola stress. */
export declare function completeSimplexConstitutiveHessianVectorN<TEvaluation extends SimplexConstitutiveEvaluationN<unknown>>(prepared: PreparedSimplexConstitutiveHessianVectorN<TEvaluation>, directionalSecondPiolaStress: MatN): SimplexConstitutiveHessianVectorEvaluationN<TEvaluation>;
export {};
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