STC-MPM: Coupled Deformation, Progressive Damage, and Cut Formation in Soft-Tissue Cutting

Kewei Zuo; Jiahe Chen; Ziao Kuang; Junsheng Zhu; Etsuko Kobayashi

cs.ROOct 5, 2026

STC-MPM: Coupled Deformation, Progressive Damage, and Cut Formation in Soft-Tissue Cutting

Authors: Kewei Zuo, Jiahe Chen, Ziao Kuang, Junsheng Zhu, Etsuko Kobayashi

Organizations: Department of Precision Engineering, The University of Tokyo, Tokyo, Japan

Abstract

Cutting is a recurring operation in robotic au tomation, from food preparation to surgical tissue resection. For highly compliant targets, blade motion may deform or displace the material rather than advance the intended cut, while progressive failure changes load transfer and subsequent tool tissue interaction. A computational description must therefore connect cut formation to the evolving mechanical response, rather than specifying the incision independently of material failure. We present STC-MPM (Soft Tissue Cutting with the Material Point Method), a framework that couples finite-strain deformation, history-driven continuum damage, and configurable post-failure treatment. Damage initiates only when a tensile strain history exceeds a material threshold within the blade process zone. Progressive degradation changes stress transmission before the post-failure policy is applied, while the remaining tissue continues to deform, move, and interact with the tool. Numerical scalpel studies using delayed particle deactivation follow this response through insertion and withdrawal. Under identical blade motion, reducing the damage-rate limit leaves the first recorded damage time unchanged but delays and increases peak reaction force, delays particle deactivation, and increases the fixed-cohort displacement statistic at maximum insertion. The matched comparison illustrates how post-initiation failure evolution alters subsequent tool loading and recorded material motion. STC-MPM thus supports joint analysis of cut formation and accompanying tissue response without a pre-inserted cutting interface.

Figures & tables

Method	Failure initiation	Failure localization	Post-initiation evolution	Separation representation	Tool–failure coupling
Ionescu et al. [ 22 ]	Matrix shear-strain and fiber-strain thresholds	Bulk material satisfying component thresholds	Abrupt loss of matrix/volumetric or fiber stress support	Component-level loss of support; no dedicated sharp cut partition	Penetration loads induce material failure; no cutting-edge initiation gate
Cohesive FEM examples [ 9 , 18 ]	Interface traction–separation law	Represented cohesive surface	Progressive loss of cohesive traction	Opening across the cohesive interface	Tool contact loads the deforming body and represented fracture surface
Cutting XFEM [ 7 ]	Geometric cut specification, not a constitutive onset law	Tool-defined surface within elements	Discontinuity update; no damage law implied by enrichment	Enriched displacement field without conforming remeshing	Cut geometry determines the represented discontinuity
MLS-MPM/CPIC cutting [ 28 ]	Geometric compatibility	Prescribed moving surface	Compatibility updates, rather than material degradation	Side-compatible particle–grid transfers	Tool/surface geometry defines the transfer discontinuity
PFF-MPM branch of CD-MPM [ 23 ]	Tensile-energy-driven variational fracture	Evolving bulk phase field	Gradient-regularized damage with fracture energy and length scale	Diffuse stiffness degradation; not a cutter-side partition	General externally loaded fracture; no cutter-specific initiation gate
DiSECt [ 5 , 6 ]	Knife-contact-force-driven weakening of cutting springs	Preprocessed cutting surface	Interface spring stiffness decreases toward zero	Virtual-node interface opens as springs lose support	Tool contact progressively weakens a prepared interface

TABLE I: Methodological comparison of representative fracture and cutting formulations.

Fig. 1: Localized mechanics at cutting onset. (a) A scalpel loads a deformable tissue block. (b) The enlarged edge neighborhood illustrates concentration of the tensile-strain history $\kappa$ , with the inset showing the initiation threshold $\varepsilon_{c}$ . Tissue is still continuous at damage onset. The colors and inset are qualitative, not computed fields or measured data; new damage also requires the blade-process-zone condition in Section IV-C .

Fig. 2: Cutting process and STC-MPM update cycle. Top: initial contact, deformation and strain concentration, damage initiation and progression, and cut formation by failed-particle deactivation. Bottom: external inputs, particle-to-grid (P2G) transfer, grid dynamics and contact, grid-to-particle (G2P) transfer, and damage/failure updates within one time step. Damage is evaluated using the updated deformation state; degraded stress and active-set changes affect the subsequent step. The numerical cycle is repeated within each physical stage, not mapped one-to-one onto the upper panels. All views are schematic.

Fig. 3: Post-failure policies and particle–grid transfer compatibility. (a) Inactive records after the delayed-erosion interval. (b) Retained failed particles that remain active with compression-only recoverable elasticity. (c), (d) Representative P2G and G2P links for the same retained failed particle with the optional transfer barrier enabled. Dark arrows denote allowed transfers; crossed grey links are excluded. The red dashed line indicates the resolved local cut side. Panels (a), (b) compare alternative policies, whereas (c), (d) show opposite transfer directions, not separate policies. Inactive records do not participate in either transfer.

Quantity	Value
Young’s modulus, $E_{Y}$	$60\,\mathrm{kPa}$
Poisson’s ratio, $\nu$	$0.45$
Density, $\rho$	$1000\,\mathrm{kg/m^{3}}$
Critical strain, $\varepsilon_{c}$	$0.22$
Reference fracture-energy parameter, $G_{c}^{\ast}$	$0.3\,\mathrm{J/m^{2}}$
Characteristic length, $l_{c}$	$0.1\,\mathrm{mm}$

TABLE II: Reference scalpel settings; the main comparison changes only

\dot{d}_{\max}

from

10

1\,\mathrm{s^{-1}}

Fig. 4: Reference scalpel response with $\dot{d}_{\max}=10\,\mathrm{s^{-1}}$ . (a) Active-tissue configurations at A–D: initial loading, damage evolution, maximum insertion, and after withdrawal, at approximately $0.200$ , $0.333$ , $0.600$ , and $1.050\,\mathrm{s}$ , respectively. (b) Local response at the same times: positive maximum principal Green–Lagrange strain in the upper row and damage $d$ in the lower row, in the fixed spatial section at $x=2.0\,\mathrm{mm}$ with thickness $0.1\,\mathrm{mm}$ . Grey crosses indicate last recorded inactive positions. (c) Axial reaction $F_{z}$ . (d) Counts of particles with $d>0$ and inactive particles; these sets are not disjoint. (e) Median displacement magnitude $U_{50}$ of the fixed initial $6720$ -particle surface cohort, including inactive records. Letters on the histories identify the saved spatial frames, while the curves cover the complete motion. Shading denotes prescribed withdrawal from $0.8$ to $1.0\,\mathrm{s}$ . The common display and sampling conventions are given in Section V-A .

Fig. 5: Matched damage-rate comparison at $27$ particles per cell under identical blade motion and otherwise matched settings. (a), (b) Local damage and particle activity for $\dot{d}_{\max}=10$ and $1\,\mathrm{s^{-1}}$ , respectively. Columns I–III show the same saved times, approximately $0.267$ , $0.400$ , and $0.600\,\mathrm{s}$ . Both rows use the fixed spatial section at $x=2.0\,\mathrm{mm}$ with thickness $0.1\,\mathrm{mm}$ and the same damage scale. Outlined markers identify displayed active members of the initial surface cohort; grey crosses show last recorded inactive positions. Values below each view report $U_{50}$ and the inactive cohort count. (c) Axial reaction histories. (d) Median displacement magnitude of the same fixed initial $6720$ -particle cohort, retaining inactive records. I–III on the histories identify the spatial samples; shading denotes withdrawal from $0.8$ to $1.0\,\mathrm{s}$ . The lower rate limit delays peak resistance and increases the displacement statistic at maximum insertion.

PPC	$\dot{d}_{\max}$	$F_{z,\mathrm{pk}}$	$t_{\mathrm{pk}}$	$U_{50}$
	( $\mathrm{s^{-1}}$ )	(N)	(s)	(mm)
8	10	0.02353	0.3078	0.06712
8	1	0.05164	0.5206	0.30990
27	10	0.02558	0.3078	0.10785
27	1	0.07218	0.5738	0.33996

TABLE III: Matched damage-rate comparison.

F_{z,\mathrm{pk}}

and

t_{\mathrm{pk}}

are the sampled force peak and its time;

U_{50}

is evaluated at the saved frame near maximum insertion.

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